Diagnostic model for patients with suspected coronary artery disease

The purpose of testing patients with suspected CAD (based on clinical symptoms) is to diagnose those patients and give, when necessary, appropriate treatment.

The prior likelihood of having CAD in patients with suspected CAD is assumed to be 10–29%, based on the clinical guideline Chest pain of recent onset.⁶³ This prior likelihood is based on some patient characteristics (age, gender, diabetes, smoking and hyperlipidaemia, and either non-anginal chest pain, atypical angina or typical angina). According to the guideline, in these patients, first a CT calcium scoring is performed and the patients referred for 64-slice CT (i.e. our population) have a score of 1–400. Patients with a higher prior likelihood than 10–29% should be referred for ICA. Some difficult-to-image subgroups could have a higher prior likelihood but how much higher is unknown. Therefore, we performed a scenario analysis where the prior likelihood was set at 30% for all subgroups. Table 17 summarises the prior likelihood of CAD in the known and suspected CAD populations.

TABLE 17

Prevalence in CAD populations

The sensitivity and specificity of ICA was assumed to be 100%, as in Mowatt et al.³ The systematic review performed for this assessment provided the estimates of the sensitivity and specificity for the NGCCT. As described in Chapter 3, Summary, estimates of sensitivity and specificity differed for the different difficult-to-image patient groups. The sensitivity and specificity of the NGCCT in the beta-blocker-intolerant patient group were assumed to be the same as the sensitivity and specificity in patients with a HHR. As beta-blockers are used to lower the heart rate of the patients, it is not the intolerance itself that makes the patient difficult to scan but rather the fact that such a patient may have a heart rate that is too high during the scan; studies reporting per-patient sensitivity and specificity in patients with a HHR did not use beta-blockers prior to scanning. Table 18 shows the sensitivity and specificity estimates for the NGCCT in the different difficult-to-image patient groups.

TABLE 18

New-generation cardiac computed tomography accuracy estimates (subgroup specific)

The result of the test and the presence of the disease determine whether a patient is classified as TP, TN, FP or FN (illustrated in Figure 14). The three strategies (ICA only, NGCCT only and NGCCT–ICA) all have other properties and therefore test outcomes differ by strategy. The four outcomes were calculated using the following formulae: TP, prior likelihood × sensitivity; TN, (1 – prior likelihood) × specificity; FP, (1 – prior likelihood) × (1 – specificity); FN, prior likelihood × (1 – sensitivity). Possible test outcomes are described by strategy.

FIGURE 14

A 2 × 2 table for patients with suspected CAD.

Patients with suspected CAD who have a positive test result are thought to have CAD according to the test and need to be treated with medication only or a revascularisation. A negative test result implies that the patient with suspected CAD does not have the disease and does not need to be treated.

• ICA-only strategy Patients diagnosed with the reference standard ICA can be defined as only TP or TN because ICA is assumed to be 100% accurate and therefore misdiagnosis is not possible.
• NGCCT-only strategy The sensitivity and specificity of the NGCCT are not 100%, and the results of these tests can therefore define patients as TP, TN, FP or FN. For the patients who are diagnosed incorrectly the test result will have consequences. A proportion of the FNs will later be identified as TPs because patients may have persistent symptoms. However, in our model, these patients could have experienced an event [e.g. MI or cardiac arrest (CA)] before the correct diagnosis is established. The FPs may receive unnecessary treatment with its attendant consequences.
• NGCCT–ICA strategy In this strategy, an ICA is performed to confirm a positive NGCCT scan. Therefore, all patients with a FP result for the NGCCT will subsequently be correctly classified by the ICA as TNs. As a result, these patients will not receive any unnecessary treatment. In the model, all of these patients are subsequently considered as TNs for the NGCCT–ICA strategy since the ICA correctly reclassified them. However, an ICA is not performed in patients with a negative NGCCT result. As the sensitivity of the NGCCT is not 100%, it is possible for FN results to arise from this NGCCT–ICA strategy. As with the FNs from the NGCCT-only strategy, a proportion of these FNs will be identified at a later stage.

Diagnostic model for population with known coronary artery disease

The purpose of testing patients with known CAD (defined as those who have previously been diagnosed with CAD and whose symptoms are no longer controlled by drug treatment and/or are being considered for revascularisation) is to inform revascularisation decisions.

The prior likelihood of performing a revascularisation in patients with known CAD is assumed to be 39.5%, based on the CE-MARC study (see Table 17).⁶⁴ The CE-MARC study⁶² calculated the cost-effectiveness of using CV MRI to determine whether or not a revascularisation is necessary. The purpose of diagnostic testing assessed in the CE-MARC study⁶² captures the aim of this economic evaluation for the known CAD population and therefore the prior likelihood of the CE-MARC population can be used in the diagnostic model.

The accuracy of the NGCCT for the known CAD population is assumed to be the same as for the suspected CAD population. This assumption was made because for some difficult-to-image patient groups there were no data or just one article for a known CAD population. Details of the reported inclusion criteria, for all studies included in the systematic review, are provided in Appendix 4.

A positive test result for the patient population who have previously been diagnosed with CAD and whose symptoms are no longer controlled by drug treatment and/or who are being considered for revascularisation indicates that the patient will benefit from a revascularisation and should undergo a CABG or a PCI. A negative test result for the same population implies that the patient will not benefit from a revascularisation and drug treatment only should be continued.

The same test outcomes apply to the known CAD population as previously described before for the suspected CAD population (Figure 15). Thus the ICA-only strategy will define only TP and TN because ICA is assumed to be 100% accurate. The NGCCT-only strategy gives four possible outcomes: TP, FP, TN and FN. The combined strategy (NGCCT–ICA) defines three outcomes: TP, TN and FN.

FIGURE 15

A 2 × 2 table for patients with known CAD.

FIGURE 17

Known CAD: NGCCT-ICA.

EUROPA model structure

The EUROPA Markov model (Figure 20) consisted of five health states that were defined as absence of primary event in the EUROPA trial: ‘trial entry’, ‘CV death’, ‘non-fatal primary event in current year’, ‘history of non-fatal event (NFE)’ and ‘non-CV death’.⁷⁰ The 3-monthly transition probabilities between the different states were based on risk equations and on UK life tables on non-CV death. The risk equations consisted of several covariates based on baseline characteristics and previous conditions, such as age, gender, previous MI, diabetes mellitus, etc. The prognosis of the patients was partly dependent on the initial test outcome and treatment decision.

