Sample size calculations for group randomized trials with unequal group sizes through Monte Carlo simulations

A Bayesian Approach for Estimating the Survivor Average Causal Effect When Outcomes Are Truncated by Death in Cluster-Randomized Trials

Many studies encounter clustering due to multicenter enrollment and nonmortality outcomes, such as quality of life, that are truncated due to death-that is, missing not at random and nonignorable. Traditional missing-data methods and target causal estimands are suboptimal for statistical inference in the presence of these combined issues, which are especially common in multicenter studies and cluster-randomized trials (CRTs) carried out among the elderly or seriously ill. Using principal stratification, we developed a Bayesian estimator that jointly identifies the always-survivor principal stratum in a clustered/hierarchical data setting and estimates the average treatment effect among them (i.e., the survivor average causal effect (SACE)). In simulations, we observed low bias and good coverage with our method. In a motivating CRT, the SACE and the estimate from complete-case analysis differed in magnitude, but both were small, and neither was incompatible with a null effect. However, the SACE estimate has a clear causal interpretation. The option to assess the rigorously defined SACE estimand in studies with informative truncation and clustering can provide additional insight into an important subset of study participants. Based on the simulation study and CRT reanalysis, we provide practical recommendations for using the SACE in CRTs and software code to support future research.

Accounting for expected attrition in the planning of cluster randomized trials for assessing treatment effect heterogeneity

BACKGROUND

Detecting treatment effect heterogeneity is an important objective in cluster randomized trials and implementation research. While sample size procedures for testing the average treatment effect accounting for participant attrition assuming missing completely at random or missing at random have been previously developed, the impact of attrition on the power for detecting heterogeneous treatment effects in cluster randomized trials remains unknown.

METHODS

We provide a sample size formula for testing for a heterogeneous treatment effect assuming the outcome is missing completely at random. We also propose an efficient Monte Carlo sample size procedure for assessing heterogeneous treatment effect assuming covariate-dependent outcome missingness (missing at random). We compare our sample size methods with the direct inflation method that divides the estimated sample size by the mean follow-up rate. We also evaluate our methods through simulation studies and illustrate them with a real-world example.

RESULTS

Simulation results show that our proposed sample size methods under both missing completely at random and missing at random provide sufficient power for assessing heterogeneous treatment effect. The proposed sample size methods lead to more accurate sample size estimates than the direct inflation method when the missingness rate is high (e.g., ≥ 30%). Moreover, sample size estimation under both missing completely at random and missing at random is sensitive to the missingness rate, but not sensitive to the intracluster correlation coefficient among the missingness indicators.

CONCLUSION

Our new sample size methods can assist in planning cluster randomized trials that plan to assess a heterogeneous treatment effect and participant attrition is expected to occur.

Methods for dealing with unequal cluster sizes in cluster randomized trials: A scoping review

In a cluster-randomized trial (CRT), the number of participants enrolled often varies across clusters. This variation should be considered during both trial design and data analysis to ensure statistical performance goals are achieved. Most methodological literature on the CRT design has assumed equal cluster sizes. This scoping review focuses on methodology for unequal cluster size CRTs. EMBASE, Medline, Google Scholar, MathSciNet and Web of Science databases were searched to identify English-language articles reporting on methodology for unequal cluster size CRTs published until March 2021. We extracted data on the focus of the paper (power calculation, Type I error etc.), the type of CRT, the type and the range of parameter values investigated (number of clusters, mean cluster size, cluster size coefficient of variation, intra-cluster correlation coefficient, etc.), and the main conclusions. Seventy-nine of 5032 identified papers met the inclusion criteria. Papers primarily focused on the parallel-arm CRT (p-CRT, n = 60, 76%) and the stepped-wedge CRT (n = 14, 18%). Roughly 75% of the papers addressed trial design issues (sample size/power calculation) while 25% focused on analysis considerations (Type I error, bias, etc.). The ranges of parameter values explored varied substantially across different studies. Methods for accounting for unequal cluster sizes in the p-CRT have been investigated extensively for Gaussian and binary outcomes. Synthesizing the findings of these works is difficult as the magnitude of impact of the unequal cluster sizes varies substantially across the combinations and ranges of input parameters. Limited investigations have been done for other combinations of a CRT design by outcome type, particularly methodology involving binary outcomes-the most commonly used type of primary outcome in trials. The paucity of methodological papers outside of the p-CRT with Gaussian or binary outcomes highlights the need for further methodological development to fill the gaps.

When is Enough? Minimum Sample Sizes for On-Road Measurements of Car Emissions

The power of remote vehicle emission sensing stems from the big sample size obtained and its related statistical representativeness for the measured emission rates. But how many records are needed for a representative measurement and when does the information gain per record become insignificant? We use Monte Carlo simulations to determine the relationship between the sample size and the accuracy of the sample mean and variance. We take the example of NO emissions from diesel cars measured by remote emission monitors between 2011 and 2018 at various locations in Europe. We find that no more than 200 remote sensing records are sufficient to approximate the mean emission rate for Euro 4, 5, and 6a/b diesel cars with 80% certainty within a ±1 g NO per kg fuel tolerance margin (∼±50 mg NO per km). Between 300 and 800 remote sensing records are needed to approximate also the variance of the mean NO emission rates for those diesel car technologies. This translates to only 2 and up to 9 measurement days to characterize the means and their variance for a car fleet typical in Europe.