Included studies

This review was conducted as part of a larger update of the NICE Lung cancer: diagnosis and management guideline (CG 121). A systematic literature search for randomised controlled trials (RCTs) with a no date limit yielded 4,241 references.

Papers returned by the literature search were screened on title and abstract, with 21 full-text papers ordered as potentially relevant systematic reviews or RCTs.

Eleven papers representing 10 unique RCTs were included after full text screening. The RCTs were: Albain 2009 (n=396, follow-up period was a minimum of 2.5 years), Eberhardt 2015 (n=161, follow-up period was a minimum of 1 year), Girard 2010 (n=46, the median follow-up period was 31.4 months), Johnstone 2002 (n=61, follow up period was a minimum of 4 years), Katakami 2012 (n=56, follow-up period was a minimum of 5 years), Pless 2015 (n=231, the median follow-up period was 52 months), Shepherd 1998 (n=31, follow-up was 24 months in one arm and 31 months in the other), Stephens 2005 (n=48, the median follow-up period was 14 months), Thomas 2008 (n=524, the median follow-up period was 70 months) and van Meerbeeck 2007 (n=208, the median follow-up period was 6 years).

For the search strategy, please see appendix C. For the clinical evidence study selection flowchart, see appendix D. For the full evidence tables and full GRADE profiles for included studies, please see appendices E and F.

Excluded studies

Details of the studies excluded at full-text review are given in appendix G along with a reason for their exclusion.

Study locations

One randomised controlled study was from the UK (Stephens 2005), 1 was from France (Girard 2010), 2 were from Germany (Eberhardt 2015, Thomas 2008), 1 was from Switzerland, Germany and Serbia (Pless 2015), 1 was from the Netherlands (van Meerbeeck 2007), 1 was from the USA (Johnstone 2002), 1 was from Canada (Shepherd 1998), 1 was from the USA and Canada (Albain 2009) and 1 was from Japan (Katakami 2012).

Outcomes and sample sizes

The reported outcomes with extractable data were mortality and adverse events. The sample sizes ranged from 31 participants to 524 across studies.

See full evidence tables and Grade profiles in appendices E and F.

Summary of original economic model

The de novo cost-utility analysis developed for this guideline included three strategies; chemoradiotherapy (CR), chemotherapy and surgery (CS) and chemoradiotherapy and surgery (CRS). It was based on a hybrid structure where the amount of time that patients spent in the progression free and progressed states, the probability of survival and the adverse events during the first five years were drawn from network meta-analyses conducted for this guideline. Survival in patients still alive after five years was modelled using patient registry data. The model included costs for the initial interventions and for treatment on progression, deaths, adverse events and routine costs associated with the progression free and progressed states. The model included utility estimates for both states as well as longer term survival and a disutility adjustment in the surgical arm. In accordance with data from the underpinning trials, not all patients in surgical strategies went on to receive surgery following chemoradiotherapy. Patients entered the model at age 60, which reflected the average age in the underpinning trials. The cycle length was one month and costs and health benefits were discounted at 3.5% per year.

The model found that CS was extendedly dominated by CR and CRS and had an ICER of £52,400/QALY versus CR. CRS was cost-effective compared to CR with an ICER of £16,900/QALY. These results were robust to a wide range of sensitivity and scenario analyses. The probabilistic sensitivity analysis showed that CRS produced more QALYs than CR and CS in 97% and 87% of iterations respectively. There were, however, key uncertainties in the underpinning clinical data with no individual pairwise studies having reported significant differences in overall survival. No subgroup analyses were performed. The full modelling report is available in Appendix K.

CRS vs CR vs CS (network meta-analysis)

Moderate quality evidence from 1 network meta-analysis that included more than 1,000 patients across 6 RCTs could not distinguish the odds of survival at 4 years between the interventions.

Moderate quality evidence from 1 network meta-analysis that included more than 1,000 patients across 5 RCTs could not distinguish the odds of survival at 5 years between the interventions.

High quality evidence from 1 network meta-analysis that included more than 1,000 patients across 6 RCTs found that CRS was associated with a longer progression-free survival time than both CS and CR at 4 years. The data could not differentiate CS from CR.

High quality evidence from 1 network meta-analysis that included more than 1,000 patients across 5 RCTs found that CRS was associated with a longer progression-free survival time than both CS and CR at 5 years. The data could not differentiate CS from CR.

High quality evidence from 1 network meta-analysis that included more than 1,000 patients across 6 RCTs could not distinguish post-progression survival time at 4 years.

High quality evidence from 1 network meta-analysis that included more than 1,000 patients across 5 RCTs could not distinguish post-progression survival time at 5 years.

Moderate quality evidence from 1 network meta-analysis that included more than 1,000 patients across 6 RCTs could not distinguish total life years at 4 years between the interventions.

Moderate quality evidence from 1 network meta-analysis that included more than 1,000 patients across 5 RCTs could not distinguish total life years at 5 years between the interventions.

High quality evidence from 1 network meta-analysis that included more than 1,000 patients across 4 RCTs found that CCRS was associated with a lower hazard ratio of adverse events at grade 3+ than both CS and CR.

CRS vs CR

Moderate-quality evidence from 1 RCT reporting data on 396 people with N2 NSCLC found that the data could not differentiate for mortality (all-cause hazard ratio). However, high to moderate-quality evidence found there were a greater number of participants who experienced anaemia, nausea and/or emesis, oesophagitis and pulmonary (adverse events grade 3 or above) in the CR group compared to the CRS group. The data could not differentiate for eukopenia, neutropenia, thrombocytopenia, worst haematologic toxicity per patient, neuropathy, stomatitis and/or mucositis, other gastrointestinal or renal, cardiac, miscellaneous infection, haemorrhage, fatigue, anorexia or allergy (adverse events grade 3 or above).

CRS vs CS

Very low to moderate-quality evidence from 3 RCTs reporting data on 333 people with NSCLC found that the data could not differentiate for mortality (all-cause hazard ratio and risk ratio for survival at 1, 2 and 3 years), stomatitis, dyspnoea and pneumonitis (adverse events grade 3 or above).

C, CRS vs C, CR boost

Moderate to high-quality evidence from 1 RCT reporting data from 161 people with potentially resectable stage IIIA (N2) or selected stage IIIB NSCLC found that the data could not differentiate for mortality at 1 year, 2 years, 3 years, 4 years, 5 years and 6 years. However, there were a greater number of participants who experienced oesophagitis in the C, CR boost group compared to the C, CRS group. The data could not differentiate for leukopenia, anaemia, thrombocytopenia, nausea/vomiting, neuropathy, mucositis/stomatitis, pulmonary, other GI or renal, cardiac, miscellaneous infection, fatigue, pain (adverse events grade 3 or above) or dropout during treatment.

CS vs CR

Very low to moderate-quality evidence from 2 RCTs reporting data from 369 people with N2 NSCLC found that the data could not differentiate for mortality at 1 year, 2 years, 3 years and 4 years. Neither could the data differentiate for treatment-related mortality nor dropout during treatment.

CS vs CRS (cisplatin + docetaxel)

Moderate to high-quality evidence from 1 RCT reporting data from 231 people who had stage IIIA (T1-3) N2 NSCLC found the CS group had a greater number of people who experienced infection compared to the CRS (cisplatin + docetaxel) group. The data could not differentiate for mortality (all-cause hazard ratio), alopecia, nausea/vomiting, fatigue, diarrhoea, neurotoxic effects, stomatitis, skin toxic effects, dyspnoea, fluid retention, constipation, febrile neutropenia, fever, allergic reaction, neutropenia, leukopenia, thrombocytopenia, anaemia (adverse events grade 3 or above), or dropout during treatment.

CS vs R

Very low to low-quality evidence from 2 RCTs reporting data from 79 people who had NSCLC T3, N1, M0 or T1-3, N2, M0 found that the data could not differentiate for mortality, lethargy (this adverse event was grade 2 or above) or dropout during treatment.

C, CRS, R vs CRS

Very low-quality evidence from 1 RCT reporting data from 524 people with NSCLC stage IIIA (T1-3, N2, M0 or central T3, N0-1, M0) or stage IIIB (T4, N1-3, M0 or T1-4, N3, M0) found that the data could not differentiate for mortality (all-cause hazard ratio or treatment related). However, there were a greater number of people who experienced haemotoxicity in the C, CRS, R group compared to the CRS group. There were a greater number of people who experienced pneumonitis in the CRS compared to the C, CRS, R group. The data could not differentiate for oesophagitis and peri-operative complications (adverse events were grade 3 or above).

Health economics evidence statements

Evidence from one directly applicable original health economic model with minor limitations built for this guideline showed that chemoradiotherapy with surgery is very likely to be more cost-effective than chemoradiotherapy (pairwise ICER = £19,800/QALY) and chemotherapy with surgery (pairwise ICER = £4,200) per QALY. The model’s conclusions were largely insensitive to changes in model parameters and assumptions.

Interpreting the evidence

Sources searched to identify economic evaluations

• NHS Economic Evaluation Database – NHS EED (Wiley) last updated Apr 2015
• Health Technology Assessment Database – HTA (Wiley) last updated Oct 2016
• Embase (Ovid)
• MEDLINE (Ovid)
• MEDLINE In-Process (Ovid)

Search filters to retrieve economic evaluations and quality of life papers were appended to the review question search strategies. For some health economics strategies additional terms were added to the original review question search strategies (see sections 4.2, 4.3 and 4.4) The searches were conducted between October 2017 and April 2018 for 9 review questions (RQ).

Searches were re-run in May 2018.

Searches were limited to those in the English language. Animal studies were removed from results.

Discounting Area Under the Kaplan Meier Curves

The economic evaluation required the area under the Kaplan Meier curve to be discounted at an annual rate of 3.5% [7]. The discounted area (up to T years) for each treatment group within each trial, as well as the SEER dataset, was calculated as

The standard error of, and correlation between, the discounted area under the Kaplan Meier curves for PFS and OS was calculated using non-parametric bootstrapping, constrained to samples where the OS curve was greater than the PFS curve [6]. The discounted areas under the Kaplan Meier curves for each RCT are provided in Table 10.

Table 10. Discounted area under the curve data required for economic modelling

To compute discounted costs of death beyond the truncated study periods (T = 4 or 5 years), a parametric survival curve was used to model the conditional SEER data, as described in the External Survival Data section above.