FIGURE 20

EUROPA Markov model. Based on Briggs et al. CA, cardiac arrest; Eq, equation.

All patients with CAD (with the exception of those who experience non-fatal complications from ICA, PCI or CABG) enter the EUROPA model in the ‘Start’ state. A patient can either stay in this state, die from a non-CV cause (and move to the ‘Non-CV death’ state), or experience a CV event and move to the ‘CV death’ state if the event is fatal or to the state ‘non-fatal event (first year)’ if the event is not fatal. The ‘non-CV death’ and the ‘CV death’ states are both mutually absorbing states. Patients can end up in the ‘non-fatal event (first year)’ state in two different ways: by experiencing a non-fatal MI from the initial ICA or revascularisation or by experiencing a non-fatal event at a later time (modelled in the EUROPA model by the risk equations). When a patient is in the ‘non-fatal event (first year)’ state he or she can remain in this state for maximum of 1 year without experiencing a subsequent event. After that, a patient can move to the ‘non-fatal event (after first year)’ state if he or she has stayed in the ‘non-fatal event (first year)’ state for a year without experiencing a new event. Patients in the ‘non-fatal event (first year)’ can also move to the ‘Non-CV death’ state if the patient dies from a non-CV cause; the ‘CV death state’ if the patient experiences a subsequent event which is fatal (‘CV death’ state) or stay in the ‘non-fatal event (first year)’ state if the subsequent event is not fatal. A patient in the ‘non-fatal event (after first year)’ state can stay there, move to the ‘non-fatal event (first year)’ state if the patient experiences a non-fatal subsequent event, move to the ‘CV death’ state if the patient experiences a fatal subsequent event, or move to the ‘non-CV death’ state if the patient dies from a non-CV cause. The risks of events and the mortality associated with events are predicted by the risk equations. Non-CV mortality was based on UK life tables.

EUROPA model entry for population with suspected coronary artery disease

The proportions of patients classified as TP and FN entering the EUROPA model were based on the calculations using prevalence of the disease, sensitivity and specificity of the tests as defined in the diagnostic model. These proportions can vary between the three strategies. Table 19 shows intermediate results of the diagnostic model in two ways. The first part shows how the four test outcomes are represented for each strategy, each difficult-to-image patient group. The second part shows the impact of immediate procedure-related mortality and morbidity on the distribution of the test outcomes. As expected the mortality rates differ considerably between the three strategies. Patients suspected of CAD diagnosed with the ICA alone have the highest overall mortality and morbidity rate. The TN proportion is the lowest in the difficult-to-image arrhythmias group due to the low specificity. The disease progression of the TP and the FN (patients with the disease) was modelled with the EUROPA model. These two outcomes were divided into three treatment possibilities: medication, PCI or CABG. The other two test outcomes (FP and TN) were modelled through a simple alive–dead Markov model (healthy population model) based on life tables, as described above (see Healthy population Markov model).

EUROPA model entry for population with known coronary artery disease

Table 20 presents the intermediate outcomes of the three strategies for the known CAD population. The first part shows how the test outcomes are distributed in each strategy for each difficult-to-image patient group. The second part incorporates also the mortality and morbidity associated with the ICA and revascularisations. The NGCCT–ICA strategy results in the lowest mortality and morbidity rates. The prognosis of patients in all four outcomes (TP, TN, FP and FN) was modelled using the EUROPA model because all patients have CAD.

TABLE 20

EUROPA entry for patients with known coronary artery disease

Every cycle a certain proportion of the FN patients in both populations will be identified as TP based on the Canadian Cardiovascular Society (CCS) angina classification. Identified TPs will be treated and they will have the same prognosis as the TPs who were identified directly by the diagnostic test. The FNs that are still not identified have a higher chance of experiencing an event.

EUROPA model risk equation adjustments

Risk equations to predict the events for patients with CAD were based on the EUROPA trial.⁶⁸ Using the EUROPA model for the evaluation of the NGCCT in the two CAD populations (suspected and known), and for the different difficult-to-image patient groups, required some adjustment of the EUROPA model. These adjustments were necessary as the baseline characteristics of the EUROPA population were not completely comparable with the subgroups in the known and suspected CAD populations.

As shown in Figure 20, four equations were used to calculate transition probabilities between the states. The first equation based on time-to-event survival analysis estimated the probability of any event that will occur in one cycle of 3 months as a function of the following covariates: age, years older than 65, perindopril usage, smoking, previous MI, existing vascular disease [stroke, transient ischaemic attack (TIA) or peripheral vascular disease], family history of CAD, symptomatic angina or history of heart failure, systolic blood pressure, total cholesterol, obese (BMI of > 30 kg/m²), gender, nitrates usage, calcium channel blockers usage, lipid-lowering treatment, units creatinine clearance below 80 ml/minute and previous revascularisation (PCI or CABG) (Table 21). The second equation of the EUROPA model estimates the odds that the event is fatal, based on age, previous MI and total cholesterol. The third equation estimates the risk of a subsequent event in the first year after a first NFE and is based on the presence of symptomatic angina or history of heart failure. The fourth equation, which predicts the risk of a subsequent event after 1 year, is the same as the first equation except that the covariate previous MI is updated by setting the covariate previous MI at ‘1’.

TABLE 21

Original EUROPA risk equations and mean values: EUROPA population

The risk equations consist of covariates based on the EUROPA trial and therefore baseline characteristics had to be established for the 12 subgroups (seven difficult-to-image patient groups in the known CAD population and five in the suspected CAD population). Means were used in the risk equation, as we used a cohort model. The accuracy of the NGCCT was based on the systematic review reported in Chapter 3, and this review was also used as a source to estimate the baseline characteristics of the different subgroups for use in the risk equations; details of the baseline characteristics of study populations included in the review are reported in Appendix 4. Only subgroup-specific publications were used, thus studies which determined the accuracy of the NGCCT in two or more difficult-to-image patient groups were not used. The baseline characteristics of the EUROPA population were used when information for a specific subgroup and baseline characteristic was not found; this approach assumes that there were no differences between the EUROPA population and the specific subgroup (see Table 21).

