Statistical methods
    Expos. Ratio          ni         σ2                   IP/FCP/CP/RCP                        GEE
Constant 3:3 6 0 0.032 0.048
    0.5 0.042 0.060
    1.0 0.048 0.066
    2.0 0.052 0.092
  6-42 0 0.038 0.062
    0.5 0.068 0.082
    1.0 0.050 0.090
    2.0 0.028 0.090
Constant 1:5 6 0 0.032 0.052
    0.5 0.048 0.052
    1.0 0.040 0.066
    2.0 0.040 0.094
  6-42 0 0.050 0.074
    0.5 0.058 0.068
    1.0 0.038 0.068
    2.0 0.048 0.110
               IP       FCP/CP       RCP       GEE       RCP_bw
Varying 6 0 0.046 0.046 0.034 0.060 0.040
    0.5 0.168 0.056 0.052 0.096 0.044
    1.0 0.284 0.058 0.050 0.088 0.040
    2.0 0.506 0.050 0.042 0.104 0.044
  6-42 0 0.046 0.044 0.034 0.060 0.038
    0.5 0.502 0.054 0.054 0.094 0.046
    1.0 0.676 0.036 0.030 0.092 0.024
    2.0 0.788 0.054 0.044 0.104 0.044
Expos. ratio=ratio of number of exposed to control subjects in a cluster; Varying ratio means the exposure ratios vary randomly from cluster to cluster; ni=number of subjects in each cluster; σ2=between cluster variance; IP=Independent Poisson model; FCP=Fixed Cluster Poisson model; CP=Conditional likelihood Poisson estimation; GEE=Generalized Estimating Equations with empirical standard error; RCP=Random Cluster effects Poisson model; RCP_bw=Random Cluster effects Poisson model where the within- and between- cluster effects were separated.
Table 2: Type I error rates obtained from 500 replications assuming β=0 and 30 clusters per replication.