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Register a new userAssessing replicability of findings across two studies of multiple features
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Added by
Ruth Heller
Publication date
2015
fields
Mathematical Statistics
and research's language is
English
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Replicability analysis aims to identify the findings that replicated across independent studies that examine the same features. We provide powerful novel replicability analysis procedures for two studies for FWER and for FDR control on the replicability claims. The suggested procedures first select the promising features from each study solely based on that study, and then test for replicability only the features that were selected in both studies. We incorporate the plug-in estimates of the fraction of null hypotheses in one study among the selected hypotheses by the other study. Since the fraction of nulls in one study among the selected features from the other study is typically small, the power gain can be remarkable. We provide theoretical guarantees for the control of the appropriate error rates, as well as simulations that demonstrate the excellent power properties of the suggested procedures. We demonstrate the usefulness of our procedures on real data examples from two application fields: behavioural genetics and microarray studies.
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Advancement in technology has generated abundant high-dimensional data that allows integration of multiple relevant studies. Due to their huge computational advantage, variable screening methods based on marginal correlation have become promising alternatives to the popular regularization methods for variable selection. However, all these screening methods are limited to single study so far. In this paper, we consider a general framework for variable screening with multiple related studies, and further propose a novel two-step screening procedure using a self-normalized estimator for high-dimensional regression analysis in this framework. Compared to the one-step procedure and rank-based sure independence screening (SIS) procedure, our procedure greatly reduces false negative errors while keeping a low false positive rate. Theoretically, we show that our procedure possesses the sure screening property with weaker assumptions on signal strengths and allows the number of features to grow at an exponential rate of the sample size. In addition, we relax the commonly used normality assumption and allow sub-Gaussian distributions. Simulations and a real transcriptomic application illustrate the advantage of our method as compared to the rank-based SIS method.
A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a true research hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal policies become more complex. In this paper we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the policies. This leads us to formulate the optimal policy problem as an explicit optimization problem with objective and constraints which describe its specific desiderata. We describe a complete solution for deriving optimal policies for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal policies that are identical to existing policies, such as Hommels procedure or the procedure of Bittman et al. (2009), while for others it yields completely novel and more powerful policies than existing ones. We demonstrate the nature of our novel policies and their improved power extensively in simulation and on the APEX study (Cohen et al., 2016).
Consider a two-by-two factorial experiment with more than 1 replicate. Suppose that we have uncertain prior information that the two-factor interaction is zero. We describe new simultaneous frequentist confidence intervals for the 4 population cell means, with simultaneous confidence coefficient 1-alpha, that utilize this prior information in the following sense. These simultaneous confidence intervals define a cube with expected volume that (a) is relatively small when the two-factor interaction is zero and (b) has maximum value that is not too large. Also, these intervals coincide with the standard simultaneous confidence intervals obtained by Tukeys method, with simultaneous confidence coefficient 1-alpha, when the data strongly contradict the prior information that the two-factor interaction is zero. We illustrate the application of these new simultaneous confidence intervals to a real data set.
We are concerned with testing replicability hypotheses for many endpoints simultaneously. This constitutes a multiple test problem with composite null hypotheses. Traditional $p$-values, which are computed under least favourable parameter configurations, are over-conservative in the case of composite null hypotheses. As demonstrated in prior work, this poses severe challenges in the multiple testing context, especially when one goal of the statistical analysis is to estimate the proportion $pi_0$ of true null hypotheses. Randomized $p$-values have been proposed to remedy this issue. In the present work, we discuss the application of randomized $p$-values in replicability analysis. In particular, we introduce a general class of statistical models for which valid, randomized $p$-values can be calculated easily. By means of computer simulations, we demonstrate that their usage typically leads to a much more accurate estimation of $pi_0$. Finally, we apply our proposed methodology to a real data example from genomics.
We offer a non-parametric plug-in estimator for an important measure of treatment effect variability and provide minimum conditions under which the estimator is asymptotically efficient. The stratum specific treatment effect function or so-called blip function, is the average treatment effect for a randomly drawn stratum of confounders. The mean of the blip function is the average treatment effect (ATE), whereas the variance of the blip function (VTE), the main subject of this paper, measures overall clinical effect heterogeneity, perhaps providing a strong impetus to refine treatment based on the confounders. VTE is also an important measure for assessing reliability of the treatment for an individual. The CV-TMLE provides simultaneous plug-in estimates and inference for both ATE and VTE, guaranteeing asymptotic efficiency under one less condition than for TMLE. This condition is difficult to guarantee a priori, particularly when using highly adaptive machine learning that we need to employ in order to eliminate bias. Even in defiance of this condition, CV-TMLE sampling distributions maintain normality, not guaranteed for TMLE, and have a lower mean squared error than their TMLE counterparts. In addition to verifying the theoretical properties of TMLE and CV-TMLE through simulations, we point out some of the challenges in estimating VTE, which lacks double robustness and might be unavoidably biased if the true VTE is small and sample size insufficient. We will provide an application of the estimator on a data set for treatment of acute trauma patients.
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