Population with suspected coronary artery disease

Baseline characteristics, such as age, gender, family history, diabetes mellitus, obesity, smoking and symptomatic angina, were collected from the articles included in the review that focused on the suspected CAD population. The richness of the information collected from the articles differed between the difficult-to-image patient groups. In all difficult-to-image patient groups except for the ‘intolerant to beta-blockers’ group, a minimum of gender and age data were found. When population specific information regarding risk-related characteristics was not found in the literature, the assumption was made that the difficult-to-image subgroup did not differ from the EUROPA population and therefore the value of the EUROPA population (see Table 21) was taken. ‘Perindopril usage’ was assumed to be 0.23 for the whole suspected CAD population.⁷¹ We will assume that the effect of perindopril does apply for any ACE inhibitor. The covariates ‘age’, ‘age > 65 years’, ‘men (y/n)’, ‘smoking (y/n)’, ‘diabetes mellitus (y/n)’, ‘positive family history (y/n)’, ‘obese (y/n)’, ‘symptomatic angina (y/n)’ differed per difficult-to-image subgroup. No subgroup-specific information was collected for the covariates ‘systolic blood pressure’, ‘creatinine clearance’, ‘total cholesterol’ and ‘the usage of lipid-lowering treatment at baseline’. The five other covariates depended on the strategy, treatment and test outcomes. Tables 22 and 23 illustrate how proportions were assigned to the covariates. The proportion that has had an MI was based on the non-fatal complications of ICA and revascularisation. FNs in strategies 2 and 3 have not experienced an MI, revascularisation or vascular disease because they do not undergo an ICA or a revascularisation. The covariate previous revascularisation was set at 1 for the TPs treated with a revascularisation. Nitrates usage was assumed to be ‘0’ for all test outcomes. Usage of calcium channel blockers was assumed to be ‘1’ for TPs who received medical treatment. This is because, although they might actually be prescribed a beta-blocker instead,⁷¹ there was only a covariate in the risk equation for calcium channel blocker and not beta-blocker. This assumption can be justified because the efficacy of calcium channel blockers does not differ from that of beta-blockers.⁷¹

TABLE 22

Input for the EUROPA risk equations: suspected CAD population

TABLE 23

Subgroup-specific input for the EUROPA risk equations: suspected CAD population

Population with known coronary artery disease

The procedure described above to establish the baseline characteristics for the suspected CAD population was also used for the known CAD population. No information about gender and age was available for the beta-blocker intolerance and high coronary calcium score groups. For the other groups these data were collected from the accuracy studies included in the systemic review. The covariates ‘age’, ‘age > 65 years’, ‘men (y/n)’, ‘smoking (y/n)’, ‘diabetes mellitus (y/n)’, ‘positive family history (y/n)’ and ‘obese (y/n)’ differed per difficult-to-image patient group. No subgroup-specific information was available for the covariates ‘symptomatic angina’, ‘systolic blood pressure’, ‘creatinine clearance’, ‘total cholesterol’ and ‘the usage of lipid-lowering treatment at baseline’. Perindopril intake proportion was set at 0.23, based on published data.⁷⁰ The proportion of patients experiencing an MI or the proportion where vascular disease is present was based on the EUROPA population. The proportions were not raised with ICA or revascularisation-induced MI. Nitrates usage and calcium channel blockers at baseline were not reported in the studies included in the systematic review and therefore these proportions were based on the EUROPA population (see Table 21). The proportion for previous revascularisation was set at ‘1’ for the TPs in all strategies, for the FPs in strategy 3, and for the subgroups' previous PCI and previous CABG this was set at ‘1’ for all test outcomes. The remaining proportions were set as for the EUROPA population (Tables 25 and 26).

TABLE 25

Subgroup-specific input for the EUROPA risk equations: known CAD population

TABLE 26

Input for the EUROPA risk equations: known CAD population

Difficult-to-image patient group-specific data

In addition to CAD population-specific adjustments of the EUROPA risk equations, adjustments were necessary for each specific difficult-to-image patient group. It is likely that some of the reasons why patients are difficult to scan may also lead to a higher probability of a CV event.

In the obese patient group, the increased risk of events was already captured in the risk equation, as it contains a covariate for obesity. For the obese group, the covariate obesity was set at ‘1’ for all test outcomes, strategies and CAD populations.

For simplicity, we treated the difficult-to-image subgroup with a previous CABG the same as the difficult-to-image subgroup with a previous PCI.⁷² The covariate ‘previous revascularisation’ is present in the first and fourth risk equations of the EUROPA model; thus, the risk of having a primary or subsequent event for these specific patient groups was captured.

For the difficult-to-image groups arrhythmias and high coronary calcium level, a relative risk (Table 24), compared with the EUROPA population, was used to adjust the risk of events. For the HCS patient group, data from an unpublished study⁷³ were used to estimate the relative risk without correcting for other factors of experiencing primary events in patients with a coronary calcium score > 400 compared with patients without a coronary calcium score of > 400. The proportion with a coronary calcium score of > 400 in the EUROPA population was not reported and therefore the study of Shemesh et al.⁷⁴ was used to estimate a proportion assuming that the populations are comparable. We assumed that this relative risk also applies for the risk of having a subsequent event.

TABLE 24

Relative risks of CV events compared with EUROPA population for arrhythmias and high coronary calcium level subgroups for the known and suspected CAD population

A relative risk, compared with the EUROPA population, was also used to estimate the risk of experiencing events for the patient group with arrhythmias. The term ‘arrhythmias’ encompasses several different conditions, with AF being the most common. A relative risk was calculated, controlling for other factors for patients with arrhythmias, based on the relative risk found in the QRISK study, which investigated the relative risk of experiencing events for patients with AF against patients without AF.⁷⁵ The proportion of the patients with AF was not reported by the EUROPA study and therefore we assumed that the proportion AF in patients with CAD is 19% based on Banasiak et al.⁷⁶

No adjustments to the risk equations were necessary for the intolerant to beta-blockers patient group because it was assumed that intolerance of beta-blockers does not lead to an increased risk of experiencing events; patients undergoing a cardiac CT receive beta-blockers to lower their heart rate in order to produce images of adequate quality, not in order to prevent events. Patients with CAD will often be treated with beta-blockers but these can be replaced with calcium channel blockers and/or ACE inhibitors and therefore intolerance to beta-blockers will probably not affect prognosis.

For the patient group with HHR the risk equations were not adjusted because it was assumed that HHRs affect only the quality of CT imaging. The patient groups with HHR and intolerance to beta-blockers were modelled with the original risk equations based on the EUROPA population.

