Individual treatment effect heterogeneity in multiple time points trials



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Kansas State University


In biomedical studies, the treatment main effect is often expressed in terms of an “average difference.” A treatment that appears superior based on the average effect may not be superior for all subjects in a population if there is substantial “subject-treatment interaction.” A parameter quantifying subject-treatment interaction is inestimable in two sample completely randomized designs. Crossover designs have been suggested as a way to estimate the variability in individual treatment effects since an “individual treatment effect” can be measured. However, variability in these observed individual effects may include variability due to the treatment plus inherent variability of a response over time. We use the “Neyman - Rubin Model of Causal Inference” (Neyman, 1923; Rubin, 1974) for analyses. This dissertation consists of two parts: The quantitative and qualitative response analyses. The quantitative part focuses on disentangling the variability due to treatment effects from variability due to time effects using suitable crossover designs. Next, we propose a variable that defines the variance of a true individual treatment effect in a two crossover designs and show that they are not directly estimable but the mean effect is estimable. Furthermore, we show the variance of individual treatment effects is biased under both designs. The bias depends on time effects. Under certain design considerations, linear combinations of time effects can be estimated, making it possible to separate the variability due to time from that due to treatment. The qualitative section involves a binary response and is centered on estimating the average treatment effect and bounding a probability of a negative effect, a parameter which relates to the individual treatment effect variability. Using a stated joint probability distribution of potential outcomes, we express the probability of the observed outcomes under a two treatment, two periods crossover design. Maximum likelihood estimates of these probabilities are found using an iterative numerical method. From these, we propose bounds for an inestimable probability of negative effect. Tighter bounds are obtained with information from subjects that receive the same treatments over the two periods. Finally, we simulate an example of observed count data to illustrate estimation of the bounds.



potential outcomes, individual effect variance, observed effect, bounds, subjects

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Doctor of Philosophy


Department of Statistics

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Gary L. Gadbury