Discounting one-off costs

The economic model includes one-off costs for progression events, which also require discounting. The non-parametric approach provides the total number of events by time T, but does not give the breakdown of these events into 1-year time periods required for discounting. To obtain the proportion of total events falling in each 1-year period, let y_i,k,s be the survival probability at s years with standard error se_i,k,s, in arm k of study i. We assume the survival probabilities follow a Normal likelihood:

Let ρ_i,k,s be the proportion of events that have occurred by T = 5-years in study i, arm k, that occur in year s. Then the proportion surviving to 4-years, _πi,k,4, is the proportion surviving to 5 years, plus for those experiencing an event by year 5 the proportion of those events that occur in the 5^th year:

Table 11. Proportion of events occurring each year (Treatment 1=CR, 2=CS and 3=CRS)

Assessing model fit

The posterior mean of the residual deviance, which measures the magnitude of the differences between the observed data and the model predictions of the data, was used to assess the goodness of fit of each model [12]. Smaller values are preferred, and in a well-fitting model the posterior mean residual deviance should be close to the number of data points in the network (each study arm contributes 1 data point) [12].

In addition to comparing how well the models fit the data using the posterior mean of the residual deviance, models were compared using the deviance information criterion (DIC). This is equal to the sum of the posterior mean deviance and the effective number of parameters, and thus penalizes model fit with model complexity [12]. Lower values are preferred and differences of at least 5 points were considered meaningful [12].

5-year Follow-up

Five studies presented survival data up to 5-years, and a network diagram summarizing the evidence is given in Figure 2

Figure 2. Network diagram of comparisons for which direct evidence on differences in restricted mean survival time up to 5-years is available. Lines are proportional to the number of studies that compare the two connected treatments

Model fit statistics for the area under the Kaplan Meier curves up to 5-years, as well as the probability of survival are given in Table 12. Convergence was satisfactory for the fixed effect model after a burn-in of 20,000 iterations and results are based on a further 40,000 samples on two chains. For the random effects model, convergence was satisfactory after a burn-in of 30,000 iterations and results are based on a further 60,000 samples on two chains.

Table 12. Model fit statistics based on 5-year follow-up data

There were no meaningful differences between the fixed and random effects models in terms of the posterior mean residual deviance and DIC for both NMAs (Table 12). The box plots of the posterior deviance values for each study arm in Figure 3 and Figure 4 show that the area under the Kaplan Meier curves and probability of survival up to 5 years are predicted fairly well by both models. The simpler fixed effect model was therefore selected in the base-case.

Figure 3. Posterior deviance values for each study arm for the area under the Kaplan Meier curves (left) and probability of survival (right) – fixed effect model

Figure 4. Posterior deviance values for each study arm for the area under the Kaplan Meier curves (left) and probability of survival (right) – random effects model

No evidence of inconsistency was found, with model fit (posterior mean residual deviance) similar for the consistency and inconsistency (unrelated means) fixed effect models, and a lower DIC for the consistency model (Table 13). The area below the line of equality in Figure 5 highlights where the inconsistency model better predicted data points, and any improvement is minimal.

Table 13. Model fit statistics for consistency and inconsistency fixed effect models based on 5-year follow-up data

Figure 5. Deviance contributions from the fixed effect consistency and inconsistency models for area under the Kaplan Meier curves (left) and probability of survival (right)

There is evidence to suggest that chemoradiotherapy + surgery is more effective in increasing progression free life years at 5-year follow-up compared to chemoradiotherapy alone, while there is no evidence to suggest the effect of chemotherapy + surgery is any different from chemoradiotherapy (Figure 6A, Table 14). There is also evidence to suggest that chemoradiotherapy + surgery improves progression free life years compared to chemotherapy + surgery (posterior median difference in RMST: 0.34 (95% CrI: 0.02, 0.65)) and it ranked the most effective intervention in increasing progression free life years (Table 14).

In terms of post progression life years at 5-year follow-up, there was not enough to conclude that any one intervention was better than any other although point estimates favoured chemoradiotherapy (Figure 6B, Table 14). There was not enough evidence to suggest any of the three treatments were different from each other in terms of improving total life years at 5-year follow-up, which is the sum of the progression free and post progression life years (Figure 6C, Table 14).

Chemotherapy + surgery and chemoradiotherapy + surgery appear to be more likely to improve the odds of being alive at 5-years compared to chemoradiotherapy alone, but there is not enough evidence to infer the direction of effects with certainty (Figure 6D, Table 14).

Table 14. Treatment differences in restricted mean survival times (RMST) up to 5 years, odds ratios of being alive at 5-years, probabilities of ranking best, ranks, and predicted RMST and probability of being alive at 5-years in the UK population for the three interventions

Discounted Area Under the Kaplan Meier Curves and Probability of Survival

The fit of the NMA models based on the discounted AUC was also assessed and were in line with the results presented in the Network meta-analysis section above. For both the 4-year and 5-year follow-up data, there were no meaningful differences between the fit of the fixed and random effects models (Table 17), and thus the fixed effect model was preferred.

Table 17. Model fit statistics based on 5-year follow-up data, discounted at 3.5% annual rate

Similarly, the fit of the consistency and inconsistency models for both 4- and 5-year follow-up data were compared (Table 18). There is no evidence of inconsistency as no meaningful differences were found in the fit of the models for both datasets. The area below the line of equality in Figure 11 and Figure 12 highlights where the inconsistency model better predicted data points, but any improvements were minimal.

Table 18. Model fit statistics for consistency and inconsistency fixed effect models based on 4-year follow-up data, discounted at 3.5% annual rate

Figure 11. Deviance contributions from the fixed effect consistency and inconsistency models for area under the Kaplan Meier curves discounted at 3.5% annual rate (left) and probability of survival (right)

Figure 12. Deviance contributions from the fixed effect consistency and inconsistency models for area under the Kaplan Meier curves discounted at 3.5% annual rate (left) and probability of survival (right)

Proportion of Events Occurring each Year

The proportion of events occurring each year pooled across studies is given in Table 19. The estimated proportions are similar across the 5-year and 4-year follow-up datasets.

Table 19. Pooled proportion of events occurring each year

References

1.

Royston, P. and M.K.B.Parmar, Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome. BMC Medical Research Methodology, 2013. 13: p. 152–152. [PMC free article: PMC3922847] [PubMed: 24314264]

2.

Guyot, P., et al, Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves. BMC Medical Research Methodology, 2012. 12: p. 9. [PMC free article: PMC3313891] [PubMed: 22297116]

3.

Therneau, T.M. and P.M.Grambsch, A Package for Survival Analysis in S. 2015.

4.

R Core Team, R: A language and environment for statistical computing. 2017, R Foundation for Statistical Computing: Vienna, Austria.

5.

Klein, J.P. and M.L.Moeschberger, Survival Analysis: Techniques for Censored and Truncated Data. 2nd Edition ed. 2003, New York: Springer-Verlag.

6.

Efron, B. and R.J.Tibshiranie, An introduction to the bootstrap. 1993, New York: Chapman & Hall.

7.

National Institute for Health and Clinical Excellence, The guidelines Manual (November 2012). Available from http://publications​.nice​.org.uk/the-guidelines-manual-pmg6. 2012, National Institute of Health and Clinical Excellence: London. [PubMed: 27905714]

8.

Surveillance Epidemiology and End Results (SEER) Program (www​.seer.cancer.gov), SEER*Stat Database: Incidence - SEER 9 Regs Research Data, Nov 2017 Sub (1973-2015)<Katrina/Rita Population Adjustment> - Linked To County Attributes - Total U.S., 1969-2016 Counties, National Cancer Institute, DCCPS, Surveillance Research Program, released April 2018, based on the November 2017 submission.

9.

Dias, S., et al, NICE DSU Technical Support Document 4: Inconsistency in networks of evidence based on randomised controlled trials, in Technical Support Document. 2011. [PubMed: 27466656]

10.

Dias, S., et al, Evidence Synthesis for Decision Making 4: Inconsistency in networks of evidence based on randomized controlled trials. Medical Decision Making, 2013. 33: p. 641–656. [PMC free article: PMC3704208] [PubMed: 23804508]

11.

van Valkenhoef, G., et al, Automated generation of node-splitting models for assessment of inconsistency in network meta-analysis. Research Synthesis Methods, 2016. 7: p. 80–93. [PMC free article: PMC5057346] [PubMed: 26461181]

12.

Spiegelhalter, D.J., et al, Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society (B), 2002. 64(4): p. 583–616.

SEER dataset

Selection criteria:

{Age at Diagnosis.Age recode with <1 year olds} = '30-34 years','35-39 years','40-44 years','45-49 years','50-54 years','55-59 years','60-64 years','65-69 years','70-74 years','75-79 years' 
AND ({Site and Morphology.CS Schema v0204+} = 'Lung' 
OR {Site and Morphology.CS Schema - AJCC 6th Edition} = 'Lung') 
AND ({Stage - AJCC.Derived AJCC Stage Group, 7th ed (2010+)} = 'IIIA' 
OR {Stage - AJCC.Derived AJCC Stage Group, 6th ed (2004+)} = 'IIIA' 
OR {Stage - AJCC.AJCC stage 3rd edition (1988-2003)} = '  31' 
OR {Stage - AJCC.SEER modified AJCC stage 3rd (1988-2003)} = '  31') 
AND ({Stage - TNM.Derived AJCC N, 7th ed (2010+)} = 'N2','N2a','N2b','N2c' 
OR {Stage - TNM.Derived AJCC N, 6th ed (2004+)} = 'N2','N2a','N2b','N2c' 
OR {Stage - TNM.N value - based on AJCC 3rd (1988-2003)} = 'N2') 

NMA Model for Adverse Events – Fixed Effects

# Poisson likelihood, log link 
# Fixed effects model for multi-arm trials 
model{ # *** PROGRAM STARTS 
for(i in 1:ns){ # LOOP THROUGH STUDIES 
 mu[i] ~ dnorm(0,.0001) # vague priors for all trial baselines 
 for (k in 1:na[i]) { # LOOP THROUGH ARMS 
 r[i,k] ~ dpois(theta[i,k]) # Poisson likelihood 
 theta[i,k] <- lambda[i,k]*E[i,k] # event rate * exposure 
 log(lambda[i,k]) <- mu[i] + d[t[i,k]] - d[t[i,1]] # model for linear predictor 
 dev[i,k] <- 2*((theta[i,k]-r[i,k]) + r[i,k]*log(r[i,k]/theta[i,k])) #Deviance contribution 
 } 
 resdev[i] <- sum(dev[i,1:na[i]]) # summed residual deviance contribution for this trial 
 } 
totresdev <- sum(resdev[]) #Total Residual Deviance 
d[1]<-0 # treatment effect is zero for reference treatment 
for (k in 2:nt){ d[k] ~ dnorm(0,.0001) } # vague priors for treatment effects  
sd ~ dunif(0,5) # vague prior for between-trial SD 
tau <- pow(sd,-2) # between-trial precision = (1/between-trial variance) 
 
