BackgroundPrevious research showed that individuals have a natural tendency to conform to others. This study investigated the temporal characteristics of neural processing involved in social conformity by recording participants’ brain potentials in performing a line judgment task. After making his initial choice, a participant was presented with the choices of four same-sex group members, which could be congruent or highly or moderately incongruent with the participant’s own choice. The participant was then immediately given a second opportunity to respond to the same stimulus.ResultsParticipants were more likely to conform to the group members by changing their initial choices when these choices were in conflict with the group’s choices, and this behavioral adjustment occurred more often as the level of incongruence increased. Electrophysiologically, group choices that were incongruent with the participant’s choice elicited more negative-going medial frontal negativity (MFN), a component associated with processing expectancy violation, than those that were congruent with the participant’s choice, and the size of this effect increased as the level of incongruence increased. Moreover, at both levels of incongruence, the MFN responses were more negative-going for incongruent trials in which participants subsequently performed behavioral adjustment than for trials in which they stuck to their initial choices. Furthermore, over individual participants, participants who were more likely to conform to others (i.e., changing their initial choices) exhibited stronger MFN effect than individuals who were more independent.ConclusionsThese findings suggest that incongruence with group choices or opinions can elicit brain responses that are similar to those elicited by violation of non-social expectancy in outcome evaluation and performance monitoring, and these brain signals are utilized in the following behavioral adjustment. The present research complements recent brain imaging studies by showing the temporal characteristics of neural processing involved in social conformity and by suggesting common mechanisms for reinforcement learning in social and non-social situations.

Unequal cluster sizes are common in cluster randomized trials (CRTs). While there are a number of previous investigations studying the impact of unequal cluster sizes on the power for testing the average treatment effect in CRTs, little is known about the impact of unequal cluster sizes on the power for testing the heterogeneous treatment effect (HTE) in CRTs. In this work, we expand the sample size procedures for studying HTE in CRTs to accommodate cluster size variation under the linear mixed model framework. Through analytical derivation and graphical exploration, we show that the sample size for the HTE with an individual‐level effect modifier is less affected by unequal cluster sizes than with a cluster‐level effect modifier. The impact of cluster size variability jointly depends on the mean and coefficient of variation of cluster sizes, covariate intraclass correlation coefficient (ICC) and the conditional outcome ICC. In addition, we demonstrate that the HTE‐motivated analysis of covariance framework can be used for analyzing the average treatment effect, and offer a more efficient sample size procedure for studying the average treatment effect adjusting for the effect modifier. We use simulations to confirm the accuracy of the proposed sample size procedures for both the average treatment effect and HTE in CRTs. Extensions to multivariate effect modifiers are provided and our procedure is illustrated in the context of the Strategies to Reduce Injuries and Develop Confidence in Elders trial.

Propensity score weighting is an important tool for comparative effectiveness research. Besides the inverse probability of treatment weights (IPW), recent development has introduced a general class of balancing weights, corresponding to alternative target populations and estimands. In particular, the overlap weights (OW) lead to optimal covariate balance and estimation efficiency, and a target population of scientific and policy interest. We develop the R package PSweight to provide a comprehensive design and analysis platform for causal inference based on propensity score weighting. PSweight supports (i) a variety of balancing weights, (ii) binary and multiple treatments, (iii) simple and augmented weighting estimators, (iv) nuisance-adjusted sandwich variances, and (v) ratio estimands. PSweight also provides diagnostic tables and graphs for covariate balance assessment. We demonstrate the functionality of the package using a data example from the National Child Development Survey (NCDS), where we evaluate the causal effect of educational attainment on income.

The modified Poisson regression coupled with a robust sandwich variance has become a viable alternative to log-binomial regression for estimating the marginal relative risk in cluster randomized trials. However, a corresponding sample size formula for relative risk regression via the modified Poisson model is currently not available for cluster randomized trials. Through analytical derivations, we show that there is no loss of asymptotic efficiency for estimating the marginal relative risk via the modified Poisson regression relative to the log-binomial regression. This finding holds both under the independence working correlation and under the exchangeable working correlation provided a simple modification is used to obtain the consistent intraclass correlation coefficient estimate. Therefore, the sample size formulas developed for log-binomial regression naturally apply to the modified Poisson regression in cluster randomized trials. We further extend the sample size formulas to accommodate variable cluster sizes. An extensive Monte Carlo simulation study is carried out to validate the proposed formulas. We find that the proposed formulas have satisfactory performance across a range of cluster size variability, as long as suitable finite-sample corrections are applied to the sandwich variance estimator and the number of clusters is at least 10. Our findings also suggest that the sample size estimate under the exchangeable working correlation is more robust to cluster size variability, and recommend the use of an exchangeable working correlation over an independence working correlation for both design and analysis. The proposed sample size formulas are illustrated using the Stop Colorectal Cancer (STOP CRC) trial.

Cluster randomized trials (CRTs) are widely used in epidemiological and public health studies assessing population‐level effect of group‐based interventions. One important application of CRTs is the control of vector‐borne disease, such as malaria. However, a particular challenge for designing these trials is that the primary outcome involves counts of episodes that are subject to right truncation. While sample size formulas have been developed for CRTs with clustered counts, they are not directly applicable when the counts are right truncated. To address this limitation, we discuss two marginal modeling approaches for the analysis of CRTs with truncated counts and develop two corresponding closed‐form sample size formulas to facilitate the design of such trials. The proposed sample size formulas allow investigators to explore the power under a large number of scenarios without computationally intensive simulations. The proposed formulas are validated in extensive simulations. We further explore the implication of right truncation on power and apply the proposed formulas to illustrate the power calculation for a malaria control CRT where the primary outcome is subject to right truncation.

IMPORTANCEDuring an ongoing longitudinal cohort study, a casino opening created a natural cash transfer experiment. Some participating families received income supplements, and others did not. The children in this study are now adults.OBJECTIVE To assess the long-term outcomes of family income supplements received in childhood.

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Motivated by a suicide prevention trial with hierarchical treatment allocation (cluster‐level and individual‐level treatments), we address the sample size requirements for testing the treatment effects as well as their interaction. We assume a linear mixed model, within which two types of treatment effect estimands (controlled effect and marginal effect) are defined. For each null hypothesis corresponding to an estimand, we derive sample size formulas based on large‐sample z‐approximation, and provide finite‐sample modifications based on a t‐approximation. We relax the equal cluster size assumption and express the sample size formulas as functions of the mean and coefficient of variation of cluster sizes. We show that the sample size requirement for testing the controlled effect of the cluster‐level treatment is more sensitive to cluster size variability than that for testing the controlled effect of the individual‐level treatment; the same observation holds for testing the marginal effects. In addition, we show that the sample size for testing the interaction effect is proportional to that for testing the controlled or the marginal effect of the individual‐level treatment. We conduct extensive simulations to validate the proposed sample size formulas, and find the empirical power agrees well with the predicted power for each test. Furthermore, the t‐approximations often provide better control of type I error rate with a small number of clusters. Finally, we illustrate our sample size formulas to design the motivating suicide prevention factorial trial. The proposed methods are implemented in the R package H2x2Factorial.