Choice of the Interim Analysis Timing in Adaptive Enrichment Designs

This thesis deals with adaptive enrichment designs, which are especially applied in the development of targeted therapies. These designs are devised for the situation in which a higher treatment effect is assumed in a specific subgroup but efficacy cannot be ruled out in the total population. The idea of this two-stage study design is to decide in an interim analysis based on observed treatment effects whether the subgroup or the total population is selected for enrichment in the second stage of the trial, and for which population a test for efficacy is conducted in the final analysis. The aim of this thesis is to investigate the impact of the interim analysis timing on the power of the study for a normally distributed endpoint. Different effect sizes and prevalences of the subgroup, as well as two different classes of selection rules were considered. The first selection rule is based on the comparison of the estimated effect difference between the subgroup and the total population with a prespecified threshold value, and the subgroup or the total population is selected, respectively. The second selection rule that is considered is based on the absolute effect estimates from the subgroup and the total population, each compared to a prespecified threshold value. Possible options of this selection rule are to select either the subgroup, the total population, both populations, or no population. The latter option leads to termination of the study (stop for futility) without rejecting any hypothesis. In the first part, the impact of the interim timing on the power of the study is investigated for a fixed overall sample size. Analytical derivation of the power was not possible, and, as a consequence, power was determined using simulation studies. Results showed that the interim timing influences the power of the study to a varying degree for different scenarios. In particular, the chosen selection rule leads to different power characteristics as a function of interim analysis timing. For example, the power is rather small in case the second selection rule, that is based on absolute effect estimates, is used, which can be explained by the incorporated option to stop for futility. In contrast, for the first selection rule, which is based on the difference between the effect estimates, the smallest power was achieved for early timings in many scenarios. Additionally, the power maximum depends on the effect sizes and the prevalence of the subgroup. This shows that there is no particular interim timing which is optimal with regard to the power in every scenario. When choosing the interim analysis timing, the assumed effect sizes, the prevalence, and the chosen selection rule should be taken into account. In the second part, an adaptive enrichment design including sample size recalculation is considered. Sample size was recalculated using conditional power arguments, where both the assumed effect from the planning phase and the mean of this effect and the observed effect in the interim analysis was used. The timing of the interim analysis was defined as the ratio of the sample size in the first stage and the sample size that would be required in a corresponding study design for demonstrating efficacy in the total population without interim analysis. In simulation studies, different interim timings were compared based on the distribution of the overall sample size. In particular, the average sample size and its standard deviation as well as the probability to achieve a sample size that is larger than the sample size for the respective design without interim analysis was considered. Results showed that different selection rules, effect sizes and prevalences have a smaller impact, and an interim analysis after half the patients have been enrolled leads to the smallest average sample size in many cases. For both situations (fixed and adapted sample size), the choice of the interim analysis timing was investigated for a clinical trial example. In summary, this thesis shows that the choice of the interim analysis timing in adaptive enrichment designs has, in many cases, a substantial effect on the power of the study or the average sample size. However, the most appropriate timing depends on the effect sizes, the prevalence of the subgroup and the chosen selection rule, and should be selected carefully in the planning phase for the specific scenario at hand