# pairwise HRs and LHRs for all possible pair-wise comparisons, if nt>2 
for (c in 1:(nt-1)) { 
 for (k in (c+1):nt) { 
 lhr[c,k] <- (d[k]-d[c]) 
 log(hr[c,k]) <- lhr[c,k] 
 } 
 }  
 
} # *** PROGRAM ENDS  
 
list(ns=4, nt=3) 
 
t[,1]  r[,1]  E[,1]  t[,2]  r[,2]  E[,2]  na[] 
2      182    285.2  3      141    299.52 2 
3      482    434.3  1      608    409.34 2 
1      137    214.4  3      150    230.04 2 
1      98     321.75 2      108    298.93 2 
 
END 
 
#chain 1 
list(d=c( NA, 0, 0), mu=c(0, 0, 0, 0)) 
#chain 2 
list(d=c( NA, -1, 1), mu=c(-3, -3, -3, -3)) 
#chain 3 
list(d=c( NA, 2, 2),  mu=c(-3, 5, -1, -3)) 

NMA Model for Adverse Events - Random Effects

# Poisson likelihood, log link 
# Random effects model for multi-arm trials 
model{ # *** PROGRAM STARTS 
for(i in 1:ns){ # LOOP THROUGH STUDIES 
 w[i,1] <- 0 # adjustment for multi-arm trials is zero for control arm 
 delta[i,1] <- 0 # treatment effect is zero for control arm 
 mu[i] ~ dnorm(0,.0001) # vague priors for all trial baselines 
 for (k in 1:na[i]) { # LOOP THROUGH ARMS 
 r[i,k] ~ dpois(theta[i,k]) # Poisson likelihood 
 theta[i,k] <- lambda[i,k]*E[i,k] # failure rate * exposure 
 log(lambda[i,k]) <- mu[i] + delta[i,k] # model for linear predictor 
 dev[i,k] <- 2*((theta[i,k]-r[i,k]) + r[i,k]*log(r[i,k]/theta[i,k])) #Deviance contribution 
 } 
 resdev[i] <- sum(dev[i,1:na[i]]) # summed residual deviance contribution for this trial 
 for (k in 2:na[i]) { # LOOP THROUGH ARMS 
 delta[i,k] ~ dnorm(md[i,k],taud[i,k]) # trial-specific LOR distributions 
 md[i,k] <- d[t[i,k]] - d[t[i,1]] + sw[i,k] # mean of LOR distributions (with multi-arm trial correction) 
 taud[i,k] <- tau *2*(k-1)/k # precision of LOR distributions (with multi-arm trial correction) 
 w[i,k] <- (delta[i,k] - d[t[i,k]] + d[t[i,1]]) # adjustment for multi-arm RCTs 
 sw[i,k] <- sum(w[i,1:k-1])/(k-1) # cumulative adjustment for multi-arm trials 
 } 
 } 
 
 
totresdev <- sum(resdev[]) #Total Residual Deviance 
d[1]<-0 # treatment effect is zero for reference treatment 
for (k in 2:nt){ d[k] ~ dnorm(0,.0001) } # vague priors for treatment effects 
sd ~ dunif(0,5) # vague prior for between-trial SD 
tau <- pow(sd,-2) # between-trial precision = (1/between-trial variance) 
# pairwise HRs and LHRs for all possible pair-wise comparisons, if nt>2 
for (c in 1:(nt-1)) { 
 for (k in (c+1):nt) { 
 lhr[c,k] <- (d[k]-d[c]) 
 log(hr[c,k]) <- lhr[c,k] 
 } 
 }  
 
} # *** PROGRAM ENDS  
 
list(ns=4, nt=3) 
 
t[,1]  r[,1]  E[,1]  t[,2]  r[,2]  E[,2]  na[] 
2      182    285.2  3      141    299.52 2 
3      482    434.3  1      608    409.34 2 
1      137    214.4  3      150    230.04 2 
1      98     321.75 2      108    298.93 2 
  
END 
 
#chain 1 
list(d=c( NA, 0, 0), sd=1, mu=c(0, 0, 0, 0)) 
#chain 2 
list(d=c( NA, -1, 1), sd=4, mu=c(-3, -3, -3, -3)) 
#chain 3 
list(d=c( NA, 2, 2), sd=2,  mu=c(-3, 5, -1, -3)) 

R code to calculate (undiscounted and discounted) area under the Kaplan Meier curves, along with correlation between the areas under PFS and OS curves and standard error based on non-parametric bootstrap sampling

##Load survival package 
library("survival") 
 
######################################################################### 
## Function to calculate area under a Kaplan Meier curve                           
## Required Input:                                                      
## data - with column names:                                            
## "stime" (survival time for each patient),                            
## "event" (1 if patient experienced event, 0 if patient censored),     
## "treat" (code for treatment patient received)                        
## rmean - time to restrict curve to                                    
## Outputs: AUC restricted to 'rmean' years and its standard error      
######################################################################### 
my.AUC<-function(data,rmean){ 
  fit<-survfit(Surv(stime,event)~1,data=data) 
  surv.stats<-summary(fit,print.rmean=TRUE,rmean=rmean)$table[5:6] 
  surv.stats 
} 
 
################################################################################ 
## Function to calculate area and discounted area under a Kaplan Meier curve  
## Required Input:                                                            
## data - with column names:                                                   
## "stime" (survival time for each patient),                                   
## "event" (1 if patient experienced event, 0 if patient censored),            
## "treat" (code for treatment patient received)                               
##        - note should only be 1 treatment in data                            
## max.time - time to restrict curve to                                        
## dis.fac - discount factor, 1/(1+annual rate)                               
## Outputs: AUC and discounted AUC restricted to 'rmean' years                 
################################################################################ 
my.disc.AUC<-function(data,max.time=5,disc.fac=1/1.035){ 
  #Fit Kaplan Meier curve to data 
  fit<-survfit(Surv(stime,event)~1,data=data) 
   
  #Calculate AUC in each one-year time interval 
  #Check to see if any patient experienced event at the end of a year 
  #If so, calculate AUC up to that time point 
  #If not, calculate AUC based on time at which an event was last observed before end of year 
  time<-0:max.time 
  X<-match(fit$time,time) 
  X<-X[-which(is.na(X))] 
  if(length(X)==0){time=time}else{time=time[-X]} 
  sum.fit<-summary(fit)  
  #Set up data required to calculate AUC in each one-year time interval 
  my.tab<-data.frame(time=sum.fit$time, 
                     n.risk=sum.fit$n.risk, 
                     n.event=sum.fit$n.event, 
                     survival=sum.fit$surv, 
                     std.err=sum.fit$std.err, 
                     time.diff=rep(NA,length(sum.fit$time)), 
                     AUC=rep(NA,length(sum.fit$time))) 
  #Add in lines for end of year time point to calculate AUC 
  temp.tab<-data.frame(time=time, 
                       n.risk=rep(NA,length(time)), 
                       n.event=rep(0,length(time)), 
                       survival=c(1,rep(NA,length(time)-1)), 
                       std.err=rep(NA,length(time)), 
                       time.diff=rep(NA,length(time)), 
                       AUC=rep(NA,length(time))) 
  my.tab<-rbind(my.tab,temp.tab) 
  my.tab<-my.tab[order(my.tab$time),] 
   
  #Make sure there are no time points beyond desired cut-off 
  test<-length(which(my.tab$time>max.time))>0 
  if(test){my.tab<-my.tab[-which(my.tab$time>max.time),]}else{my.tab<-my.tab} 
   
  #Calculate AUC between observed time points 
  for(i in 1:(length(time)-1)){ 
    row.ind<-which(my.tab$time==time[i+1]) 
    my.tab$survival[row.ind]=my.tab$survival[row.ind-1] 
  } 
  for(j in 2:length(my.tab[,1])){ 
    my.tab$time.diff[j]<-my.tab$time[j]-my.tab$time[j-1] 
    my.tab$AUC[j]<-my.tab$survival[j-1]*my.tab$time.diff[j] 
  }     
   
  #Which rows contain end of year data 
  time.ind<-which(match(my.tab$time,0:max.time)!="NA") 
   
  #Calculate and output the AUC and discounted AUC in each one year time interval 
  undisc.AUC<-matrix(nrow=max.time,ncol=2) 
  disc.AUC<-matrix(nrow=max.time,ncol=2) 
  undisc.AUC[,1]<-1:max.time 
  disc.AUC[,1]<-1:max.time 
  for(k in 1:max.time){ 
    undisc.AUC[k,2]<-sum(my.tab$AUC[(time.ind[k]+1):time.ind[k+1]]) 
    disc.AUC[k,2]<-sum(my.tab$AUC[(time.ind[k]+1):time.ind[k+1]])*(disc.fac^(k-1)) 
  } 
  t(rbind(undisc.AUC,disc.AUC)) 
   
} 
 
################################################################################## 
## Calculate SE of discounted AUC, correlation between AUC of PFS and OS curves  via bootstrapping                                                             
################################################################################## 
 
#Prepare tables to record AUC and Discounted AUC 
#AUC at 5 years 
AUC.tab.5<-matrix(ncol=24,nrow=5) 
colnames(AUC.tab.5)<-c("t1","t2","PFS1.boot","OS1.boot","sePFS1.boot","seOS1.boot","corr1", 
                       "PFS2.boot","OS2.boot","sePFS2.boot","seOS2.boot","corr2", 
                       "S1","seS1","S2","seS2", 
                       "PFS1","OS1","sePFS1","seOS1", 
                       "PFS2","OS2","sePFS2","seOS2") 
 
#Discounted AUC at 5 years 
disc.AUC.tab.5<-matrix(ncol=20,nrow=5) 
colnames(disc.AUC.tab.5)<-c("t1","t2","PFS1.boot","OS1.boot","sePFS1.boot","seOS1.boot","corr1", 
                            "PFS2.boot","OS2.boot","sePFS2.boot","seOS2.boot","corr2", 
                            "S1","seS1","S2","seS2", 
                            "PFS1","OS1","PFS2","OS2") 
 
#Load data for PFS and OS curves 
 
data.pfs <- read.csv("filename.csv", stringsAsFactors=FALSE) 
data.os <- read.csv("filename.csv", stringsAsFactors=FALSE) 
 
####################################################################### 
### Bootstrap each curve, for each treatment and outcome separately  
####################################################################### 
 
time.horizon<-5     #Cut off time (e.g., 5 years) 
B<-5000             #Number of bootstrap samples 
 
