arXiv subjects

Monica Taljaard

Publications and source records attributed to Monica Taljaard.

9 recordsLinked to original sources

arXiv2026

Cluster randomized crossover trials with very few clusters but multiple periods: which analyses for continuous outcomes should be used?

Cluster randomized crossover (CRXO) trials are often used when individual randomization is impractical and the number of available clusters is limited. However, statistical analysis of CRXO trials is complex because of the need to account for complex correlation structures over time. It becomes especially challenging when very few clusters are used because standard modeling assumptions may lead to unstable variance estimates, poor confidence interval coverage, and inflated type I error. This study evaluates individual-level mixed-effects and fixed-effects models with and without a cluster-period random effect, cluster-period summary analysis using normal- or $t$-based inference, and two-period crossover-difference estimators. Using extensive simulation studies under both nested exchangeable and discrete time decay correlation structures, we compare model performance in terms of bias, root mean squared error, coverage probability, type I error, and convergence. Across scenarios, all models produced approximately unbiased treatment effect estimates, but their inferential performance differed substantially. Models that explicitly accounted for cluster-period heterogeneity generally provided the most reliable control of coverage and type I error, whereas simpler exchangeable models performed adequately only when the true correlation structure closely matched their assumptions. Cluster-period level analysis performance improved with increasing numbers of periods but was unreliable in the sparsest designs. Overall, the findings suggest that in CRXO trials with very few clusters, accurate modeling of cluster-period correlation is more important than the choice between fixed and random cluster intercepts, and that results from extremely sparse designs should be interpreted with caution.

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arXiv2026

Which Small-Sample Correction Should Be Used When Analyzing Stepped-Wedge Designs with Time-Varying Treatment Effects?

Stepped-wedge cluster randomized trials (SW-CRTs) evaluate interventions rolled out across clusters over time. Standard analyses typically use immediate-treatment (IT) models, which assume effects begin at crossover and remain constant thereafter. When effects vary with exposure duration, IT models may misrepresent target effects. Exposure-time indicator (ETI) models address this by allowing treatment effects to differ by time since exposure and by targeting the time-averaged treatment effect (TATE) and long-term effect (LTE). Like IT models, ETI models require specification of a random-effects structure, which is often misspecified, and the performance of robust variance estimators (RVEs) in this setting is not well understood. We review RVEs for ETI models and evaluate them in simulation studies with continuous and binary outcomes under correctly specified (binary only) and misspecified random-effects structures. We compare the classic sandwich, Kauermann-Carroll (KC), Mancl-DeRouen (MD), and Morel-Bokossa-Neerchal (MBN) estimators for inference on the TATE and LTE. Our simulations show that under misspecified random-effects structures, model-based standard errors (SE) produced undercoverage, whereas RVEs improved performance. For continuous outcomes, MD with a t-distribution and degrees of freedom equal to the number of clusters minus two gave the most consistent coverage probabilities. For binary outcomes, MBN was the only consistently reliable option. MD, however, could be unstable in one-cluster-per-sequence designs because of data sparsity. Across scenarios, both model-based SE and RVE for LTE were unstable, indicating that greater caution is needed when targeting LTE under ETI models.

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arXiv2025

Can discrete-time analyses be trusted for stepped wedge trials with continuous recruitment?

In stepped wedge cluster randomized trials (SW-CRTs), interventions are sequentially rolled out to clusters over multiple periods. It is common practice to analyze data from SW-CRTs using linear mixed models that treat time as discrete. However, a recent systematic review found that 95.1% of cross-sectional SW-CRTs recruit individuals continuously over time. Despite the high prevalence of such continuous recruitment designs, there has been limited guidance on how to draw model-robust inference when analyzing such SW-CRTs. In this article, we investigate through simulations the implications of using such discrete-time linear mixed models in the case of continuous recruitment designs with a continuous outcome. Specifically, in the data-generating process, we characterize continuous recruitment using a continuous-time exponential decay correlation structure in the presence or absence of a fixed continuous period effect, addressing scenarios both with and without a random or exposure-time-dependent intervention effect. We then analyze the simulated data under three popular discrete-time working correlation structures: simple exchangeable, nested exchangeable, and discrete-time exponential decay, with a robust sandwich variance estimator. Our results demonstrate that discrete-time analysis often yields negligible bias and that the robust variance estimator with the Mancl and DeRouen correction consistently achieves nominal coverage and type I error rate. One important exception occurs when recruitment patterns vary systematically between control and intervention periods, where discrete-time analysis leads to slightly biased estimates. Finally, we illustrate these findings by reanalyzing a completed SW-CRT.

