Use of between-within degrees of freedom as an alternative to the Kenward–Roger method for small-sample inference in generalized linear mixed modeling of clustered count data

Abstract

Clustered count data, common in health-related research, are routinely analyzed using generalized linear mixed models. There are two well-known challenges in small-sample inference in mixed modeling: bias in the naïve standard error approximation for the empirical best linear unbiased estimator, and lack of clearly defined denominator degrees of freedom. The Kenward–Roger method was designed to address these issues in linear mixed modeling, but neither it nor the simpler option of using between-within denominator degrees of freedom has been thoroughly examined in generalized linear mixed modeling. We compared the Kenward–Roger and between-within methods in two simulation studies. For simulated cluster-randomized trial data, coverage rates for both methods were generally close to the nominal 95% level and never outside 93-97%, even for 5 clusters with an average of 3 observations each. For autocorrelated longitudinal data, between-within intervals were more accurate overall, and under some conditions both the original and improved Kenward–Roger methods behaved erratically. Overall, coverage for Kenward–Roger and between-within intervals was generally adequate, if often conservative. Based on the scenarios examined here, use of between-within degrees of freedom may be a suitable or even preferable alternative to the Kenward–Roger method in some analyses of clustered count data with simple covariance structures.