#Subset data in first treatment group 
treat.num1<-sort(unique(data.pfs$treat))[1] 
data.pfs1<-subset(data.pfs,treat==treat.num1) 
data.os1<-subset(data.os,treat==treat.num1) 
 
dim(data.pfs1)[1]    #check number of patients 
dim(data.os1)[1]     #check number of patients - should equal above 
 
#Create empty matrices to fill in for bootstrapping 
boot.auc.pfs1<-matrix(nrow=B,ncol=(2*time.horizon)+2) 
colnames(boot.auc.pfs1)<-c(paste(rep("AUC",time.horizon),1:time.horizon,sep="."), 
                           paste(rep("dAUC",time.horizon),1:time.horizon,sep="."), 
                           "AUC","dAUC") 
boot.auc.os1<-matrix(nrow=B,ncol=(2*time.horizon)+2) 
colnames(boot.auc.os1)<-c(paste(rep("AUC",time.horizon),1:time.horizon,sep="."), 
                          paste(rep("dAUC",time.horizon),1:time.horizon,sep="."), 
                          "AUC","dAUC") 
 
#Set the seed 
set.seed(1234) 
 
#Bootstrap data, throw out bootstrap samples where OS curve is lower than PFS curve 
i<-1 
k<-0     #counter for discards 
while(i<(B+1)){ 
  #Calculate number of patients reporting PFS and OS 
  samp.pfs<-dim(data.pfs1)[1] 
  samp.os<-dim(data.os1)[1] 
  inds1<-sample(1:samp.pfs,replace=TRUE) 
  inds2<-sample(1:samp.os,replace=TRUE) 
  boot.data.pfs1<-data.pfs1[inds1[1:dim(data.pfs1)[1]],] 
  boot.data.os1<-data.os1[inds2[1:dim(data.os1)[1]],]   
 
  #Fit KM curves to resampled data 
  fit.pfs<-survfit(Surv(stime,event)~treat,data=boot.data.pfs1) 
  fit.os<-survfit(Surv(stime,event)~treat,data=boot.data.os1) 
   
  #Check to see if P(OS) >= P(PFS) 
  surv.test<-rep(NA,length(summary(fit.os)$time)) 
  for(j in 1:length(summary(fit.os)$time)){ 
    time.test<-which(summary(fit.os)$time[j]>=summary(fit.pfs)$time) 
        if(length(time.test)==0){ 
          surv.test[j]<-FALSE 
        } else{ 
          surv.test[j]<-summary(fit.os)$surv[j]>=summary(fit.pfs)$surv[max(time.test)]           
        } 
  } 
  surv.test.test<-sum(1*(surv.test=="FALSE"),na.rm=TRUE)   
 
  if(surv.test.test==0){ 
    boot.auc.pfs1[i,1:(2*time.horizon)]<-my.disc.AUC(boot.data.pfs1,max.time=time.horizon)[2,] 
    boot.auc.pfs1[i,((2*time.horizon)+1):((2*time.horizon)+2)]<-c(sum(boot.auc.pfs1[i,1:time.horizon]),sum(boot.auc.pfs1[i,(time.horizon+1):(2*time.horizon)])) 
    boot.auc.os1[i,1:(2*time.horizon)]<-my.disc.AUC(boot.data.os1,max.time=time.horizon)[2,] 
    boot.auc.os1[i,((2*time.horizon)+1):((2*time.horizon)+2)]<-c(sum(boot.auc.os1[i,1:time.horizon]),sum(boot.auc.os1[i,(time.horizon+1):(2*time.horizon)])) 
     
    i<-i+1 
  } else { 
    i<-i 
    k<-k+1 
  } 
   
} 
 
#Number of samples thrown away 
k 
 
#Record results, fill in tables 
AUC.tab.5[study.num,"t1"]<-treat.num1 
disc.AUC.tab.5[study.num,"t1"]<-treat.num1 
 
AUC.tab.5[study.num,"PFS1.boot"]<-mean(boot.auc.pfs1[,((2*time.horizon)+1)]) 
disc.AUC.tab.5[study.num,"PFS1.boot"]<-mean(boot.auc.pfs1[,((2*time.horizon)+2)]) 
AUC.tab.5[study.num,"sePFS1.boot"]<-sd(boot.auc.pfs1[,((2*time.horizon)+1)]) 
disc.AUC.tab.5[study.num,"sePFS1.boot"]<-sd(boot.auc.pfs1[,((2*time.horizon)+2)]) 
 
AUC.tab.5[study.num,"OS1.boot"]<-mean(boot.auc.os1[,((2*time.horizon)+1)]) 
disc.AUC.tab.5[study.num,"OS1.boot"]<-mean(boot.auc.os1[,((2*time.horizon)+2)]) 
AUC.tab.5[study.num,"seOS1.boot"]<-sd(boot.auc.os1[,((2*time.horizon)+1)]) 
disc.AUC.tab.5[study.num,"seOS1.boot"]<-sd(boot.auc.os1[,((2*time.horizon)+2)]) 
 
AUC.tab.5[study.num,"corr1"]<-cor(boot.auc.pfs1[,((2*time.horizon)+1)],boot.auc.os1[,((2*time.horizon)+1)]) 
disc.AUC.tab.5[study.num,"corr1"]<-cor(boot.auc.pfs1[,((2*time.horizon)+2)],boot.auc.os1[,((2*time.horizon)+2)]) 
 
fit.os1<-survfit(Surv(stime,event)~1,data=data.os1) 
 
AUC.tab.5[study.num,"S1"]<-summary(fit.os1,time=time.horizon)$surv 
AUC.tab.5[study.num,"seS1"]<-summary(fit.os1,time=time.horizon)$std.err 
disc.AUC.tab.5[study.num,"S1"]<-summary(fit.os1,time=time.horizon)$surv 
disc.AUC.tab.5[study.num,"seS1"]<-summary(fit.os1,time=time.horizon)$std.err 
 
AUC.tab.5[study.num,"PFS1"]<-my.AUC(data.pfs1,rmean=5)[1] 
AUC.tab.5[study.num,"sePFS1"]<-my.AUC(data.pfs1,rmean=5)[2] 
AUC.tab.5[study.num,"OS1"]<-my.AUC(data.os1,rmean=5)[1] 
AUC.tab.5[study.num,"seOS1"]<-my.AUC(data.os1,rmean=5)[2] 
 
disc.AUC.tab.5[study.num,"PFS1"]<-sum(my.disc.AUC(data.pfs1,max.time=5,disc.fac=1/1.035)[2,6:10]) 
disc.AUC.tab.5[study.num,"OS1"]<-sum(my.disc.AUC(data.os1,max.time=5,disc.fac=1/1.035)[2,6:10]) 
 
#Save a copy of results from each bootstrapped sample 
write.csv(boot.auc.pfs1,"filename pfs treat 1.csv") 
write.csv(boot.auc.os1,"filename os treat 1.csv") 
 
###################################### 
 
#Subset data in first treatment group 
treat.num2<-sort(unique(data.pfs$treat))[2] 
data.pfs2<-subset(data.pfs,treat==treat.num2) 
data.os2<-subset(data.os,treat==treat.num2) 
 
dim(data.pfs2)[1]    #check number of patients 
dim(data.os2)[1]     #check number of patients - should equal above 
 
#Create empty matrices to fill in for bootstrapping 
boot.auc.pfs2<-matrix(nrow=B,ncol=(2*time.horizon)+2) 
colnames(boot.auc.pfs2)<-c(paste(rep("AUC",time.horizon),1:time.horizon,sep="."), 
                           paste(rep("dAUC",time.horizon),1:time.horizon,sep="."), 
                           "AUC","dAUC") 
boot.auc.os2<-matrix(nrow=B,ncol=(2*time.horizon)+2) 
colnames(boot.auc.os2)<-c(paste(rep("AUC",time.horizon),1:time.horizon,sep="."), 
                          paste(rep("dAUC",time.horizon),1:time.horizon,sep="."), 
                          "AUC","dAUC") 
 
#Set the seed 
set.seed(1234) 
 
#Bootstrap data, throw out bootstrap samples where OS curve is lower than PFS curve 
i<-1 
k<-0     #counter for discards 
while(i<(B+1)){ 
  #Calculate number of patients reporting PFS and OS 
  samp.pfs<-dim(data.pfs2)[1] 
  samp.os<-dim(data.os2)[1] 
  inds1<-sample(1:samp.pfs,replace=TRUE) 
  inds2<-sample(1:samp.os,replace=TRUE) 
  boot.data.pfs2<-data.pfs2[inds1[1:dim(data.pfs2)[1]],] 
  boot.data.os2<-data.os2[inds2[1:dim(data.os2)[1]],] 
   
  #Fit KM curves to resampled data 
  fit.pfs<-survfit(Surv(stime,event)~treat,data=boot.data.pfs2) 
  fit.os<-survfit(Surv(stime,event)~treat,data=boot.data.os2) 
   
  #Check to see if P(OS) > P(PFS) 
  surv.test<-rep(NA,length(summary(fit.os)$time)) 
  for(j in 1:length(summary(fit.os)$time)){ 
    time.test<-which(summary(fit.os)$time[j]>=summary(fit.pfs)$time) 
    #Added this ifelse statement on 22 January 2019 to account for cases where first OS event happened before first PFS event 
    if(length(time.test)==0){ 
      surv.test[j]<-FALSE 
    } else{ 
      surv.test[j]<-summary(fit.os)$surv[j]>=summary(fit.pfs)$surv[max(time.test)]           
    } 
  } 
  surv.test.test<-sum(1*(surv.test=="FALSE"),na.rm=TRUE) 
   
  if(surv.test.test==0){ 
    boot.auc.pfs2[i,1:(2*time.horizon)]<-my.disc.AUC(boot.data.pfs2,max.time=time.horizon)[2,] 
    boot.auc.pfs2[i,((2*time.horizon)+1):((2*time.horizon)+2)]<-c(sum(boot.auc.pfs2[i,1:time.horizon]),sum(boot.auc.pfs2[i,(time.horizon+1):(2*time.horizon)])) 
    boot.auc.os2[i,1:(2*time.horizon)]<-my.disc.AUC(boot.data.os2,max.time=time.horizon)[2,] 
    boot.auc.os2[i,((2*time.horizon)+1):((2*time.horizon)+2)]<-c(sum(boot.auc.os2[i,1:time.horizon]),sum(boot.auc.os2[i,(time.horizon+1):(2*time.horizon)])) 
     
    i<-i+1 
  } else { 
    i<-i 
    k<-k+1 
  } 
   
} 
 
#Number of samples thrown away 
k 
 
#Record results, fill in tables 
AUC.tab.5[study.num,"t2"]<-treat.num2 
disc.AUC.tab.5[study.num,"t2"]<-treat.num2 
 