Biological effects of radiation

The dose of ionised radiation absorbed by a body is measured in grays (Gy). However, the health-relevant (and harmful) energy absorbed depends on the tissue and type of radiation and is expressed in sieverts (Sv). Because of the small doses of imaging radiation, more often millisieverts (mSv) are used (1000 mSv = 1 Sv). Also, 1 Sv = 1 Gy × a weighting factor (e.g. for a breast scan the weighting factor is 0.05).

Exposure to ionised radiation has mainly three biological adverse effects.⁷⁷ First, radiation has a harmful effect on developing embryos when the expecting mother is exposed to radiation. This is not relevant in our application. Second, radiation exposure might affect reproductive health, i.e. radiation exposure may lead to adverse congenital health outcomes of later offspring. There is, however, no convincing evidence for this effect in humans, only in animal experiments. The third, most harmful, effect is an increased lifetime risk of cancer incidence. For low doses, sparse clinical evidence exists. A prominent source is a cohort study of Japanese atomic bomb survivors who were exposed to radiation. These data provide strong evidence of an increased cancer mortality risk at equivalent doses of > 100 mSv, good evidence of an increased risk for doses between 50 and 100 mSv, and reasonable evidence for an increased risk for doses between 10 and 50 mSv.⁷⁸

The standard epidemiological risk models use a linear relationship between radiation exposure and lifetime probability of solid cancer without assuming a threshold, i.e. even a minimal exposure is assumed to increase the lifetime risk of cancer incidence. The younger the age at exposure, the higher is the lifetime probability of cancer incidence for a given amount of radiation, partly because children have on average more life-years remaining to develop cancer. The cumulative lifetime risk of an individual for repeated exposure to radiation is calculated by summing the probabilities for lifetime cancer incidence over each exposure.

In a recent report, the Centre for Radiation, Chemical and Environmental Hazards (CRCE), formerly the National Radiological Protection Board (NRPB), of the Health Protection Agency (HPA), has calculated lifetime risks for cancer incidence by age and sex for different levels of radiation.⁷⁹ Those calculations are based on a 2007 publication of the International Commission on Radiological Protection (ICRP).⁸⁰

Structure of York Radiation Model

The calculations for health consequences of radiation exposure are based on an adjusted version of the YRM (Figure 21). The YRM consists mainly of four elements: a radiation module, a cancer module, a utility module and a main module combining all intermediate calculations.

FIGURE 21

Stylised overview of YRM.

In the radiation module, the YRM estimates the lifetime probability of an individual, given the timing and the amount of radiation exposure. To translate the cumulative radiation dose into the probability of lifetime cancer incidence the HPA model is used (see Table 47).⁸⁰

TABLE 47

Lifetime risks of cancer incidence for all cancers by age and sex at exposure based on HPA data

The cancer module is based on prior research.⁶¹ In the absence of cancer models for all types of cancer, four common cancers are modelled: lung and colorectal cancer for both sexes, breast cancer only for females, and prostate cancer only for males. For each cancer, the module contains the further expected QALYs and disease costs for patients with cancer at the average age at diagnosis (see Table 46). For each sex, these values are then combined and weighted according the relative incidence of radiation-induced cancer. For males, the weights are approximately 46% colorectal, 42% lung and 12% prostate, whereas for females the weights are 16% colorectal, 50% lung and 34% breast.

TABLE 46

Total costs and QALYs lost due to cancer, discounted at 3.5% per annum to age at cancer diagnosis (SD in parentheses)

The utility module is based on data for the general UK population (see Table 49).⁶¹ For patients who do not get cancer, the remaining lifetime QALYs from the age at first radiation exposure are calculated. For patients who do get cancer, the utility module calculates the QALYs until the age at diagnosis of cancer, i.e. the timespan without cancer.

TABLE 49

Age-specific utilities based on underlying health of the general UK population

The main module combines the outcome of the three prior modules. So for a given age at first exposure, the share of patients who get radiation-induced cancer during their lifetime is calculated. For those patients, their QALYs until age at cancer diagnosis equal the general UK population and after that the remaining QALYs and the (additional) disease costs owing to cancer are taken from the cancer module. For the rest of the patients, just the remaining QALYs based on the general UK population are calculated. These values are combined and weighted by the sex ratio of the patient population. Both QALYs and disease costs are discounted to the age at first exposure to radiation. The intervention, i.e. the reduction in radiation exposure through the comparator technology, is modelled via the reduction in the probability of lifetime radiation-induced cancer. The YRM allows to conduct a probabilistic sensitivity analysis (PSA) accounting for the uncertainties in age at cancer incidence, cancer costs and QALYs lost due to cancer.

Radiation dose and patient populations

Computer tomography is a relatively high-dose X-ray imaging technique. The effective dose, i.e. absorbed radiation dose by a patient measured in sieverts, depends on a number of factors such as age of patient, the region of the body scanned, tissue type involved, precise type of CT, and scanning protocol for the particular diagnosis in question. Furthermore, CTs are an evolving technology in which the radiation doses vary with CT generation and by manufacturer. Moreover, scanning protocols themselves change over time. In particular, multislice CTs allow for increasingly rapid scans and lower radiation doses. Although 64-slice scanners have increasingly become the standard, earlier-generation CTs are still in use.

The broad range of CT types and CT applications compels studies which aim to quantify the radiation burden attributable to CTs in the general population to measure the radiation dose by scan for a particular body region/diagnosis type, for example head or full chest, roughly differentiating only by CT type (mostly single slice vs multislice). To account for the particular diagnostic needs of the disease assessed, we conducted expert surveys to obtain the relevant dosages by scanning strategy. The results are shown in Table 52 (for patients with CAD) and Table 66 (for patients with congenital heart disease).

TABLE 52

Radiation dose (in millisieverts) of scanning strategies for CAD patients based on a disease-specific expert survey

TABLE 66

Scenario analysis: prior likelihood, suspected population 0.3

The results of our expert surveys are in line with the literature that focuses on general chest CTs (Table 27). A study by the NRPB for the UK, conducted in 2003, shows slightly higher results than our expert survey, as its results were mostly based on single-slice and four-slice technology,⁸¹ which usually have higher radiation doses than 64-slice technology. More recent studies, such as the UNSCEAR 2008 report, assessing the trends in worldwide radiation exposure,⁸² and a review article focusing on children's exposure and based on German data,⁸³ support the overall lower radiation dose for CT64 indicated by our expert survey. Note that in Table 27 values are also presented for younger age groups, as those values are required for the analysis presented below (see Cost-effectiveness of new-generation cardiac computed tomography in congenital heart disease).

