While online FDR control is studied extensively, there is less work on FWER control in an online multiple testing setting. In 2021, Tian & Ramdas introduced the Adaptive-Discard-Spending (ADDIS-Spending) as online procedure with FWER control. In my master’s thesis we built on this and developed the ADDIS-Graph, which combines the ADDIS concept with the graphical approach by Bretz et al. (2009). In addition to easier interpretability, our ADDIS-Graph leads to a higher power in the case of locally dependent p-values and asynchronous testing setups than the ADDIS-Spending. We further exhausted the significance level under independence of the p-values to obtain uniformly superior ADDIS procedures. Moreover, we formulated a new closure principle for online multiple testing and derived a condition under which a closed procedure is indeed an online procedure. In this talk, I summarise our theoretical findings that are supported by simulations.

For event-driven designs the objective is to complete a clinical trial within a given time frame. Blinded sample size reestimation (BSSR) methods use non-comparative blinded interim trial data to adjust the sample size if the planning assumptions are wrong. In clinical trials with time-to-event outcomes the estimated survival function based on the interim data needs to be extrapolated for the purpose of BSSR. The current practice is to fit standard parametric models (e.g. exponential or Weibull models), which may however not always be suitable. For example, some real life datasets exhibit complex hazard functions that cannot be captured by simple parametric models. The aim of the current article was to propose a flexible parametric approach for BSSR in clinical trials with time-to-event outcomes and to compare it to existing parametric approaches. Specifically, we propose to carry out the extrapolation based on the Royston-Parmar spline model. We carried out a simulation study based on exponential, Weibull and Gompertz distributed data and considered a practical application of spline BSSR to a Secondary Progressive Multiple Sclerosis (SPMS) trial. In our simulation study we found that a 1-knot spline BSSR was unbiased in the exponential and Weibull setting and performed best in the Gompertz misspecification scenario. In our case study we found spline BSSR to perform well and to outperform the Weibull BSSR. Overall, if planning assumptions are wrong this more robust spline BSSR could help event-driven designs to more accurately adjust recruitment numbers and to finish on time.

Random forest is a popular machine learning approach that is increasingly applied in genetic association studies. Genetic association studies aim at identifying genetic variants that are associated with a disease. This can be achieved, e.g. via the variable importance measures of the random forest. However, in the presence of confounders, disease-unrelated variants that are affected by a confounder could receive high importance scores, potentially masking associations with relevant variants. Zhao et al. [1] suggested to use the residuals from generalized linear models to adjust random forests for confounding. However, using the residuals from global linear models might not be sufficient if the influence of a confounder varies across unknown subgroups.

In this work, I use the model-based recursive partitioning algorithm [2] in the construction of the random forest trees to automatically identify these subgroups. Since the model-based recursive partitioning algorithm uses computationally expensive generalized M-fluctuation tests to determine the splits of the random forest trees, it might not be feasible for large genetic association studies. Therefore, I develop and compare two modifications of the algorithm that use the residuals from local linear models to determine the splits: the residual variance splitting and the maximally selected residual rank statistic splitting rule. The first modification is similar to the original CART algorithm [3], whereas the latter is based on the maximally selected rank statistic [4].

The results of my simulation studies show that only the maximally selected residual rank statistic splitting rule is able to adjust for confounding. Further, this method performs slightly better than the global adjustment if the confounder model only holds for subgroups of the population. On real data from a European cohort study on child health, the proposed method leads to a sparser solution, i.e., it selects fewer variants, but still identifies those that are known to be associated with the outcome.

References

[1] Zhao, Y. et al. (2012). ”Correction for Population Stratification in Random Forest Analysis”. In: International Journal of Epidemiology 41.6, pp. 1798–1806. doi: 10.1093/ije/dys183.

[2] Zeileis, A., T. Hothorn, and K. Hornik (2008). ”Model-Based Recursive Partitioning”. In: Journal of Computational and Graphical Statistics 17.2, pp. 492–514. doi: 10.1198/106186008X319331.

[3] Breiman, L. et al. (1984). Classification and Regression Trees. New York: Chapman & Hall/CRC. doi: 10.1201/9781315139470.

[4] Lausen, B. and M. Schumacher (1992). ”Maximally Selected Rank Statistics”. In: Biometrics 48.1, pp. 73–85. doi: 10.2307/2532740.

Meta-analyses frequently include trials that report multiple outcomes based on a common set of study participants. These outcomes will generally be correlated. Cluster-robust variance-covariance estimators are a fruitful approach for synthesizing dependent outcomes. However, when the number of studies is small, state-of-the-art robust estimators can yield inflated Type 1 errors. Therefore, two new cluster-robust estimators are presented, in order to improve small sample performance. For both new estimators the idea is to transform the estimated variances of the residuals using only the diagonal entries of the hat matrix. The proposals are asymptotically equivalent to previously suggested cluster-robust estimators such as the bias reduced linearization approach. The methods are applied to a dataset of 81 trials examining overall and disease-free survival in neuroblastoma patients with amplified versus normal MYC-N genes. Furthermore, their performance is compared and contrasted in an extensive simulation study. The focus is on bivariate meta-regression, although the approaches can be applied more generally.

Doctors and other care providers desire to implement decision rules that, when applied to individuals in the population of interest, yield the best possible outcomes. For example, the current focus on precision medicine reflects the search for individualized treatment decisions, adapted to a patient's characteristics. In this presentation, I will consider how to formulate, choose and estimate effects that guide individualized treatment decisions. In particular, I will introduce a class of regimes that are guaranteed to outperform conventional optimal regimes. I will further argue that identification of these "superoptimal" regimes and their values requires exactly the same assumptions as identification of conventional optimal regimes in several common settings. The superoptimal regimes can also be identified in data fusion contexts, in which experimental data and (possibly confounded) observational data are available. The performance of the superoptimal regimes will be illustrated in two clinical examples.