Summary Cluster randomized trials often exhibit a three-level structure with participants nested in subclusters such as health care providers, and subclusters nested in clusters such as clinics. While the average treatment effect has been the primary focus in planning three-level randomized trials, interest is growing in understanding whether the treatment effect varies among prespecified patient subpopulations, such as those defined by demographics or baseline clinical characteristics. In this article, we derive novel analytical design formulas based on the asymptotic covariance matrix for powering confirmatory analyses of treatment effect heterogeneity in three-level trials, that are broadly applicable to the evaluation of cluster-level, subcluster-level, and participant-level effect modifiers and to designs where randomization can be carried out at any level. We characterize a nested exchangeable correlation structure for both the effect modifier and the outcome conditional on the effect modifier, and generate new insights from a study design perspective for conducting analyses of treatment effect heterogeneity based on a linear mixed analysis of covariance model. A simulation study is conducted to validate our new methods and two real-world trial examples are used for illustrations.

The marginal Fine‐Gray proportional subdistribution hazards model is a popular approach to directly study the association between covariates and the cumulative incidence function with clustered competing risks data, which often arise in multicenter randomized trials or multilevel observational studies. To account for the within‐cluster correlations between failure times, the uncertainty of the regression parameters estimators is quantified by the robust sandwich variance estimator, which may have unsatisfactory performance with a limited number of clusters. To overcome this limitation, we propose four bias‐corrected variance estimators to reduce the negative bias of the usual sandwich variance estimator, extending the bias‐correction techniques from generalized estimating equations with noncensored exponential family outcomes to clustered competing risks outcomes. We further compare their finite‐sample operating characteristics through simulations and two real data examples. In particular, we found the Mancl and DeRouen (MD) type sandwich variance estimator generally has the smallest bias. Furthermore, with a small number of clusters, the Wald t‐confidence interval with the MD sandwich variance estimator carries close to nominal coverage for the cluster‐level effect parameter. The t‐confidence intervals based on the sandwich variance estimator with any one of the three types of multiplicative bias correction or the z‐confidence interval with the Morel, Bokossa and Neerchal (MBN) type sandwich variance estimator have close to nominal coverage for the individual‐level effect parameter. Finally, we develop a user‐friendly R package crrcbcv implementing the proposed sandwich variance estimators to assist practical applications.

For multicenter randomized trials or multilevel observational studies, the Cox regression model has long been the primary approach to study the effects of covariates on time‐to‐event outcomes. A critical assumption of the Cox model is the proportionality of the hazard functions for modeled covariates, violations of which can result in ambiguous interpretations of the hazard ratio estimates. To address this issue, the restricted mean survival time (RMST), defined as the mean survival time up to a fixed time in a target population, has been recommended as a model‐free target parameter. In this article, we generalize the RMST regression model to clustered data by directly modeling the RMST as a continuous function of restriction times with covariates while properly accounting for within‐cluster correlations to achieve valid inference. The proposed method estimates regression coefficients via weighted generalized estimating equations, coupled with a cluster‐robust sandwich variance estimator to achieve asymptotically valid inference with a sufficient number of clusters. In small‐sample scenarios where a limited number of clusters are available, however, the proposed sandwich variance estimator can exhibit negative bias in capturing the variability of regression coefficient estimates. To overcome this limitation, we further propose and examine bias‐corrected sandwich variance estimators to reduce the negative bias of the cluster‐robust sandwich variance estimator. We study the finite‐sample operating characteristics of proposed methods through simulations and reanalyze two multicenter randomized trials.

Background Blood pressure (BP) elevations are commonly treated in hospitalized patients; however, treatment is not guideline directed. Our objective was to assess BP response to commonly prescribed antihypertensives after the development of severe inpatient hypertension (HTN). Methods This is a cohort study of adults, excluding intensive care unit patients, within a single healthcare system admitted for reasons other than HTN who developed severe HTN (systolic BP>180 or diastolic BP >110 mmHg at least 1 hour after admission). We identified the most commonly administered antihypertensives given within 6 hours of severe HTN (given to >10% of treated patients). We studied the association of treatment with each antihypertensive vs. no treatment on BP change in the 6 hours following severe HTN development using mixed-effects model after adjusting for demographics and clinical characteristics. Results Among 23,147 patients who developed severe HTN, 9,166 received antihypertensive treatment. The most common antihypertensives given were oral metoprolol (n = 1991), oral amlodipine (n = 1812), oral carvedilol (n = 1116), IV hydralazine (n = 1069) and oral hydralazine (n = 953). In the fully adjusted model, treatment with IV hydralazine led to 13 [-15.9, -10.1], 18 [-22.2, -14] and 11 [-14.1, -8.3] mmHg lower MAP, SBP, and DBP in the 6 hours following severe HTN development compared to no treatment. Treatment with oral hydralazine and oral carvedilol also resulted in significantly lower BPs in the 6 hours following severe HTN development (6 [-9.1, -2.1 and -7 [-9.1, -4.2] lower MAP, respectively) compared to no treatment. Receiving metoprolol and amlodipine did not result in a drop in BP compared to no treatment. Conclusion Among commonly used antihypertensives, IV hydralazine resulted in the most significant drop in BP following severe HTN, while metoprolol and amlodipine did not lower BP. Further research to assess the effect of treatment on clinical outcomes and if needed which antihypertensives to administer are necessary.

Diminished visual attention to faces of social partners represents one of the early characteristics of autism spectrum disorder (ASD). Here we examine if the introduction of puppets as social partners alters attention to speakers' faces in young children with ASD and typically developing (TD) controls. Children with ASD (N = 37; Mage = 49.44 months) and TD (N = 27; Mage = 40.66 months) viewed a video depicting a puppet and a human engaged in a conversation. Dwell time on these faces was analyzed as a function of group and speaker's identity. Unlike TD controls, the ASD group exhibited limited visual attention to and chance‐level visual preference for the human speaker. However, attention to and preference for the puppet speaker's face was greater than chance and comparable across the two groups. While there was a strong association between low human speaker preference and high autism severity, no association with autism severity was found for puppet speaker preference. Unlike humans, expressive and verbal puppets attracted the attention of children with ASD at levels comparable to that of TD controls. Considering that puppets can engage in reciprocal interactions and deliver simplified, salient social‐communicative cues, they may facilitate therapeutic efforts in children with ASD. Lay Summary While studies have shown support for therapeutic uses of robots with children with autism, other similar agents such as puppets remain to be explored. When shown a video of a conversation between a puppet and a person, young children with ASD paid as much attention to the puppet's face as typically‐developing (TD) children. Since puppets can engage in back‐and‐forth interactions and model social interactions and communication, they may play a promising role in therapeutic efforts for young children with ASD.