TABLE 27

Comparative radiation dose by age at exposure from diagnostic examination of ‘chest’ with a CT (in millisieverts)

The YRM was used for the two patient populations under assessment, the patients with CAD (this section) and the congenital heart disease patients (see Cost-effectiveness of new-generation cardiac computed tomography in congenital heart disease). The adjusted version of the YRM does not model benefits of the different CT strategies, but only the harmful consequences of radiation exposure. Hence, it can be used for both patient populations without further modifications; only the key parameter age at exposure, radiation dose (dependent on type and number of scans) and sex are used. In the case of the patients with CAD, the YRM output was used for further analysis. For an overview of the radiation doses in the patient populations for the different strategies under assessment see Tables 52 and 69.

TABLE 69

Radiations dose (baseline and range) for diagnosis in patients with congenital heart disease with a CT scan based on disease-specific expert reply (in millisieverts)

Costs

The costs included in the diagnostic model were the costs for the diagnostic tests and the costs of the two revascularisation procedures (Table 31). Medication-induced costs were modelled as part of the background costs in the disease progression model. The average cost prices for the revascularisation procedures and the ICA were calculated based on the NHS reference prices 2010–11.⁸⁴ An average cost price is calculated by multiplying the number of admissions with the costs for each different specific procedure. An ICA was estimated as costing on average £1003. A CABG would cost £8280 per procedure, and £9242 in combination with a ICA. A PCI in combination with an ICA would cost £4196, and a PCI without an ICA would cost £3633 per procedure.

TABLE 31

Costs of diagnostic tests and treatment

Given that the cost of ICA (invasive CA) was estimated using the NICE reference cost, for comparability a reference cost would have been useful for each of the different types of scan – both standard 64-slice and the NGCT. However, the only data available were for any CT, i.e. not specifically for CTCA (Table 29).

TABLE 29

Costs for any CT

Therefore, a bottom-up costing was performed, which attempted to use the categories that the reference cost would be composed of, which are shown below (Table 30).

TABLE 30

Estimated costs for any cardiac CT

The final costs of 64-slice and NGCCT are calculated to be £132.62 and £169.26, respectively. The estimated costs of 64-slice CT are higher than the reference costs. However, this is plausible given that much of the capital cost of existing scanners is probably not included in the reference costs. This is because many scanners are actually purchased using non-NHS money, i.e. by private donations (Valerie Fone, Trust Imaging Services Manager, Royal Brompton and Harefield NHS Foundation Trust, personal communication; see Appendix 7). Also, the staff costs for CTCA are higher given the considerable use of consultant as opposed to more junior or no radiologist time. Scenario analyses will be performed for 4160 scans per year (cost price NGCCT: £150) and 2080 scans per year (cost price NGCCT: £207).

Prior likelihood

The prior likelihood for the suspected and known CAD populations is presented above (see Model structure and methodology, Diagnostic model).

Initial treatment decision

Diagnostic tests, using the NGCCT, are performed to determine if treatment is necessary for a difficult-to-image patient. The cost-effectiveness of the NGCCT was estimated for two CAD populations which are treated differently. For the assumptions concerning the treatment options for the suspected CAD population expert opinion was used.

Suspected coronary artery disease population

Patients with suspected CAD and a positive cardiac CT or ICA test result can be treated with drug therapy alone, a CABG or a PCI. The proportions undergoing either revascularisation (18.1%) or medication (81.9%) after a positive test result were based on expert opinion (Hofstra, 2011, personal communication; which was based on an unpublished study conducted in the Netherlands⁷³). The proportion of PCI compared with CABG in patients requiring revascularisation was based on UK procedure figures, which showed a 70%:30% proportion for PCI compared with CABG.⁸⁸

Patients treated with medication only are treated with beta-blockers or calcium channel blockers.¹² When the symptoms are not controlled with one of the two drugs, then a combination can be given or a nitrate can be prescribed. A revascularisation is then considered if symptoms of patients are still uncontrolled by drug treatment alone. The proportions undergoing revascularisation or medication treatment is comparable with a previously published article based on the Euro Heart Survey, which reported a revascularisation rate of 13%.⁷⁰ Furthermore, expert opinion indicated that the results of this study were also appropriate for the difficult-to-image patient groups considered in this assessment.

Population with known coronary artery disease

Given a positive CT or ICA test for patients with known CAD, two treatment options are considered: either PCI or CABG. The proportions undergoing PCI or CABG in patients with known CAD were also assumed to be 70%:30%, based on the same expert opinion used for the suspected CAD population.

Procedure-related mortality and morbidity

Invasive coronary angiography and revascularisation are accompanied by a risk of serious complications, including stroke, non-fatal MI and death (Table 32). The mortality rates are important for the impact on QALYs of the three strategies. The strategy in which all patients will undergo an ICA has the highest test-related mortality rate and this mortality rate influences the cost-effectiveness ratio by lowering the expected QALYs.

TABLE 32

Complications of ICA and revascularisations

The complication rate used in this model is based on published data.⁸⁹ A literature search for UK guidelines for performing coronary angiography was conducted to identify a study that provided primary data on complications caused by diagnostic ICA. Seventeen UK guidelines were found and these were checked for studies presenting primary data; 17 potentially relevant studies were found. A further four primary studies^89–92 were identified after checking the references of the initial 17 studies and performing a citation search. Two studies^90,91 did not present a complication rate based on the UK population but were conducted in Turkey and Canada, respectively. One study⁹² reported a complication rate for a UK population but was based on a single centre. A multicentre study⁸⁹ on diagnostic angiography in the UK (and the most recently performed study) was considered to be the most appropriate study to inform the model. This study reported a complication rate of 7.4 (95% CI 7.0 to 7.7) and a mortality rate of 0.7 (95% CI 0.6 to 0.9) per 1000 patients, based on 219,227 procedures undertaken between 1991 and 1999. The mortality rate and the cerebrovascular accident rate presented in this study were comparable with data from another of the identified studies.⁹⁰ The overall complication rate and the MI rate presented were considerably lower than those presented in the other studies. We assumed that the complication rate of coronary angiography presented by the selected study is applicable regardless of the underlying risk of CV events particularly in difficult-to-image patient groups.