AUC.tab.5[study.num,"PFS2.boot"]<-mean(boot.auc.pfs2[,((2*time.horizon)+1)]) 
disc.AUC.tab.5[study.num,"PFS2.boot"]<-mean(boot.auc.pfs2[,((2*time.horizon)+2)]) 
AUC.tab.5[study.num,"sePFS2.boot"]<-sd(boot.auc.pfs2[,((2*time.horizon)+1)]) 
disc.AUC.tab.5[study.num,"sePFS2.boot"]<-sd(boot.auc.pfs2[,((2*time.horizon)+2)]) 
 
AUC.tab.5[study.num,"OS2.boot"]<-mean(boot.auc.os2[,((2*time.horizon)+1)]) 
disc.AUC.tab.5[study.num,"OS2.boot"]<-mean(boot.auc.os2[,((2*time.horizon)+2)]) 
AUC.tab.5[study.num,"seOS2.boot"]<-sd(boot.auc.os2[,((2*time.horizon)+1)]) 
disc.AUC.tab.5[study.num,"seOS2.boot"]<-sd(boot.auc.os2[,((2*time.horizon)+2)]) 
 
AUC.tab.5[study.num,"corr2"]<-cor(boot.auc.pfs2[,((2*time.horizon)+1)],boot.auc.os2[,((2*time.horizon)+1)]) 
disc.AUC.tab.5[study.num,"corr2"]<-cor(boot.auc.pfs2[,((2*time.horizon)+2)],boot.auc.os2[,((2*time.horizon)+2)]) 
 
fit.pfs2<-survfit(Surv(stime,event)~1,data=data.pfs2) 
fit.os2<-survfit(Surv(stime,event)~1,data=data.os2) 
 
AUC.tab.5[study.num,"S2"]<-summary(fit.os2,time=time.horizon)$surv 
AUC.tab.5[study.num,"seS2"]<-summary(fit.os2,time=time.horizon)$std.err 
disc.AUC.tab.5[study.num,"S2"]<-summary(fit.os2,time=time.horizon)$surv 
disc.AUC.tab.5[study.num,"seS2"]<-summary(fit.os2,time=time.horizon)$std.err 
 
AUC.tab.5[study.num,"PFS2"]<-my.AUC(data.pfs2,rmean=5)[1] 
AUC.tab.5[study.num,"sePFS2"]<-my.AUC(data.pfs2,rmean=5)[2] 
AUC.tab.5[study.num,"OS2"]<-my.AUC(data.os2,rmean=5)[1] 
AUC.tab.5[study.num,"seOS2"]<-my.AUC(data.os2,rmean=5)[2] 
 
disc.AUC.tab.5[study.num,"PFS2"]<-sum(my.disc.AUC(data.pfs2,max.time=5,disc.fac=1/1.035)[2,6:10]) 
disc.AUC.tab.5[study.num,"OS2"]<-sum(my.disc.AUC(data.os2,max.time=5,disc.fac=1/1.035)[2,6:10]) 
 
#Save a copy of results from each bootstrapped sample 
write.csv(boot.auc.pfs2,"filename pfs treat 2.csv") 
write.csv(boot.auc.os2,"filename os treat 2.csv") 

WinBUGS code for NMA of area under the Kaplan Meier curves and Probability of Surviving up to 5 years – Fixed effect model. Notes: WinBUGS files, including data and initial values are available upon request. Same code may be used for 4-year and discounted AUC data

model{ 
 
#Code for 5-year Survival 
for (i in 1:ns){ 
 mu.S[i]~dnorm(0,.0001) 
 for (k in 1:na[i]){ 
  prec.S[i,k]<-pow(se.S[i,k],-2) 
  y.S[i,k]~dnorm(pi[i,k],prec.S[i,k])  
  dev.S[i,k]<-(y.S[i,k]-pi[i,k])*(y.S[i,k]-pi[i,k])*prec.S[i,k] 
  logit(pi[i,k])<-mu.S[i] + delta.S[i,k] 
  delta.S[i,k]<- d.S[t[i,k]] - d.S[t[i,1]] 
 } 
    resdev.S[i] <- sum(dev.S[i,1:na[i]])  
} 
totresdev.S<-sum(resdev.S[]) 
 
 
#Code for 5-year AUCs (Bivariate for PFS and OS) 
for (i in 1:ns){ 
 mu.PFS[i]~dnorm(0,.0001) 
 mu.PPS[i]~dnorm(0,.0001) 
 for (k in 1:na[i]){ 
  #Set precision matrix 
  Sigma[i,k,1,1]<-pow(se.PFS[i,k],2) 
  Sigma[i,k,2,2]<-pow(se.OS[i,k],2)   
  Sigma[i,k,1,2]<-corr[i,k]*se.PFS[i,k]*se.OS[i,k] 
  Sigma[i,k,2,1]<-Sigma[i,k,1,2] 
  Prec[i,k,1:2,1:2]<-inverse(Sigma[i,k,1:2,1:2]) 
 
  y[i,k,1:2]~dmnorm(theta[i,k,1:2],Prec[i,k,1:2,1:2]) 
  for (j in 1:2){  
   diff[i,k,j]<- y[i,k,j]-theta[i,k,j] 
   z[i,k,j]<- inprod2(Prec[i,k,j,1:2],diff[i,k,1:2]) 
  } 
 dev[i,k]<-inprod2(diff[i,k,1:2],z[i,k,1:2]) 
 
 theta[i,k,1]<- mu.PFS[i] + delta.PFS[i,k] 
 theta[i,k,2]<- theta[i,k,1] + phi[i,k] 
 phi[i,k]<- mu.PPS[i] + delta.PPS[i,k] 
  
 delta.PFS[i,k]<- d.PFS[t[i,k]] - d.PFS[t[i,1]] 
 delta.PPS[i,k]<-  d.PPS[t[i,k]] - d.PPS[t[i,1]] 
 
 } 
 
    resdev[i] <- sum(dev[i,1:na[i]])  
    } 
totresdev<-sum(resdev[]) 
 
#Chemoradiotherapy (treatment code 1) is reference 
d.S[1]<-0 
d.PFS[1]<-0 
d.PPS[1]<-0 
 
for (k in 2:nt){ 
 d.S[k]~dnorm(0,.0001) 
 d.PFS[k]~dnorm(0,.0001) 
 d.PPS[k]~dnorm(0,.0001) 
} 
 
#Assumed log odds of survival, mean PPS and PFS time over 5-years on reference treatment 1 in UK  
m.S<-mu.S[5] 
m.PFS<-mu.PFS[5] 
m.PPS<-mu.PPS[5] 
 
#Predicted probability of survival and mean survival times in UK population for each treatment 
for (k in 1:nt){ 
 #Up to 5 years 
 logit(S5[k])<- m.S + d.S[k] 
 meanPFS5[k]<- m.PFS + d.PFS[k] 
 meanPPS5[k]<- m.PPS + d.PPS[k] 
 meanOS5[k]<-meanPFS5[k]+meanPPS5[k] 
  
 #Long-term 
meanPFS[k]<- meanPFS5[k] + S5[k]*C 
 meanPPS[k]<- meanPPS5[k] 
 meanOS[k]<-meanPFS[k]+meanPPS[k] 
} 
 
#Overall Survival at 5 Years, OR of Survival, Overall Survival relative to CR 
for (k in 1:nt){ 
 d.OS5[k]<-d.PFS[k]+d.PPS[k] 
 OR.S[k]<-exp(d.S[k]) 
 d.OS[k]<-(meanPFS[k]-meanPFS[1])+(meanPPS[k]-meanPPS[1]) 
 } 
 
#Rank treatments 
for (k in 1:nt)  {  
 # PFS 
 rk.PFS[k]  <- nt+1-rank(d.PFS[],k) 
 best.PFS[k]  <- equals(rk.PFS[k],1)    # Largest is best (i.e. rank 1) 
 # PPS 
 rk.PPS[k]  <- nt+1-rank(d.PPS[],k) 
 best.PPS[k]  <- equals(rk.PPS[k],1)    # Largest is best (i.e. rank 1) 
 # OS at 5 years 
 rk.OS5[k]  <- nt+1-rank(d.OS5[],k) 
 best.OS5[k]  <- equals(rk.OS5[k],1)    # Largest is best (i.e. rank 1) 
 # OR of Survival 
 rk.OR.S[k]  <- nt+1-rank(OR.S[],k) 
 best.OR.S[k]  <- equals(rk.OR.S[k],1)    # Largest is best (i.e. rank 1) 
 # OS 
 rk.OS[k]  <- nt+1-rank(d.OS[],k) 
 best.OS[k]  <- equals(rk.OS[k],1)    # Largest is best (i.e. rank 1) 
} 
 
} 

WinBUGS code for NMA of area under the Kaplan Meier curves and Probability of Surviving up to 5 years – Random effects model. Notes: WinBUGS files, including data and initial values are available upon request. Same code may be used for 4-year and discounted AUC data

model{ 
 
#Code for 5-year Survival 
for (i in 1:ns){ 
 delta.S[i,1]<-0 
 mu.S[i]~dnorm(0,.0001) 
 for (k in 1:na[i]){ 
  prec.S[i,k]<-pow(se.S[i,k],-2) 
  y.S[i,k]~dnorm(pi[i,k],prec.S[i,k])  
  dev.S[i,k]<-(y.S[i,k]-pi[i,k])*(y.S[i,k]-pi[i,k])*prec.S[i,k] 
  logit(pi[i,k])<-mu.S[i] + delta.S[i,k] 
  } 
    resdev.S[i] <- sum(dev.S[i,1:na[i]])  
  
     md.S[i,2] <- d.S[t[i,2]] - d.S[t[i,1]] 
 delta.S[i,2] ~ dnorm(md.S[i,2],tau.S) 
  
} 
totresdev.S<-sum(resdev.S[]) 
 
