Skip to main content

Table 1 Type I errors, Bias and Mean Square Error (MSE) for non parsimonious PS model according to the method used (PS matching (PSm) or IPTW) and to the strength of the association between baseline covariates, treatment/outcome

From: Evaluation of the Propensity score methods for estimating marginal odds ratios in case of small sample size

N   OR(a) = 1.5, OR(b) = 1.5 OR(a) = 2.5, OR(b) =1.5 OR(a) = 1.5, OR(b) = 2.5 OR(a) = 2.5, OR(b) = 2.5
   PSm IPTW PSm IPTW PSm IPTW PSm IPTW
40 Type I error 0.055 0.048 0.053 0.056 0.052 0.039 0.052 0.047
  Bias 0.05 0.057 0.049 0.07 0.059 0.055 0.048 0.079
  % 5.6 6.5 5.4 7.8 7.1 6.6 5.7 9.4
  Variance 0.875 0.593 0.918 0.694 0.873 0.576 0.903 0.683
  MSE 0.878 0.597 0.92 0.699 0.876 0.579 0.905 0.690
60 Type I error 0.045 0.046 0.047 0.046 0.044 0.039 0.044 0.039
  Bias 0.058 0.036 0.058 0.049 0.048 0.022 0.05 0.033
  % 6.4 4 6.4 5.4 5.7 2.6 6 3.9
  Variance 0.511 0.36 0.553 0.414 0.484 0.329 0.516 0.388
  MSE 0.514 0.362 0.556 0.416 0.486 0.33 0.519 0.389
100 Type I error 0.049 0.046 0.047 0.046 0.047 0.034 0.04 0.036
  Bias 0.023 0.018 0.02 0.022 0.021 0.015 0.025 0.016
  % 2.6 2 2.2 2.5 2.5 1.8 2.9 1.9
  Variance 0.254 0.194 0.282 0.223 0.242 0.177 0.261 0.204
  MSE 0.255 0.194 0.283 0.223 0.243 0.177 0.262 0.204
500 Type I error 0.049 0.046 0.05 0.048 0.041 0.038 0.042 0.037
  Bias 0.01 0.007 0.012 0.008 0.01 0.005 0.013 0.005
  % 1.1 0.8 1.3 0.9 1.2 0.6 1.5 0.6
  Variance 0.04 0.034 0.045 0.038 0.037 0.032 0.042 0.035
  MSE 0.04 0.034 0.045 0.038 0.037 0.032 0.042 0.035
  1. This table specially details the sample sizes ranging from 40 to 500. Prevalence of the treatment was set at 0.5. Conditional treatment effect was set at log(2.5) except for Type I errors estimations (log(1)). (N: number of subjects; PS: propensity score; IPTW: inverse probability of treatment weighting, OR(a) and OR(b): strengths of the association between baseline covariates and treatment or outcome respectively, as defined on an odds ratio scale).
\