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arXiv2025

On Anticipation Effect in Stepped Wedge Cluster Randomized Trials

In stepped wedge cluster randomized trials (SW-CRTs), the intervention is rolled out to clusters over multiple periods. A standard approach for analyzing SW-CRTs utilizes the linear mixed model, where the treatment effect is only present after the treatment adoption, under the assumption of no anticipation. This assumption, however, may not always hold in practice because stakeholders, providers, or individuals who are aware of the treatment adoption timing (especially when blinding is challenging or infeasible) can inadvertently change their behaviors in anticipation of the forthcoming intervention. We provide an analytical framework to address the anticipation effect in SW-CRTs and study its impact. We derive expectations of the estimators based on a collection of linear mixed models and demonstrate that when the anticipation effect is ignored, these estimators give biased estimates of the treatment effect. We also provide updated sample size formulas that explicitly account for anticipation effects, exposure-time heterogeneity, or both in SW-CRTs and illustrate their impact on study power. Through simulation studies and empirical analyses, we compare the treatment effect estimators with and without adjusting for anticipation, and provide some practical considerations.

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arXiv2025

A tutorial on conducting sample size and power calculations for detecting treatment effect heterogeneity in cluster randomized trials with linear mixed models

Cluster-randomized trials (CRTs) are a well-established class of designs for evaluating community-based interventions. An essential task in planning these trials is determining the number of clusters and cluster sizes needed to achieve sufficient statistical power for detecting a clinically relevant effect size. While methods for evaluating the average treatment effect (ATE) for the entire study population are well-established, sample size methods for testing heterogeneity of treatment effects (HTEs), i.e., treatment-covariate interaction or difference in subpopulation-specific treatment effects, in CRTs have only recently been developed. For pre-specified analyses of HTEs in CRTs, effect-modifying covariates should, ideally, be accompanied by sample size or power calculations to ensure the trial has adequate power for the planned analyses. Power analysis for testing HTEs is more complex than for ATEs due to the additional design parameters that must be specified. Power and sample size formulas for testing HTEs via linear mixed effects (LME) models have been separately derived for different cluster-randomized designs, including single and multi-period parallel designs, crossover designs, and stepped-wedge designs, and for continuous and binary outcomes. This tutorial provides a consolidated reference guide for these methods and enhances their accessibility through an online R Shiny calculator. We further discuss key considerations for conducting sample size and power calculations to test pre-specified HTE hypotheses in CRTs, highlighting the importance of specifying advanced estimates of intracluster correlation coefficients for both outcomes and covariates, and their implications for power. The sample size methodology and calculator functionality are demonstrated through a real CRT example.

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arXiv2024

Maintaining the validity of inference from linear mixed models in stepped-wedge cluster randomized trials under misspecified random-effects structures

Linear mixed models are commonly used in analyzing stepped-wedge cluster randomized trials (SW-CRTs). A key consideration for analyzing a SW-CRT is accounting for the potentially complex correlation structure, which can be achieved by specifying a random effects structure. Common random effects structures for a SW-CRT include random intercept, random cluster-by-period, and discrete-time decay. Recently, more complex structures, such as the random intervention structure, have been proposed. In practice, specifying appropriate random effects can be challenging. Robust variance estimators (RVE) may be applied to linear mixed models to provide consistent estimators of standard errors of fixed effect parameters in the presence of random-effects misspecification. However, there has been no empirical investigation of RVE for SW-CRT. In this paper, we first review five RVEs (both standard and small-sample bias-corrected RVEs) that are available for linear mixed models. We then describe a comprehensive simulation study to examine the performance of these RVEs for SW-CRTs with a continuous outcome under different data generators. For each data generator, we investigate whether the use of a RVE with either the random intercept model or the random cluster-by-period model is sufficient to provide valid statistical inference for fixed effect parameters, when these working models are subject to misspecification. Our results indicate that the random intercept and random cluster-by-period models with RVEs performed similarly. The CR3 RVE estimator, coupled with the number of clusters minus two degrees of freedom correction, consistently gave the best coverage results, but could be slightly conservative when the number of clusters was below 16. We summarize the implications of our results for linear mixed model analysis of SW-CRTs in practice.

