Skip to main content
. Author manuscript; available in PMC: 2016 Aug 7.
Published in final edited form as: Biometrics. 2015 Nov 19;72(2):546–553. doi: 10.1111/biom.12435

Table 2.

Simulation results from piecewise Poisson regression analysis under various two-stage sample designs

α 1 α 2 α 3 β 1 β 2
True parameter values −5.404 −4.893 −4.605 1.609 1.609
PPS(t)+SSRS(x2) with intracluster correlation ρ(x1) = 0
Relative bias (×102) 0.078 −0.017 −0.131 0.269 0.134
Empirical variance estimates (×103) 2.494 2.490 5.795 5.266 1.121
Ratio of vara to empirical variance estimates 0.937 0.916 1.029 0.953 1.149
Ratio of linearization to empirical variance estimates 0.949 0.961 1.055 0.960 1.028
PPS(t)+SSRS(x2) with intracluster correlation ρ(x1) > 0
Relative bias (×102) −0.066 −0.159 −0.291 0.552 −0.235
Empirical variance estimates (×103) 5.212 4.493 7.776 36.986 1.661
Ratio of vara to empirical variance estimates 0.443 0.509 0.766 0.132 0.768
Ratio of linearization to empirical variance estimates 1.063 1.065 1.038 1.053 1.028
a

var considers differential weighting effect but ignores the clustering effect, computed as the sum of the variance of weighted Taylor deviates in cases and the variance in sampled subcohort.