Both revascularisation procedures, CABG and PCI, are associated with complications including stroke, non-fatal MI and death. These complications are included in the diagnostic model. The mortality rate (0.018) of a CABG is based on Bridgewater et al.⁹³ CABG-related stroke was taken from the study.⁹³ As there were no studies that reported CABG-related MI, we used the study by Serruys et al.⁹⁵ to give an estimate of CABG-related MI. A survival curve (patients without MI and stroke) presented in the Serruys study⁹⁵ was used: at 30 days, the survival was 96%; thus, 4% experienced a stroke or a MI. As we found a stroke rate of 1.6%⁹⁴ related to the procedure we used 2.4% as an estimate for CABG-related MI assuming that within 30 days after the procedure it is still related to the procedure. This could lead to an overestimation of the MI rate, because the 4% reported by Serruys et al.⁹⁵ is not related to the procedure per se.

The complication rates induced by PCI were based on the study of Rajani et al.;⁹⁶ mortality due to a PCI is 0.0029, to a MI 0.0005 and stroke due to PCI 0.0005.

Finally, it has also been suggested that the intravenous contrast used in ICA, PCI and the NGCCT may carry a small risk of contrast-induced renal failure, dialysis and mortality.⁹⁷ However, a paper reviewing this risk in CT scans showed a negligible risk. In a total of six studies in patients receiving contrast fluid for a CT, no patients needed dialysis or died out of 1175 patients.⁹⁸ Thus, we have added no complications for the NGCCT. Contrast-related mortality may be assumed to be part of overall mortality due to ICA and PCI discussed earlier. Thus, the only remaining issue is a potential underestimation of the complications of these invasive procedures. As the complication rate can be greatly influenced by taking prophylactic measures in patients who are more at risk, this additional risk is here considered to be negligible.⁹⁹

Survival

Three-monthly, age-dependent transition probabilities were used to model mortality for TN and FP patients in the suspected CAD population. The transition probabilities were based on UK life tables for all-cause mortality (Table 33).⁶⁵ All-cause mortality life tables were used, as these patients can still develop and die from CAD in the future.

TABLE 33

Quarterly mortality rates (all causes)

Utility for patients without coronary artery disease

Patients from the suspected CAD population with a TN or FP test outcome are patients without CAD and it is therefore assumed that the health-related quality of life (HRQoL) for these patients would be equal to the population norms by gender and age (Table 34).¹⁰⁰ Of course, when patients presented they must have had similar symptoms to those who actually have CAD. However, we have assumed that these symptoms resolve over time, either through spontaneous improvement or through appropriate treatment. Additionally, it should be realised that the general population utility already is based on the presence of some illness, which implies that the difference between the utility of suspected CAD population who do not have CAD and the general population may be expected to be small. QALYs are discounted with 3.5%.⁹⁷

TABLE 34

Population norm by European Quality of Life-5 Dimensions (EQ-5D) (Kind et al.)

Background costs

Background costs are costs which are applied to the trial entry state and the NFE states. The background costs are based on age, the existence of vascular diseases or diabetes mellitus, medication usage, creatinine clearance and symptomatic disease. For each combination of difficult-to-image patient group, strategy, treatment decision, test outcome and known or suspected CAD population background costs (Tables 37 and 38) were estimated with the linear regression presented in Table 35. The costs of medication for patients who are treated with medication only were included in this background cost. An example is presented below for a patient from the known CAD population who is obese and defined TP in the ICA-only strategy.

TABLE 37

Monthly background costs EUROPA: suspected CAD population (£)

TABLE 38

Monthly background costs EUROPA: known CAD population (£)

The average age of an obese patient with known CAD and a TP test outcome is 63 years; 34% have diabetes mellitus and 25% are symptomatic. Creatinine clearance below 80 ml/minute is on average 6.9 ml/minute, nitrates usage at baseline 44%, the presence of existing vascular disease is 10.1%, calcium channel blocker usage at baseline 32% and lipid-lowering therapy at baseline 55.9%. So, in total, £298.05 is assigned per cycle of 3 months as a background cost (Table 36).

TABLE 36

Example background cost calculation

Non-fatal event costs

For the year in which a NFE occurs, £11,805 was added to the background cost. For subsequent years, the additional cost was estimated as £986. In the year that a fatal CV event occurs, the additional cost was estimated as £3641. When a fatal non-CV event occurred, an additional cost of £12,421 was added.

Utilities for patients with coronary artery disease

Health-related quality-of-life estimates were assigned to the states in the Markov model based on age, gender, baseline CCS classification and whether or not the patient had undergone treatment. Patients modelled through the disease progression model are assumed to have a CCS class (Campeau¹⁰²) of 2. The HRQoL estimates were based on three sources: population norm for the EQ-5D,¹⁰⁰ EQ-5D scores per CCS class¹⁰³ and treatment effect on quality of life (QoL) based on the Randomized Intervention Treatment of Angina (RITA-2) trial.⁶⁴

Baseline EQ-5D – untreated patients with CAD

Combining the population norm values with the EQ-5D scores per CCS class (0–4) (Tables 39 and 40) generates relative HRQoL by CCS class and gender. Longworth's scores¹⁰³ were based on a median age of 61 years and these were divided by population norms for the age group 55–64 years. To obtain HRQoL by CCS class and age, the HRQoL by CCS class was multiplied by the age-specific HRQoL scores from Kind et al.,¹⁰⁰ assuming that the relative HRQoL by CCS class compared with the general population would hold across all ages. This multiplication was taken for the patients with CAD at baseline (without treatment).

TABLE 39

Baseline HRQoL: male

TABLE 40

Baseline HRQoL: female

Treatment EQ-5D – patients with coronary artery disease, treated

The RITA-2 trial provided data on the initial CCS class and the CCS class following revascularisation to estimate the HRQoL for a patient who is treated. The long-term effects of PCI and medical treatment in patients with CAD are compared in the RITA-2 trial. The baseline EQ5D score was combined with the RITA 2 trial to generate HRQoL scores by baseline CCS (i.e. CCS before treatment), age and gender following revascularisation (Tables 41 and 42). Improvement in HRQoL (a better CCS class) was estimated by combining the changes in CCS after treatment with association seen between baseline CCS and baseline HRQoL. A new HRQoL was calculated from the shifts to the other CCS classes. For example, 20% of the patients will have a better CCS class after treatment, 10% will have a worse CCS class after treatment and 70% will stay in the same CCS class. The product of the proportion and the HRQoL in each specific CCS class after treatment provided an updated HRQoL for a patient by baseline CCS class. The assumption was made that the effect of revascularisation on HRQoL continues. The same HRQoL values were used for patients treated with medication only.

