Abstract:
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In enriched clinical trials, the study population is selected in hopes of increasing the power to detect treatment effect. For example, in enriched multiple sclerosis (MS) clinical trials, patients are often chosen based on their disease activity (as measured by the presence of brain lesions). While lesion counts in the general population of MS patients over the course of a trial are well-described by the negative binomial (NB) distribution, counts in this specially chosen subpopulation are not NB distributed. Previous work suggests that bias in the treatment effect estimator results when the NB model is naively fit to such data, and that standard inferential procedures may be invalid. In this paper, we show how to quantify this bias analytically. More importantly, we propose an alternative, simple estimator that is approximately unbiased and can form the basis of approximately valid inferential procedures. Our estimator and its standard error have the advantage of being distribution-free; hence, our results apply not only to counts arising from enriched MS trials, but extend to responses with any distribution, regardless of whether an enrichment design is used.
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