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arXiv2023

Power calculation for cross-sectional stepped wedge cluster randomized trials with a time-to-event endpoint

Stepped wedge cluster randomized trials (SW-CRTs) are a form of randomized trial whereby clusters are progressively transitioned from control to intervention, with the timing of transition randomized for each cluster. An important task at the design stage is to ensure that the planned trial has sufficient power. While methods for determining power have been well-developed for SW-CRTs with continuous and binary outcomes, limited methods for power calculation are available for SW-CRTs with censored time-to-event outcomes. In this article, we propose a stratified marginal Cox model to analyze cross-sectional SW-CRTs and then derive an explicit expression of the robust sandwich variance to facilitate power calculations without the need for computationally intensive simulations. Power formulas based on both the Wald and robust score tests are developed, assuming constant within-period and between-period correlation parameters, and are further validated via simulation under different finite-sample scenarios. Finally, we illustrate our methods in the context of a SW-CRT testing the effect of a new electronic reminder system on time to catheter removal in hospital settings. We also offer an R Shiny application to facilitate sample size and power calculations using our proposed methods.

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arXiv2022

Power analyses for stepped wedge designs with multivariate continuous outcomes

Multivariate outcomes are common in pragmatic cluster randomized trials. While sample size calculation procedures for multivariate outcomes exist under parallel assignment, none have been developed for a stepped wedge design. In this article, we present computationally efficient power and sample size procedures for stepped wedge cluster randomized trials (SW-CRTs) with multivariate outcomes that differentiate the within-period and between-period intracluster correlation coefficients (ICCs). Under a multivariate linear mixed model, we derive the joint distribution of the intervention test statistics which can be used for determining power under different hypotheses and provide an example using the commonly utilized intersection-union test for co-primary outcomes. Simplifications under a common treatment effect and common ICCs across endpoints and an extension to closed cohort designs are also provided. Finally, under the common ICC across endpoints assumption, we formally prove that the multivariate linear mixed model leads to a more efficient treatment effect estimator compared to the univariate linear mixed model, providing a rigorous justification on the use of the former with multivariate outcomes. We illustrate application of the proposed methods using data from an existing SW-CRT and present extensive simulations to validate the methods.

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arXiv2022

Power analysis for cluster randomized trials with continuous co-primary endpoints

Pragmatic trials evaluating health care interventions often adopt cluster randomization due to scientific or logistical considerations. Previous reviews have shown that co-primary endpoints are common in pragmatic trials but infrequently recognized in sample size or power calculations. While methods for power analysis based on $K$ ($K\geq 2$) binary co-primary endpoints are available for CRTs, to our knowledge, methods for continuous co-primary endpoints are not yet available. Assuming a multivariate linear mixed model that accounts for multiple types of intraclass correlation coefficients (endpoint-specific ICCs, intra-subject ICCs and inter-subject between-endpoint ICCs) among the observations in each cluster, we derive the closed-form joint distribution of $K$ treatment effect estimators to facilitate sample size and power determination with different types of null hypotheses under equal cluster sizes. We characterize the relationship between the power of each test and different types of correlation parameters. We further relax the equal cluster size assumption and approximate the joint distribution of the $K$ treatment effect estimators through the mean and coefficient of variation of cluster sizes. Our simulation studies with a finite number of clusters indicate that the predicted power by our method agrees well with the empirical power, when the parameters in the multivariate linear mixed model are estimated via the expectation-maximization algorithm. An application to a real CRT is presented to illustrate the proposed method.

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