The Burden of Demonstrating HTE
Background
Heterogeneity of treatment effect (HTE) is demonstrated by either
- showing that there is variation in individuals’ responses to treatment using a multi-period crossover study, or
- in a more restricted sense demonstrating an interaction between treatment and patient characteristics on a scale for which it is possible that such interaction may be absent even if the main effect for treatment is nonzero.
There are at least three reasons to assume that HTE is absent by default.
- Some researchers who claim that HTE exists have vested interests, because it is a new research area for which there is grant money and fame to be made, and papers to be published. And journal reviewers are not properly equipped to review HTE methodologies used in clinical papers.
- There is scant evidence to date that HTE exists, is clinically meaningful, and should influence treatment choices.
- When HTE is absent or is weak, personalizing treatments can result in worse decisions than just assuming that the average treatment effect is what applies to every patient.
This article provided a real clinical trial example where HTE was formally tested and quantified. The purpose of the present article is to demonstrate point 3. above.
Example
Suppose that the response variable in a randomized clinical trial is systolic blood pressure (SBP), and suppose that the between-patient standard deviation in SBP is 10mmHg. When comparing post-randomization SBP for treatment A vs. treatment B, let’s first suppose that every patient has the same expected reduction in SBP due to treatment, which for our analyses is irrelevant. If SBP has a normal distribution with SD of 10mmHg, and a total sample size of n patients is included in the trial, with half randomized to each treatment, the variance of the estimated treatment effect equals the sum of the variances of the two sample means, which is
Now suppose that males and females have differing efficacy of treatment B relative to A, that we wish to estimate the efficacy in females, and that the proportion of females in the trial is
What if we use the entire male+female data to estimate the SBP effect for females? Suppose that the difference in efficacy between males and females is
For females, the MSE of the ignoring-sex pooled treatment estimate is
If there is no treatment heterogeneity (
Preferred Analyses for Future Applications
Bayesian models allow for the most clinically sensible as well as practical solutions to modeling HTE when HTE exceeds zero. With a Bayesian model, interactions are not “in” or “out” of a model but are “half in.” A skeptical prior distribution is used for interaction effects. This shrinks interaction effects. In the example given above, this would allow the efficacy estimate for females to borrow some of the efficacy estimate from males. But as the sample size increases, the efficacy estimates will become more customized, i.e., sex-specific. This methods was proposed by Simon and Freedman. Bayesian shrinkage will result in superior MSE of patient-specific efficacy estimates.
Other Resources
- Responder despondency: myths of personalized medicine by Stephen Senn
- Chapter 9 of Statistics Issues in Drug Development 2nd Edition by Stephen Senn
Discussion
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