The manufacturer’s calculated relative risk for hyperammonemic crisis (HAC) appears to be a potential key driver of results, especially within the model in Subgroup 2 and Subgroup 4, in which dietary control is considered as the comparator for glycerol phenylbutyrate (GPB). As outlined in the preceding sections, the estimates for the relative risk of HAC are based on an extrapolation of already estimated points. Any linear interpolation of this type is inherently risky, as the relationships that underlie data within a given range do not necessarily determine the data over other ranges. In particular, the studies appear to compare the incidence of HACs in periods when patients receive GPB and periods when they receive sodium phenylbutyrate (NaPBA).

To illustrate the difficulty with using linear interpolation in this way, we present three diagrams. Figure 2 displays the reported relative risks for differences in ammonia levels versus GPB outcomes. These data are presented in the manufacturer’s submission Table 3, with error bars displaying the confidence intervals for each data point. The manufacturer proposes using a linear interpolation between the data points at a difference of 10 and a difference of 25. When plotted, it is noticeable that this relationship does not explain the points at differences of one and five very well at all. (There is an additional point at zero; trivially, if there is no difference, we would expect a relative risk of HACs of one.)

Figure 2

Manufacturer’s Reported Relative Risks and Alternative. RR = relative risk.

The second fitted curve shows the estimated relationship if there is a linear interpolation between a difference of zero and a difference of 10. This line passes within the confidence intervals for every one of the data points, and provides an arguably more robust fit.

Figure 3 shows these curves extended to allow them to explain points outside the range of the data. At the difference in ammonia levels claimed by the manufacturer for dietary control of 91.7 μmol/L, the difference is between the relative risk of 8.42 claimed by the manufacturer and relative risk of 5.62 in the alternative extrapolation. This establishes that, if using these points, there may be significant uncertainty about which point to use.

Figure 3

Manufacturer’s Reported Relative Risks and Alternative, Extrapolated. NaPBA = sodium phenylbutyrate; RR = relative risk.

Although the manufacturer uses linear interpolation, this is not consistent with the analysis that underlies the data presented (including the error bars, etc.). That is, the analysis determines the relationship between the two variables, and defines how this should be approached in any interpretation of that analysis.

In this case, the analysis appears to fit a linear relationship between log-relative risk and difference in ammonia levels. Since this estimated relationship can be extracted, the estimates based on this analysis are available and shown in Figure 4.

Figure 4

Relative Risk Inferred Using Prior Analysis, Versus Prior Estimates.

However, this leads to a relative risk of 42.18. As the GPB analysis uses an average of 0.27 HACs per patient, per year, this suggests 11.4 HACs per year under dietary control, so that those on dietary control are assumed to have HACs nearly every month if using this analysis.