Sample size estimation for modified Poisson analysis of cluster randomized trials with a binary outcome

Abstract

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.

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

“…It is possible to extend their approach to accommodate continuous co-primary endpoints as an alternative to our proposed method. However, previous work has shown that a GEE with an independence working correlation structure can result in an inflated sample size compared to an efficient GEE with correct working correlation model even with a single primary endpoint (Li and Tong, 2021). It would be interesting to formally quantify the efficiency gain by MLMM versus independence GEE with co-primary endpoints.…”

“…, K) T , and specify the variance component matrices Σ φ and Σ e based on the marginal variances and ICCs. To further assess the accuracy of our approximate power procedure under unequal cluster sizes, we consider mean cluster size m = 60, and coefficient of variation of cluster size CV ∈ {0, 0.2, 0.4, 0.8}, representing different degrees of variability in cluster size used in previous simulations (Li and Tong, 2021). When CV > 0, the cluster sizes m i 's are drawn from a Gamma distribution with shape and scale parameter 1/CV 2 and mCV 2 ), rounded to the nearest integer.…”

“…They derived a closed-form expression for the joint distribution of the multivariate Wald test statistic, which facilitates analytical sample size and power calculations given assumptions on multiple ICC parameters. However, the working independence assumption is often not fully efficient and can lead to a larger sample size than necessary in CRTs even with a single endpoint (Li and Tong, 2021). Furthermore, to date, there has been no work investigating power analysis for CRTs with continuous co-primary endpoints.…”

“…Finally, we derive the approximate joint distribution of the multivariate test statistic allowing for an unbalanced design with variable cluster sizes. While the impact of variable cluster sizes on sample size calculation for CRTs with a single endpoint has been previously studied (van Breukelen et al, 2007;Rutterford et al, 2015;Li and Tong, 2021), the impact of variable cluster sizes in CRTs with co-primary endpoints remains unclear. Through analytical derivation and numerical illustration, we show that the efficiency loss due to cluster size variability can be mitigated to some extent by accounting for the co-primary endpoint, thus providing new motivation for the recommendation to account for co-primary endpoints through a MLMM in both the design and analysis phases of a CRT.…”

Interval Estimation of Relative Risks for Combined Unilateral and Bilateral Correlated Data

“…which have been discussed in many papers [23] [24][25] [26] [27]. The log-binomial model uses the log link function for the binomial regression, while the modified Poisson regression applies the Poisson regression to binomial data and uses a robust error variance procedure known as the sandwich estimation to account for the model mis-specification.…”