1 ()2       3
  Expos. ratio       ni      σ2           IP/FCP/CP/RCP                      GEE         theory
Constant 3:3 6 0 0.141 (0.133) 0.138 (0.133) 0.141
    0.5 0.125 (0.118) 0.121 (0.118) 0.124
    1.0 0.112 (0.113) 0.106 (0.113) 0.109
    2.0 0.090 (0.091) 0.082 (0.091) 0.085
  6-42 0 0.070 (0.069) 0.068 (0.069) 0.070
    0.5 0.063 (0.058) 0.060 (0.059) 0.062
    1.0 0.056 (0.054) 0.054 (0.055) 0.055
    2.0 0.046 (0.044) 0.043 (0.047) 0.043
Constant 1:5 6 0 0.181 (0.176) 0.178 (0.176) 0.181
    0.5 0.161 (0.144) 0.155 (0.144) 0.159
    1.0 0.144 (0.136) 0.135(0.136) 0.141
    2.0 0.117 (0.118) 0.107 (0.118) 0.110
  6-42 0 0.090 (0.092) 0.088 (0.092) 0.090
    0.5 0.081 (0.082) 0.076 (0.082) 0.080
    1.0 0.072 (0.074) 0.068 (0.074) 0.070
    2.0 0.059 (0.057) 0.054 (0.060) 0.055
                IP       FCP/CP       RCP       GEE      RCP_bw
Varying 6 0 0.141 (0.141) 0.154 (0.153) 0.142 (0.142) 0.136 (0.142) 0.154 (0.153)
  0.5 0.126 (0.180) 0.138 (0.141) 0.135 (0.141) 0.130 (0.141) 0.138 (0.141)
  1.0 0.113 (0.213) 0.123 (0.124) 0.122 (0.123) 0.115 (0.122) 0.123 (0.124)
  2.0 0.091 (0.293) 0.099 (0.107) 0.099 (0.107) 0.090 (0.107) 0.099 (0.107)
  6-42 0 0.070 (0.069) 0.089 (0.089) 0.071 (0.068) 0.067 (0.069) 0.089 (0.090)
  0.5 0.063 (0.186) 0.080 (0.085) 0.079 (0.083) 0.075 (0.083) 0.080 (0.085)
  1.0 0.057 (0.272) 0.072 (0.074) 0.071 (0.073) 0.067 (0.074) 0.072 (0.074)
  2.0 0.047 (0.405) 0.058 (0.060) 0.058 (0.060) 0.054 (0.066) 0.058 (0.060)
Exposure 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 a 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.
1, average of procedure standard errors across 500 samples
2, standard deviation of the 500 estimates of β
3, theoretical standard error in (4) calculated from expected information
Table 1: Precision of estimates of β obtained from 500 replications with β=0.25 and 30 clusters per replication.