 
#Code for 5-year AUCs (Bivariate for PFS and OS) 
for (i in 1:ns){ 
 delta.PFS[i,1]<-0 
 delta.PPS[i,1]<-0 
 mu.PFS[i]~dnorm(0,.0001) 
 mu.PPS[i]~dnorm(0,.0001) 
 for (k in 1:na[i]){ 
  #Set precision matrix 
  Sigma[i,k,1,1]<-pow(se.PFS[i,k],2) 
  Sigma[i,k,2,2]<-pow(se.OS[i,k],2)   
  Sigma[i,k,1,2]<-corr[i,k]*se.PFS[i,k]*se.OS[i,k] 
  Sigma[i,k,2,1]<-Sigma[i,k,1,2] 
  Prec[i,k,1:2,1:2]<-inverse(Sigma[i,k,1:2,1:2]) 
 
  y[i,k,1:2]~dmnorm(theta[i,k,1:2],Prec[i,k,1:2,1:2]) 
  for (j in 1:2){  
   diff[i,k,j]<- y[i,k,j]-theta[i,k,j] 
    
   z[i,k,j]<- inprod2(Prec[i,k,j,1:2],diff[i,k,1:2]) 
  } 
 dev[i,k]<-inprod2(diff[i,k,1:2],z[i,k,1:2]) 
 
 theta[i,k,1]<- mu.PFS[i] + delta.PFS[i,k] 
 theta[i,k,2]<- theta[i,k,1] + phi[i,k] 
 phi[i,k]<- mu.PPS[i] + delta.PPS[i,k] 
  
 } 
  
 md.PFS[i,2] <- d.PFS[t[i,2]] - d.PFS[t[i,1]] 
 md.PPS[i,2] <- d.PPS[t[i,2]] - d.PPS[t[i,1]] 
 delta.PFS[i,2] ~ dnorm(md.PFS[i,2], tau.PFS) 
 delta.PPS[i,2] ~ dnorm(md.PPS[i,2], tau.PPS) 
 
    resdev[i] <- sum(dev[i,1:na[i]])  
    } 
totresdev<-sum(resdev[]) 
 
#Chemoradiotherapy (treatment code 1) is reference 
d.S[1]<-0 
d.PFS[1]<-0 
d.PPS[1]<-0 
 
#Priors on between-study SDs 
sd.S ~ dunif(0,5) 
sd.PFS ~ dunif(0,5) 
sd.PPS ~ dunif(0,5) 
tau.S <- pow(sd.S, -2) 
tau.PFS <- pow(sd.PFS, -2) 
tau.PPS <- pow(sd.PPS, -2) 
 
for (k in 2:nt){ 
 d.S[k]~dnorm(0,.0001) 
 d.PFS[k]~dnorm(0,.0001) 
 d.PPS[k]~dnorm(0,.0001) 
} 
 
#Assumed log odds of survival, mean PPS and PFS time over 5-years on reference treatment 1 in UK  
m.S<-mu.S[5] 
m.PFS<-mu.PFS[5] 
m.PPS<-mu.PPS[5] 
 
#Predicted probability of survival and mean survival times in UK population for each treatment 
for (k in 1:nt){ 
 #Up to 5 years 
 logit(S5[k])<- m.S + d.S[k] 
 meanPFS5[k]<- m.PFS + d.PFS[k] 
 meanPPS5[k]<- m.PPS + d.PPS[k] 
 meanOS5[k]<-meanPFS5[k]+meanPPS5[k] 
  
 #Long-term 
meanPFS[k]<- meanPFS5[k] + S5[k]*C 
 meanPPS[k]<- meanPPS5[k] 
 meanOS[k]<-meanPFS[k]+meanPPS[k] 
} 
 
#Overall Survival at 5 Years, OR of Survival, Overall Survival relative to CR 
for (k in 1:nt){ 
 d.OS5[k]<-d.PFS[k]+d.PPS[k] 
 OR.S[k]<-exp(d.S[k]) 
 d.OS[k]<-(meanPFS[k]-meanPFS[1])+(meanPPS[k]-meanPPS[1]) 
 } 
 
# Rank treatments 
for (k in 1:nt)  {  
 # PFS 
 rk.PFS[k]  <- nt+1-rank(d.PFS[],k) 
 best.PFS[k]  <- equals(rk.PFS[k],1)    # Largest is best (i.e. rank 1) 
 # PPS 
 rk.PPS[k]  <- nt+1-rank(d.PPS[],k) 
 best.PPS[k]  <- equals(rk.PPS[k],1)    # Largest is best (i.e. rank 1) 
 # OS at 5 years 
 rk.OS5[k]  <- nt+1-rank(d.OS5[],k) 
 best.OS5[k]  <- equals(rk.OS5[k],1)    # Largest is best (i.e. rank 1) 
 # OR of Survival 
 rk.OR.S[k]  <- nt+1-rank(OR.S[],k) 
 best.OR.S[k]  <- equals(rk.OR.S[k],1)    # Largest is best (i.e. rank 1) 
 # OS 
 rk.OS[k]  <- nt+1-rank(d.OS[],k) 
 best.OS[k]  <- equals(rk.OS[k],1)    # Largest is best (i.e. rank 1) 
 # QALY 
} 
 
} 

WinBUGS code to estimate proportion of events occurring each year up to 5 years. Notes: WinBUGS files, including data and initial values are available upon request

model{ 
 
 for (i in 1:ns){ 
  for (k in 1:na[i]){ 
   for (s in 1:5){ 
  #Likelihood for Survival at times s=1,2,3,4,5 
    prec.S[i,k,s]<-pow(se.S[i,k,s],-2) 
    y.S[i,k,s]~dnorm(pi[i,k,s],prec.S[i,k,s])  
    dev.S[i,k,s]<-(y.S[i,k,s]-pi[i,k,s])*(y.S[i,k,s]-pi[i,k,s])*prec.S[i,k,s]   
   } 
 
#Model for Survival probs, pi, as a function of the proportion of events in each 1-year time period, rho, by treatment    
  pi[i,k,5]~dbeta(1,1) 
  pi[i,k,4]<- pi[i,k,5] + rho[5]*(1-pi[i,k,5]) 
  pi[i,k,3]<- pi[i,k,5] + sum(rho[4:5])*(1-pi[i,k,5]) 
  pi[i,k,2]<- pi[i,k,5] + sum(rho[3:5])*(1-pi[i,k,5]) 
  pi[i,k,1]<- pi[i,k,5] + sum(rho[2:5])*(1-pi[i,k,5]) 
  }  
    resdev.S[i] <- sum(dev.S[i,1:na[i], 1:5])  
 } 
  totresdev<- sum(resdev.S[])  
 
#Dirichlet prior (using Gamma formulation) 
  for (s in 1:5){  
   x[s]~dgamma(alpha0[s],1) 
   rho[s]<- alpha[s]/sum(alpha[1:5]) 
  alpha0[s]<- max(alpha[s],0.1) 
  log(alpha[s])<- beta[s] 
  beta[s]~dnorm(0,.01) 
 } 
 
dum<-t[1,1]  
} 

WinBUGS code to estimate proportion of events occurring each year up to 4 years. Notes: WinBUGS files, including data and initial values are available upon request

model{ 
 
 for (i in 1:ns){ 
  for (k in 1:na[i]){ 
   for (s in 1:4){ 
  #Likelihood for Survival at times s=1,2,3,4 
    prec.S[i,k,s]<-pow(se.S[i,k,s],-2) 
    y.S[i,k,s]~dnorm(pi[i,k,s],prec.S[i,k,s])  
    dev.S[i,k,s]<-(y.S[i,k,s]-pi[i,k,s])*(y.S[i,k,s]-pi[i,k,s])*prec.S[i,k,s]   
   } 
 
#Model for Survival probs, pi, as a function of the proportion of events in each 1-year time period, rho, by treatment    
  pi[i,k,4]~dbeta(1,1) 
  pi[i,k,3]<- pi[i,k,4] + rho[4]*(1-pi[i,k,4]) 
  pi[i,k,2]<- pi[i,k,4] + sum(rho[3:4])*(1-pi[i,k,4]) 
  pi[i,k,1]<- pi[i,k,4] + sum(rho[2:4])*(1-pi[i,k,4]) 
  }  
    resdev.S[i] <- sum(dev.S[i,1:na[i], 1:4])  
 } 
  totresdev<- sum(resdev.S[])  
 
#Dirichlet prior (using Gamma formulation) 
  for (s in 1:4){  
   x[s]~dgamma(alpha0[s],1) 
   rho[s]<- alpha[s]/sum(alpha[1:4]) 
  alpha0[s]<- max(alpha[s],0.1) 
  log(alpha[s])<- beta[s] 
  beta[s]~dnorm(0,.01) 
 } 
 
dum<-t[1,1]  
} 

WinBUGS code to estimate proportion of progressions that are deaths. Fixed effects model. Notes: WinBUGS files, including data and initial values are available upon request

model{ # *** PROGRAM STARTS 
for(i in 1:ns){ # LOOP THROUGH STUDIES 
 mu[i] ~ dnorm(0,.0001) # vague priors for all trial baselines 
 for (k in 1:na[i]) { # LOOP THROUGH ARMS 62 
 r[i,k] ~ dbin(p[i,k],n[i,k]) # binomial likelihood 
 logit(p[i,k]) <- mu[i] + d[t[i,k]] - d[t[i,1]] # model for linear predictor 
 rhat[i,k] <- p[i,k] * n[i,k] # expected value of the numerators 
 dev[i,k] <- 2 * (r[i,k] * (log(r[i,k])-log(rhat[i,k])) #Deviance contribution 
 + (n[i,k]-r[i,k]) * (log(n[i,k]-r[i,k]) - log(n[i,k]-rhat[i,k]))) 
 } 
 resdev[i] <- sum(dev[i,1:na[i]]) # summed residual deviance contribution for this trial 
 } 
totresdev <- sum(resdev[]) #Total Residual Deviance 
d[1]<-0 # treatment effect is zero for reference treatment 
for (k in 2:nt){ d[k] ~ dnorm(0,.0001) } # vague priors for treatment effects 
 
for (l in 1:nt) { pbest[l]<-equals(rank(d[],l),5) } 
 
for (z in 1:(nt-1)) 
{ 
caterpillar[z] <- exp(d[z+1])-d[1] 
} 
 
# pairwise ORs and LORs for all possible pair-wise comparisons, if nt>2 
for (c in 1:(nt-1)) { 
for (k in (c+1):nt) { 
or[c,k] <- exp(d[k] - d[c]) 
lor[c,k] <- (d[k]-d[c]) 
} 
}} 

WinBUGS code to estimate proportion of progressions that are deaths. Random effects model. Notes: WinBUGS files, including data and initial values are available upon request

