Electronic Table

This page holds electronic tables of type I error rates of various small-sample corrected tests in logistic and Poisson GLMMs under a cluster-randomized trial setting from the two simulations in “Evaluating tests for cluster-randomized trials with few clusters under generalized linear mixed models with covariate adjustment: a simulation study”. Both electronic tables are filterable and sortable. The raw data are available at simulation1_typeIerror.csv and simulation2_typeIerror.csv.

Variables in the tables:

• outcome.type: type of the outcome (binary vs count).
• n.cluster: number of clusters (10 vs 20).
• mean.size: mean cluster size (50 vs 100).
• coef.var: coefficient of variation of cluster sizes, the ratio of standard deviation of cluster sizes to mean cluster size (0, 0.75, 1.5).
• ICC: intraclass correlation coefficient (0.001, 0.01, 0.05, 0.1, 0.2). A high ICC corresponds to a high variance of the random intercept. More details in the paper. This variable is defined in the following paper:

                   Nakagawa S, Johnson PC, Schielzeth H. The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded. Journal of the Royal Society Interface 2017; 14(134): 20170213.

• ICC2: mean intraclass correlation coefficient under the alternative definition based on linear mixed models. This is called the mean LMM ICC in the paper. Unlike ICC which is set to fixed values, ICC2 is computed from simulation and reported as a reference. More details in the paper. We refer to the following papers for this definition:

                   Donner A, Koval JJ. The estimation of intraclass correlation in the analysis of family data. Biometrics 1980: 19–25.

                   Stanish WM, Taylor N. Estimation of the intraclass correlation coefficient for the analysis of covariance model. The American Statistician 1983; 37(3): 221–224.

• model: fitted model (1, 2, 3, 4). More details in the paper.
  1. Correctly specified model with no redundant covariates.
  2. One additional redundant individual-level covariate based on 1.
  3. One additional redundant cluster-level covariate based on 1.
  4. One additional redundant individual-level covariate and one additional redundant cluster-level covariate based on 1.
• true.model: the data-generating model (1st table: A, B, C, D; 2nd table: B, D). More details in the paper.
  1. No prognostic covariates.
  2. Simulation 1: one individual-level prognostic covariate; Simulation 2: three individual-level prognostic covariates.
  3. One cluster-level prognostic covariate.
  4. Simulation 1: one individual-level prognostic covariate and one cluster-level prognostic covariate; Simulation 2: three individual-level prognostic covariates and one cluster-level prognostic covariate.
• method: the form of the test of the treatment effect (LRT vs Wald).
• ddf: method to compute the denominator degree of freedom (BW1, BW2, containment, residual).
• type.I.error: type I error rate of the test (estimated from 5,000 Monte Carlo runs).

In the figures in the paper, we present

1. scenarios with true model D and fitted model 1 in Simulation 1
2. scenarios with true model D and fitted model 4 in Simulation 2

Type I error rates from Simulation 1

Type I error rates from Simulation 2