Power and Sample Size for Fixed-Effects Inference in Reversible Linear Mixed Models

ABSTRACT

Despite the popularity of the general linear mixed model for data analysis, power and sample size methods and software are not generally available for commonly used test statistics and reference distributions. Statisticians resort to simulations with homegrown and uncertified programs or rough approximations which are misaligned with the data analysis. For a wide range of designs with longitudinal and clustering features, we provide accurate power and sample size approximations for inference about fixed effects in the linear models we call reversible. We show that under widely applicable conditions, the general linear mixed-model Wald test has noncentral distributions equivalent to well-studied multivariate tests. In turn, exact and approximate power and sample size results for the multivariate Hotelling–Lawley test provide exact and approximate power and sample size results for the mixed-model Wald test. The calculations are easily computed with a free, open-source product that requires only a web browser to use. Commercial software can be used for a smaller range of reversible models. Simple approximations allow accounting for modest amounts of missing data. A real-world example illustrates the methods. Sample size results are presented for a multicenter study on pregnancy. The proposed study, an extension of a funded project, has clustering within clinic. Exchangeability among the participants allows averaging across them to remove the clustering structure. The resulting simplified design is a single-level longitudinal study. Multivariate methods for power provide an approximate sample size. All proofs and inputs for the example are in the supplementary materials (available online).     

企业集群与贵州中药、民族药业的健康发展

企业集群是发达国家在产业结构调整、资源整合过程中普遍存在的一种经济现象,它不仅是产业发展成长过程中的一种必然结果,而且凸显出了现代产业发展过程中的某些特征。改革开放的20多年间,我国东部地区的经济发展也呈现了“集群成长”态势,并已经成为东部地区经济快速发展的主要因素之一。近年来,我国西部地区也可以看到一些初步具备集群成长特征的企业网络,但与国际上以及我国东部地区中小企业聚集区域相比,准确的说,我国西部地区目前还没有出现真正意义上的中小企业集群。针对企业集群现象及如何采取有效措施,积极推进西部地区企业集群,促进贵州中药、民族药业健康发展进行探讨。     

地理集群的企业竞争研究

地理集群是近年来学术界的一个热门话题。人们对集群企业间的合作已经进行了深入的研究,并取得了丰硕的成果;相比之下,对集群的企业竞争的研究则比较零散。本文对地理集群的企业竞争研究进行了介绍与分析,以图抛砖引玉,引起人们对地理集群的企业竞争研究的重视。     

Robustness and monotonicity properties of generalized correlation coefficients

A new class of generalized correlation coefficients that contains the Pearson and Kendall statistics as special cases was defined by Chinchilli et al. (2005) and applied to the estimation of correlations coefficients within the context of 2×2 cross-over designs for clinical trials. In this paper, we determine the infinitesimal robustness and local stability properties of these generalized correlation coefficients by deriving their corresponding influence functions. For cases in which the population distribution is a bivariate normal or a mixture of bivariate normal distributions we obtain explicit formulas, and establish monotonicity and sign-reverse rule properties of the generalized correlation coefficients.     

Potential surrogate endpoints in cancer research – some considerations and examples

We present an introductory survey of the use of surrogates in cancer research, in particular in clinical trials. The concept of a surrogate endpoint is introduced and contrasted with that of a biomarker. It is emphasized that a surrogate endpoint is not universal for an indication but will depend on the mechanism of treatment. We discuss the measures of validity of a surrogate and give examples of both cancer surrogates and biomarkers on the path to surrogacy. Circumstances in which a surrogate endpoint may actually be preferred to the clinical endpoint are described. We provide pointers to the recent substantive literature on surrogates. Copyright © 2009 John Wiley & Sons, Ltd.     

A simple approach to analyzing clustered longitudinal data

When modeling correlated binary data in the presence of informative cluster sizes, generalized estimating equations with either resampling or inverse-weighting, are often used to correct for estimation bias. However, existing methods for the clustered longitudinal setting assume constant cluster sizes over time. We present a subject-weighted generalized estimating equations scheme that provides valid parameter estimation for the clustered longitudinal setting while allowing cluster sizes to change over time. We compare, via simulation, the performance of existing methods to our subject-weighted approach. The subject-weighted approach was the only method that showed negligible bias, with excellent coverage, for all model parameters.     

Bayesian prediction for two-stage sequential analysis in clinical trials

This article deals with a Bayesian predictive approach for two-stage sequential analyses in clinical trials, applied to both frequentist and Bayesian tests. We propose to make a predictive inference based on the notion of satisfaction index and the data accrued so far together with future data. The computations and the simulation results concern an inferential problem, related to the binomial model.     

Treatment effect quantification for time‐to‐event endpoints–Estimands,analysis strategies,and beyond

A draft addendum to ICH E9 has been released for public consultation in August 2017. The addendum focuses on two topics particularly relevant for randomized confirmatory clinical trials: estimands and sensitivity analyses. The need to amend ICH E9 grew out of the realization of a lack of alignment between the objectives of a clinical trial stated in the protocol and the accompanying quantification of the “treatment effect” reported in a regulatory submission. We embed time‐to‐event endpoints in the estimand framework and discuss how the four estimand attributes described in the addendum apply to time‐to‐event endpoints. We point out that if the proportional hazards assumption is not met, the estimand targeted by the most prevalent methods used to analyze time‐to‐event endpoints, logrank test, and Cox regression depends on the censoring distribution. We discuss for a large randomized clinical trial how the analyses for the primary and secondary endpoints as well as the sensitivity analyses actually performed in the trial can be seen in the context of the addendum. To the best of our knowledge, this is the first attempt to do so for a trial with a time‐to‐event endpoint. Questions that remain open with the addendum for time‐to‐event endpoints and beyond are formulated, and recommendations for planning of future trials are given. We hope that this will provide a contribution to developing a common framework based on the final version of the addendum that can be applied to design, protocols, statistical analysis plans, and clinical study reports in the future.     

Model‐free causal inference of binary experimental data

For binary experimental data, we discuss randomization‐based inferential procedures that do not need to invoke any modeling assumptions. In addition to the classical method of moments, we also introduce model‐free likelihood and Bayesian methods based solely on the physical randomization without any hypothetical super population assumptions about the potential outcomes. These estimators have some properties superior to moment‐based ones such as only giving estimates in regions of feasible support. Due to the lack of identification of the causal model, we also propose a sensitivity analysis approach that allows for the characterization of the impact of the association between the potential outcomes on statistical inference.