# Binomial likelihood, logit link 
# Random effects model for multi-arm trials 
# based on 
# Dias, S., Welton, N.J., Sutton, A.J. & Ades, A.E. 
# NICE DSU Technical Support Document 2: A Generalised Linear Modelling Framework 
# for Pairwise and Network Meta-Analysis of Randomised Controlled Trials. 2011. 
# http://www.nicedsu.org.uk 
 
model {                           
for(i in 1:NumStudies) {                             # indexes studies 
  mu[i] ~ dnorm(0, .0001)                            # vague priors for all trial baselines 
  delta[i,1] <- 0                                    # effect is zero for control arm 
  w[i,1] <- 0                                        # multi-arm adjustment = zero for ctrl 
  for (j in 1:NumArms[i]) {                          # indexes arms 
    k[i,j]        ~  dbin(p[i,j],N[i,j])             # binomial likelihood 
    logit(p[i,j]) <- mu[i] + delta[i,j]              # model for linear predictor 
    rhat[i,j]     <- p[i,j] * N[i,j]                 # expected value of the numerators  
    dev[i,j]      <- 2 * (k[i,j] * (log(k[i,j])-log(rhat[i,j])) 
                     + (N[i,j]-k[i,j]) * (log(N[i,j]-k[i,j]) - log(N[i,j]-rhat[i,j]))) 
                                                     # deviance contribution 
#    dummy[i,j]    <- ArmNo[i,j]                      # data not used in this model 
    }                                                # close arm loop 
  for (j in 2:NumArms[i]) {                          # indexes arms 
    delta[i,j]  ~  dnorm(md[i,j],taud[i,j])          # trial-specific LOR distributions 
    md[i,j]     <- d[Rx[i,j]] - d[Rx[i,1]] + sw[i,j] # mean of LOR distributions (with                                                             multi-arm trial correction) 
    taud[i,j]   <- tau *2*(j-1)/j                    # precision of LOR distributions (with                                                        multi-arm trial correction) 
    w[i,j]      <- (delta[i,j] - d[Rx[i,j]] + d[Rx[i,1]]) 
                                                     # adjustment for multi-arm RCTs 
    sw[i,j]     <- sum(w[i,1:j-1])/(j-1)             # cumulative adjustment for multi-arm                                                         trials 
    } 
  resdev[i]     <- sum(dev[i,1:NumArms[i]])          # summed deviance contribution 
#  dummy2[i]     <- Yrs[i] * RefID[i]                 # data not used in this model 
  }                                                  # close study loop 
totresdev     <- sum(resdev[])                       # total residual deviance 
 
d[1]<-0                                              # effect is 0 for reference treatment 
for (j in 2:NumRx) {                                 # indexes treatments 
  d[j] ~ dnorm(0, .0001)                             # vague priors for treatment effects 
  }                                                  # close treatment loop 
#sdu ~  dunif(RFXpriorParam1, RFXpriorParam2)         # uniform between-trial prior 
#sdn ~  dnorm(RFXpriorParam1, RFXpriorParam2)         # normal between-trial prior 
#sdl ~  dlnorm(RFXpriorParam1, RFXpriorParam2)        # lognormal between-trial prior 
#sd  <- sdu * equals(RFXpriorD,1) + sdn * equals(RFXpriorD,2) + sdl * equals(RFXpriorD,3) 
                                                     # select correct between-trial prior 
tau <- pow(sd,-2)                                    # between-trial precision 
 
sd ~ dunif(0,10) 
 
# Provide estimates of treatment effects T[k] on the natural (probability) scale 
#AMean ~ dnorm(meanA, precA) 
#APred ~ dnorm(predA, predPrecA) 
#for (j in 1:NumRx) { 
 # logit(Tmean[j]) <- AMean + d[j] 
  #logit(Tpred[j]) <- APred + d[j] 
#  } 
 
# pairwise ORs and LORs for all possible pair-wise comparisons 
for (c in 1:(NumRx-1)) { 
  for (j in (c+1):NumRx) { 
    lOR[c,j] <- (d[j]-d[c]) 
    OR[c,j]  <- exp(d[j]-d[c]) 
    } 
  } 
 
# ranking on relative scale 
for (j in 1:NumRx) { 
  rk[j]       <- blnHiGood*(NumRx+1-rank(d[],j)) + (1-blnHiGood)*rank(d[],j) 
  best[j]     <- equals(rk[j],1)                     # probability that treat j is best 
  for (h in 1:NumRx) { 
    pRk[h,j]  <- equals(rk[j],h)                     # probability that treat j is hth best 
    } 
  } 
#dummy3        <- YrsA                                # not used in this model 
} 

Utility Data

No direct health related quality of life data for progression free and post progression survival were available for patients with stage IIIA-N2 NSCLC. However, a targeted search was undertaken and a large number of potentially relevant data sources were identified that related to people with Stage III NSCLC undergoing surgery. Of these, the three studies the committee thought the most relevant are displayed in Table 24. A random effects model was chosen to pool these data because the I-squared statistic equalled 80%, indicating high between study heterogeneity.

No relevant post-progression utility estimates were identified so a generic post-progression adjustment value taken from a study widely used in economic models for advanced NSCLC was used (Nafees 2008). The committee agreed that it was likely patients undergoing surgery would experience some reduction in health related quality of life for about three months while they recovered. This was borne out in the evidence from Bendixen 2016^e, a trial that investigated HRQoL in patients having surgery for NSCLC. We used data on EQ-5D measured at various time points in the thoracotomy arm of the trial to calculate the QALY loss from surgery by assuming that any dips below a linear trajectory between the time periods of 0 weeks and 12 weeks were due to surgery. The resulting difference between the areas under the curve for the observed values and the linear trajectory, calculated using simple averaging methods between observed time points, gave a QALY loss due to surgery of −0.012. This value was applied only to people actually undergoing surgery (see the section further down discussing drop-out rates).

Table 24. Utility Parameters

For the long term portion of the model, in which people were assumed to remain progression-free until death, the progression-free utility value was multiplied by the age specific decrements that would be expected in the general population (Kind et al 1999). More specifically, the age specific value at each cycle was looked up from a table containing general population utility values and divided by the population level age specific utility value at cycle 0 of the long term model. This figure was then multiplied by the progression free survival utility value to give the utility at future cycles including any appropriate decrements for advanced age. Weighted averages were used for men and women assuming 53.4% of people in the model were men (NCLA 2017 data on general lung cancer presentation). To reflect the population in the underpinning trials, the starting age in the model was 60 (and therefore 65 in the long term model).

Table 25. General Population Utility Estimates for Use in Long Term Multiplier

Adverse events were assumed to be acute in nature and not contribute meaningfully to QALY losses. Since adverse event rates did not differ greatly between the interventions, this limitation was assessed as minor.

Progression Free and Post Progression Survival Time (Short Term Model)

A single bivariate NMA model produced the estimates for discounted PFS and PPS. A brief discussion of this contained in the Model Structure section above and a full write up of this analysis can be found in Appendix I. The NMA had 50,000 burn-in iterations that were then discarded. 10,000 values that had been thinned by 5 were taken from the next 50,000 iterations and used in the economic model. For each run of the model, discounted PFS and PPS values for all three interventions came from a randomly sampled line of this CODA output. The use of a single line of CODA for all data points was essential to preserve the correlation structure in the posterior distributions.

The discounted average pre and post progression survival time were multiplied by the relevant utility values to produce QALYs over 5 years. A surgery specific QALY decrement (see above) was applied to people receiving surgery in the CR and CRS model arms.

Survival at study endpoint

The probability of survival at study endpoint came from the relevant NMA (see Appendix I for a full discussion). The NMA had 50,000 burn-in iterations that were then discarded. 10,000 values that had been thinned by 5 were taken from the next 50,000 iterations and used in the economic model. For each run of the model, probability values for all three interventions came from a randomly sampled line of this CODA output. The use of a single line of CODA for all data points was essential to preserve the correlation structure in the posterior distributions. Patients who survived the short term section of the model proceeded into the long term section.

Table 26. NMA Results - Fixed Effects

Table 27. NMA Results - Random Effects

While the relative effects derived from the NMA are insensitive to the choice of baseline values for chemoradiotherapy for PFS, PPS and probability of survival, the absolute values shown in Table 26 and Table 27 are highly sensitive to this choice. We chose to base this data on van Meerbeeck et al 2007 because it the largest study and because it was not characterised by the limitations of the other chemoradiotherapy studies; Eberhardt 2015 (a partially indirect population) and Albain 2009 (a US healthcare setting). The choice of study is expected to make little difference to the model’s results as they relate to PFS and PPS but this is not true for the probability of survival. The relative effect for this outcome is an odds ratio, which is then multiplied by the odds of surviving into the long term model on chemotherapy. If the odds of surviving are very large or very small (prob = 0% or 100%) then the resulting absolute difference in probabilities, and therefore differential number of patients in the long term model, will be small. If the odds are close to even (prob = 50%), as in the case of the Eberhardt data then the resulting differential will be large. We used data from Eberhardt as a sensitivity analysis.

Adverse Events

The committee indicate that we should assume adverse events were acute in nature and that they would be unlikely to materially affect patients’ health related quality of life for any extended period. The numbers of reported adverse events at grade 4 were extremely low and therefore it was highly uncertain whether they differed meaningfully between interventions. The committee asked us to account for only grade 3+ adverse events in the model as these would be expected to incur a hospital admission and were therefore would potentially influence the net monetary benefit associated with the interventions. Grade 3+ adverse events were treated homogenously in the model (i.e. no difference between grades 3 and 4 and no difference between the clinical nature of events). This approach was taken for several reasons; as mentioned above, grade 4 events were rare, events were reported heterogeneously among trials and the specific nature of events was not expected to affect the net monetary benefit calculations within the model due to lack of meaningful differences in HRQoL loss or costs accrued.

We examined the data and determined that only the larger trials conducted by Pless 2015, Eberhardt 2015 and Albain 2009 had reported adverse events comprehensively enough to give us some confidence in the homogeneity of their data collection and reporting methods. We fitted a baseline incidence rate meta-analysis to the arms containing CRS (as the intervention with the most data and trial arms) where events were the total number of events at grade 3 and above and person years at risk were determined by multiplying the sample size by the total area under the overall survival curve at 5 years (which is equal to restricted mean person years lived for the patients in those trial arms). The test for heterogeneity was significant (p<0.0001) so we preferred to use results from a random effects model for the base case analysis.

We then used the same data on events and person years at risk from both arms of the Pless trial to calculate the incidence rate ratio for CS vs CRS. The incidence rate ratio for CR vs CRS was calculated by pooling the data from the Albain and Eberhardt trials in a meta-analysis with random effects again being preferred due to heterogeneity (p=0.019).