TABLE 41

Health-related quality of life following treatment: male

TABLE 42

Health-related quality of life following treatment: female

A 3-monthly disutility of 0.010225¹⁰⁴ was assigned to the non-fatal event states because an event has occurred. We assumed that the disutility owing to a MI is the same as for a cardiac arrest. Of the NFEs only 2.5% will be a cardiac arrest; thus, the impact of changes in the disutility of a cardiac arrest will be minimal.

Population with known coronary artery disease

For the suspected CAD population, the baseline HRQoL applies for the patients with CAD, but not treated with a revascularisation or medication (FNs). In the EUROPA model, after a while a FN patient with CAD could be identified and would be treated; for this identified patient the HRQoL following treatment applies. The TPs from the suspected CAD population have CAD and will be treated with a revascularisation or medication and therefore the HRQoL following treatment applies (Table 43).

TABLE 43

Health-related quality of life per population and test outcome

Population with known coronary artery disease

Patients from the known CAD population all have CAD irrespective of their test outcome. Therefore, they are already identified and the TPs who are treated will have the HRQoL following treatment. The TNs do not need a revascularisation; therefore they have a HRQoL of being treated because we assume that these patients are in such a good state that a revascularisation is not necessary and therefore they have the highest HRQoL, namely that of treated patients. The FPs are treated with a revascularisation although this was not necessary. Therefore, we assumed that patients being FP and who are treated have the highest HRQoL, namely that of patients who are treated. The FNs need a revascularisation so the HRQoL of patients who are not treated applies for these patients (see Table 43).

Transition probabilities

Tables 44 and 45 present the 3-monthly transition probabilities for the suspected and known CAD populations for each subgroup. These transition probabilities were based on the risk equations which are explained in Model structure and methodology, EUROPA.

TABLE 44

Transition probabilities: CAD suspected population

TABLE 45

Transition probabilities: known CAD population

Survival

Mortality rates were based on UK life tables⁶⁵ and a relative risk of 2.5 to reflect the increased risk of mortality following a stroke.¹⁰⁵ Survival for each subgroup modelled in this study was therefore not simply dependent on stroke but also on the average age in that subgroup.

Costs

Sandercock et al.⁶⁶ estimated a cost of approximately £6260 in the first year after a stroke. As Sandercock et al.⁶⁶ presented both 12-month and lifetime costs, we estimated the average annual costs of treating stroke patients after the first year to be approximately £3400. These costs were then inflated to reflect costs for 2009–10 and then discounted at a rate of 3.5%.

Quality-adjusted life-year

Calibration of the model to fit with the results by Sandercock et al.⁶⁶ resulted in an average health utility of 0.37. This value was combined with survival and the resulting QALYs were discounted using at a rate of 3.5%.

Population with suspected coronary artery disease

As expected, the ICA had 100% correct diagnostic classification due to the assumption of 100% sensitivity and 100% specificity. Unfortunately, this comes with higher mortality and morbidity rates due to the complications of the test itself. The strategy where each patient will undergo an ICA had the highest test-induced mortality and morbidity rate, and the strategy that uses only the NGCCT to diagnose patients has test-induced mortality and morbidity rates of zero. Conversely, revascularisation-induced mortality and morbidity rates were highest in the NGCCT-only strategy due to the FPs who undergo unnecessary revascularisations with the associated complications. The NGCCT–ICA strategy had the lowest revascularisation-induced mortality and morbidity rates because only TPs are treated and the FNs who are not correctly diagnosed will not receive a revascularisation where they should have. The NGCCT-only strategy has the lowest overall mortality rate in the suspected population. The NGCCT-only strategy, as expected, had the lowest correct classification proportion.

Population with known coronary artery disease

The same results apply for the known CAD population; the ICA classifies 100% of patients correctly, the ICA strategy has the highest test mortality and morbidity rates and the NGCCT-only strategy has the highest revascularisation mortality and morbidity. However, in the known population the overall mortality and morbidity is lowest in the NGCCT–ICA strategy. ICA only has the highest overall mortality and morbidity rate.

Population with suspected coronary artery disease

Most of the costs in the EUROPA model do not differ significantly between the three strategies. The difference in costs between the strategies is mainly due to the difference in the costs in the diagnostic model. The ICA-only strategy has the highest costs in the diagnostic model because the test itself is much more expensive than NGCCT. The impact of treating FPs unnecessary with a revascularisation in the NGCCT-only strategy is marginal because the proportion that receives a revascularisation is just 18%. The incremental cost induced due to radiation is lowest in the NGCCT-only strategy because the radiation dose is lowest in the NGCCT-only strategy. Also, not surprisingly, the costs in the stroke model are the highest for the ICA-only strategy due to the largest proportion having non-fatal complications of the initial ICA and revascularisations.

Population with known coronary artery disease

In the known population, the costs in the diagnostic model are still the highest for the ICA-only strategy. However, the NGCCT–ICA strategy instead of the NGCCT-only strategy has the lowest cost in the diagnostic model. This is different from the suspected CAD population because the treatment decision differs between the two models. The known FPs of the NGCCT-only strategy are always treated with a revascularisation with accompanying extra costs. In the suspected CAD population, only 18% of FPs receive a revascularisation and, as medication costs are modelled in the EUROPA model, it will lead to fewer costs for the FPs.

The same applies for the stroke model because the non-fatal complication rate of the NGGCT-only strategy in the known group is higher than that of the NGCCT–ICA strategy and in the suspected population the NGGCT-ICA has a higher non-fatal complication rate. The proportion of the suspected CAD population that receives a revascularisation after a positive test is 18%, and corresponding proportion in the known population is 100%, therefore the proportion that experience a stroke due to the revascularisation is higher in the known population.

Population with suspected coronary artery disease

In the EUROPA model the ICA-only strategy obtains, in every difficult-to-image patient group, the highest number of QALYs. This is because of the lower HRQoL FNs experienced in the NGCCT-only strategy and in the NGCCT–ICA strategy owing to lower sensitivity and specificity of the NGCCT. FNs do not occur in the ICA-only strategy; they will all be classified as TP with a higher HRQoL. The QALYs in the healthy population model are the lowest in the ICA-only population because the proportion of TNs is the lowest for this strategy. The NGCCT–ICA and NGCCT-only strategies have larger proportion in the TNs because less ICA-related mortality occurs. Table 19 shows the four test outcomes; the proportion that is modelled with the healthy population model is the sum of the proportions classified as TN and FP. The QALYs from the stroke model are highest in the ICA-only strategy because in this strategy the largest proportion of patients is modelled with this model due to the highest morbidity induced by the initial treatment and initial ICA.

