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978-3-8439-1844-2, Reihe Medizin
Rüdiger Paul Laubender
Estimation of a joint distribution with two normally distributed treatment responses as marginals generated in a randomized controlled trial based on the parallel-group design by using a normally distributed covariate.
335 Seiten, Dissertation Ludwig-Maximilians-Universität München (2014), Softcover, A5
In randomized controlled trials based on the parallel-group design only the marginal distributions of the responses of two compared treatments can be observed due to the fact that not all possible responses of a subject under these two treatments can be simultaneously observed. However, knowledge of the joint distribution of these responses would allow discerning subjects who profit from a new treatment compared to a standard treatment from subjects who profit from the standard treatment compared to the new treatment. In such a case, the individual treatment effects differ from one subject to another so that subject-treatment interactions are present in a RCT. The following work proposes a restricted heterogeneous treatment effects model which allows the reconstruction of the joint distribution of two normally distributed marginal distributions of the considered responses by interpreting a normally distributed baseline covariate as an indicator of the sum of the possible responses and by relying on a trivariate normal distribution of the possible responses and of the covariate when the data are generated by a RCT based on the parallel-group design where only one of the two possible responses per subject are observable. The maximum likelihood approach is used to derive estimators for reconstructing the joint distribution of the responses given the covariate. However, certain conditions of the parameter space of the trivariate normal distribution have to be fulfilled so that subject-treatment interactions can reconstruct the joint distribution of the possible responses. Based on these estimators, it is possible to derive estimators for the presentation of the results of the reconstructed joint distribution of the responses. On the one hand, estimators for presenting the overall extend of the presence of subject-treatment interactions for given data are derived. On the other hand, estimators for clinical decision-making, especially for allocating the best of two effective treatments to a subject based on his or her covariate value, are derived what forms the statistical basis of individualized medicine. Further, power and sample size considerations are presented. Two simulation studies are conducted which reveal that the reconstruction estimators and the estimators for presenting the results do not perform well in terms of consistency, bias and coverage probability for small sample sizes due to the asymptotic nature of the estimators.