Late on in development we received additional data from the EORTC on adverse events in the van Meerbeeck trial. This enabled us to fit a network meta-analysis for this outcome using the data from all four large trials. We decided that because the adverse events would be expected to occur within a reasonably short time frame (certainly those that were directly attributable to the interventions) we could assume a homogenous follow up time in our analysis. We therefore used the person years at risk as detailed above and selected a poisson likelihood, log link model for the analysis (the WinBUGS code is available in Appendix I). The NMA calculated hazard ratios, which we applied directly to the baseline incidence rate and overall survival AUC to calculate total events. The deviance information criterion for the random effects model was only 2 points lower so we preferred the fixed effects model in the base case. The credible intervals for the random effects model are very wide so introduce significant uncertainty into the model but have been examined in a sensitivity analysis. Of note, we decided to use a multivariate normal distribution to incorporate these data into the probabilistic sensitivity analysis rather than using the CODA outputs from the NMA so as not to slow down the model. We do not expect this to have affected the results.

The committee examined the resulting data and noted that the total number of events for CS and CR remained roughly the same and that they were both higher than CRS The committee were unsure about the clinical plausibility of this, given that CRS is the more intense intervention but they noted that it could be explained to some extent by the finding that more people in the CS strategy actually go on to have surgery. Ultimately they decided to prefer the pairwise approach over the NMA in the base case as it introduced less uncertainty into the probabilistic sensitivity analysis but in interpreting the results were mindful that few significant differences has been observed in the GRADE tables. A sensitivity analysis where event rates were equal was therefore also specified.

For the 4-year sensitivity analysis we calculated the baseline incident rates using the same number of adverse events and the 4-year person years at risk data. We assumed the pairwise incident rate ratios would remain the same. These data were multiplied by the total person years at risk to give total adverse events at 4 years. These were very similar to using the 5-year data. We did not fit a 4-year NMA because the base case analysis was chosen to be pairwise.

Table 28. Adverse event output data

Costs of Initial Treatment

The committee examined the dosing regimens in the RCTs and noted that the interventions were delivered quite heterogeneously (varied number of cycles of chemotherapy, grays and fractions of radiotherapy and timing of both interventions). They noted that none of the studies were set in the UK and decided on a set of resource uses that they felt were broadly representative of UK practice as well as being similar to the range observed in the trials. This was four cycles of chemotherapy and 55 grays in 20 fractions for radiotherapy in the base case. There are a large number of possible platinum doublet chemotherapy combinations used in current UK practice, which all cost a similar amount. As costing all these individually and taking a weighted average would not have meaningfully added to the accuracy of the model, we decided to cost a representative treatment. The committee decided that we should use carboplatin and oral vinorelbine for this purpose and supplied us with the typical doses.

Surgery was costed using the NHS reference cost for “Complex Thoracic Procedures, 19 years and over, with CC Score 3-5”. The committee felt this was the most representative cost as the procedure was expected to be more complicated than most lobectomy operations, which were costed at “…CC score 0-2”. A proportion of operations for N2 stage disease are pneumonectomies which the committee also felt would be covered by this reference cost.

Progressions (costs and events)

Since progression-free survival represents both patients who have not either progressed to a more advanced stage of disease or died, obtaining the number of progressions that are in fact deaths is necessary. These data were available in Albain 2009 and Pless 2015 and in a personal communication from the EORTC, who hold the data for van Meerbeeck 2007. The data from Pless and van Meerbeeck was pooled in a fixed effects meta-analysis (heterogeneity p=0.18) to obtain the proportion of progressions that were deaths for the CS intervention, the log-odds ratios were then analysed in NMA (see Appendix J for details) and applied to the pooled CS estimate to calculate the proportions for CR and CRS. These data were assessed as having good face validity as it would be reasonable to expect the surgical intervention arms to include more early deaths due to the invasive nature of the interventions. These parameters were only important for costs in the economic model, however, as all survival data of interest had already been taken into account via the other NMAs..

Upon progressions that were not deaths, patients were assumed to be treated with another round of systemic therapy. We had no data on the specific types of progression and it was not clear that progression type or the indicated treatment would be expected to differ significantly between the interventions so the committee thought this simplifying assumption reasonable. There are a very large number of systemic therapy options available in NSCLC (see RQ 3.3 of this update for a full algorithm) so costing them all and factoring in their differential benefits in this patient population would have been impractical and subject to high uncertainty. These treatment options have typically been the subject of NICE Technology Appraisals and therefore represent cost-effective additions to the care pathway, but additions that the committee was aware were unlikely to add much in terms of net monetary benefit. This is because Technology Appraisal approved drugs in advanced cancer rarely have base case ICERs significantly lower than the upper limit of the ICER range normally considered cost effective by NICE. The committee also noted that much of the evidence in this model came from survival data collected before many of these drugs were widely available. They therefore thought that the net monetary benefit associated with systemic therapy could reasonably be approximated using the costs of platinum doublet chemotherapy. Four cycles of oral vinorelbine with carboplatin was again chosen for this purpose and the overall cost of systemic therapy for progression was explored in sensitivity analysis.

Table 29. Progressions that are deaths

The committee noted the convergence of the overall and progression free survival curves and made the assumption that progression-free survival would equal overall survival at the study endpoint of 5 years. They felt that NSCLC would be highly unlikely to recur in the vast majority of patients who were alive and unprogressed at this point. The number of progressions for each intervention during the first 5 years was therefore calculated by multiplying one minus the proportion still alive by one minus the proportion of progressions that were deaths.

The total number of deaths was equal to one minus the probability of survival at study endpoint and a cost of death representing a total package of end-of-life care was applied that was drawn from a study including the costs accrued by cancer patients in their last 90 days of life (Georghiou and Bardsley 2014^k). This data source had also been used by NICE’s recently published guideline on Early and Locally Advanced Breast Cancer. The cost of existing in the pre and post progression states for 90 days, weighted by the proportion of people who were expected to die directly from each state was then subtracted to give the total death-attributable cost. We assigned the overall value an arbitrary high standard error equal to a quarter of the mean as these data were quite uncertain.

Table 30. Death costs

Discounting

Discounting was implemented at 3.5% throughout the model. While the NMAs already discussed provided discounted values for PFS and PPS and probability of OS, which could be multiplied directly by state membership and utility estimates to produce appropriate discounted values, another solution was needed for event costs. Another two NMAs were therefore conducted (see full discussion in Appendix I) that calculated the proportion of progressions and deaths that occurred in each year. These proportions were multiplied by the total number of deaths and progression events and the appropriate discount factor for each year of the model to give a total weighted discounted average cost for both types of events.

Table 31. Proportion of events occurring in each year

Drop Out Rates

The overall and progression-free survival curves provided intention-to-treat effectiveness data for each arm of each study. Not all patients in the surgery arms actually had surgery, however, through either dying, not being fit enough or changing their mind by the end of chemoradiotherapy. The committee therefore thought that the cost of the strategies including surgery should reflect these data. We were able to obtain the proportion of people actually undergoing surgery from the CS and CRS arms of all the trials. We pooled the data for proportion of patients undergoing surgery and used a random effects model due to high statistical heterogeneity. Because the smaller studies were less certain and contributed quite a lot of heterogeneity to this calculation we excluded them and pooled only the large studies in a fixed effects meta-analysis. We repeated this same procedure for CS; both the meta-analyses with and without large trials were fitted using random effects models to account for statistical heterogeneity. In the base case, we used the data containing only large trials because we thought it more reliable but the value obtained using all the trials and a value of 100% were examined in sensitivity analysis.

Table 32. Proportion in surgical arm continuing to surgery

Health State Costs

No background healthcare resource use data was available for patients with NSCLC stage IIIA-N2. We examined the literature for inspiration and presented a number of possible resource uses to the committee. The committee debated these data and, incorporating their own clinical experience, settled on the assumptions in Table 33 and Table 34 as being broadly representative of a typical patient in the progression free and progressed states. The total monthly average cost is the sum of the product of % of patients, units and costs for each type of resource.

Table 33. Monthly Progression Free State Costs

Table 34. Monthly Progressed State Costs

To calculate total costs for the short term model these costs were multiplied by the average discounted time that patients spent in each state, which was derived from the relevant NMA.

Long Term Model

Patients surviving the short term model entered the long term model, which was a partitioned survival model with two states; dead and alive + progression free. It was assumed that no progressions took place among the surviving patients and they had, to all intents and purposes been cured of their lung cancer. Death events were accrued at a rate equivalent to the difference in the death state membership from cycle to cycle. The long term model was run on a monthly cycle length and a half-cycle correction using the life table method was applied. As discussed earlier, progression-free utility estimates were adjusted to reflect the decline in HRQoL in the general population at older ages. Progression-free costs continued to be applied in the model but at a rate of only 20% to reflect the assumptions that patients would be permanently remitted after 5 years but the committee felt patients would still continue to interact with services to some degree, especially if they had impaired lung function following radical treatment.

In order to obtain appropriate survival curves we interrogated the SEER registry^l, which was chosen because it was the only registry we knew about with the ability to extract the data we needed. The database was queried for survival data for patients who were diagnosed between 1988-2003, aged 35-79, had stage IIIA-N2 lung cancer upon diagnosis and had survived five years after their initial diagnosis. We fit survival curves to the data and selected the two with the lowest AIC statistics for use within the model as the base case and in sensitivity analysis. These were Weibull and exponential curves fitted to data from 2,865 patients. From Figure 14, it can be seen that they fitted the survival data well. The AUC (or mean survival time) for these curves was about seven years. The data were somewhat out of date and we were unable to identify any data that would enable us to differentiate these curves by initial treatment but the committee thought that as they were meant to represent a cured population, these limitations were minor. The same process as this was undertaken to parameterise the 4-year sensitivity analysis, with Weibull and Exponential curves again providing the best fit to the data (N=3,703).

Table 35. Long term survival curve parameters

Figure 14. SEER Survival Data and Parametric Models

Sensitivity Analysis

Sensitivity and scenario analyses was conducted by altering key parameters or groups of parameters including changing the short term element of the model to cover four years instead of five, using random effects NMAs instead of fixed effects, changing key cost and utility parameters, setting probability of survival at study endpoints and various other uncertain data equal among interventions, using different survival curves and altering the discount rate.

Probabilistic sensitivity analysis was performed by assigning parameters with appropriate probability distributions that reflected our uncertainty about their mean values. Of note, the NMAs used the relevant CODA. The very bottom end of the posterior distributions for AUC values for PFS and PFS in the random effects models had to be truncated at 0. This was because the NMA input and output data were on the natural scale (i.e. number of years) and so some impossible negative AUC values arose due to the wide credible intervals in the posterior distribution of the random effects models. This was only a small amount of data so was noted as a minor limitation for the PSA in the random effects scenario analysis.

Particularly uncertain costs that were heavily influenced by assumptions (such as the state membership costs and the cost of death) were arbitrarily assigned a high standard error equal to the mean divided by four. As noted in the adverse events section, the hazard ratios derived from NMAs were parameterised using a multivariate normal distribution on the log scale to reduce model size and running time.