Population with known coronary artery disease

In the known population there is little difference between the three strategies, as all test outcomes are modelled with the EUROPA model. In the known population, every patient has CAD and therefore the healthy population model is not used for this population. In all cases, the ICA only has the lowest QALYs in the EUROPA model. This could be because ICA only has the largest overall mortality rate and therefore fewer people are modelled with the EUROPA model. The morbidity rate was the highest for the ICA-only strategy and therefore it accumulates the highest number of QALYs in the stroke model. The NGCCT–ICA strategy has the lowest morbidity rate and therefore it obtains fewer QALYs than the other strategies in the stroke model. More QALYs obtained in the stroke model can lead to less QALY gain in the EUROPA model; as the HRQoL in the stroke model is lower than in the EUROPA model, the higher complication rate of ICA is not favourable for the ICA-only strategy. The disutilities associated with the YRM are the largest (Table 58 shows no difference between the first two strategies but this is due to rounding) for the ICA-only strategy owing to the higher radiation dose of the ICA compared with the NGCCT.

Population with suspected coronary artery disease

Table 59 presents very small differences in QALYs; however, the ICA-only strategy is in general more effective than the other two strategies. In most subgroups, the NGCCT–ICA strategy achieves fewer QALYs than the other strategies. The ICA-only strategy is the most expensive strategy; the NGCCT-only strategy is cost saving compared with the other strategies. The negative incremental costs of the NGCCT-only strategy are due to the lower costs in the diagnostic model. The lower costs in the diagnostic model are the result of the large difference between the cost prices of the NGCCT and the ICA. After combining the results of the subgroups, we see that the NGCCT-only strategy might be considered the most attractive. The ICER of NGCCT–ICA compared with NGCCT only is so high (£71,000) that, given conventional willingness-to-pay threshold of £20,000–30,000, it is unlikely that commissioners of health care would consider this a cost-effective use of NHS resources.

Population with known coronary artery disease

In the known CAD population the cost-effectiveness differed by subgroup (Table 60). The NGCCT–ICA and the NGCCT-only strategies are, in all subgroups, more effective than the ICA-only strategy. In the subgroups obese, HCS, HHR, and beta-blocker intolerance, the NGCCT–ICA strategy dominated the other strategies, being more effective and of lower cost than the other two strategies. In all subgroups, the NGCCT–ICA strategy was less expensive than the other strategies. When results of the subgroups are combined, the most attractive strategy would be to perform a NGCCT with ICA; this scenario yields the highest cost saving, and dominates ICA only. The ICER of NGCCT only compared with NGCCT–ICA is so high (£726,230) that it is unlikely to be considered cost-effective, given conventional willingness-to-pay threshold of £20,000 to £30,000.

Scenario analysis: new-generation cardiac computed tomography £150, coronary artery disease

A lower cost price means that the NGCCT–ICA and the NGCCT-only strategies become less expensive. The overall results do not change.

Scenario analysis: new-generation cardiac computed tomography £207, coronary artery disease

This scenario shows the impact of a higher NGCCT cost price on the cost-effectiveness. There is little change in the incremental costs, even when the cost of the NGCCT increases. In the suspected population the ICA-only strategy is still the most expensive strategy and NGCCT only the least expensive strategy. The higher price of the NGCCT led to a change in cost rank in the known CAD population. In the base case ICA only was the most expensive strategy but when the price is increased the NGCCT-only strategy is the most expensive strategy. Based on the ICER, for the suspected population NGCCT only remains the most favourable strategy, whereas for the known population the most favourable strategy remains NGCCT–ICA.

Scenario: prior likelihood, suspected population 0.3

‘ICA only’ is still the most expensive strategy and it gains the most QALYs. However, a higher prior likelihood leads to an increase in costs and a decrease in QALYs for all strategies. A higher prior likelihood means that more patients will have CAD and therefore more patients must be treated, which leads to higher costs. Furthermore, fewer patients will be modelled with the healthy population model resulting in a decrease in QALYs and more costs in the EUROPA model. With regards to the ICER, the NGCCT-only strategy remains the most favourable.

Scenario analysis complication rates

In the best-case scenario (Table 67) for the NGCCT, the complication rates are set at the upper limit of the 95% CI. ICA only is still the most effective strategy. However, the incremental QALYs gained by the ICA-only strategy have become smaller in comparison with the base-case analysis. As the ICA induces more complications than the NGCCT, this scenario analysis can be seen as the best-case scenario for the NGCCT strategies.

In the worst-case scenario (Table 68) for the NGCCT, the complication rates are set at the lower limit of the 95% CI, the ICA-only strategy is the most effective strategy. The incremental QALYs gained by ICA only increased compared with the base-case analysis. When assessing the balance between costs and effects, in both scenarios NGCCT only remains the most favourable strategy.

Scenario analysis covariates used in risk equation for obese subgroup

A study by Oreopoulos et al.¹⁰⁶ examines the association between obesity and HRQoL in patients with CAD. It gives a good representation of an obese population with CAD (BMI of 25–30 kg/m², n = 2310; BMI of 30–35 kg/m², n = 1331; BMI of 35–40 kg/m², n = 446; BMI of > 40 kg/m², n = 178). The baseline characteristics that were found in the Oreopoulos et al. study¹⁰⁶ are similar to the baseline characteristics used in our model. The baseline characteristics in the model are based on the systematic review and on the EUROPA trial. Not all covariates for the risk equations are presented in the Oreopoulos et al. study¹⁰⁶ but gender, diabetes, existing vascular disease and previous MI are presented. We have performed scenario analyses within the obese group to study the effect of changing these covariates. The baseline values used in the obese known subgroup are existing vascular disease (stroke, TIA and peripheral vascular disease) 9.8%, female 34.1%, previous MI 64.7% and diabetes milletus proportion 34.1%. These values were changed to the following: existing vascular disease 7.5% and 13.5%; female 30%; previous MI 50% and diabetes milletus proportion 60%. These analyses (results not shown) show that these changes have no impact on our conclusions.