Simulation of Different Methods of Adjusting for confounders in a Cox Regression

Stata files each produce 10000 simulated datasets (N=3605) containing:

• confounder 1 (binary)
• confounder 2 (continuous)
• confounder 3 (binary)
• exposure group 1 (true hazards ratio: 1.5; N=463)
• exposure group 2 (true hazards ratio: 1.5; N=322)
• outcome variable (binary)

1_simulate_data_unconfounded.do produces unconfounded datasets, where confounders 1-3 are not associated with exposure groups.

In each do file, a cox model is run to obtain estimated coefficients for each of the 10000 simulated models. A different method of controlling for confounding is implemented for each:

• 2_weighted_yoshida.do - the weighting method described in this paper: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5378668/pdf/nihms845429.pdf
• 3_simulation_control_in_model.do - adjusting for all 3 confounders
• 4_simulation_pair_wise_matchingl.do - separate models are run to compare exposure group 1 vs controls, exposure group 2 vs controls. Exposure propensity scores are estimated using logistic regression with the dependent variables as confounder 1-3. Exposed are matched to unexposed controls 1:2 using nearest neighbour matching without replacement.
• 5_simulation_pair_wise_andcontrol - same as previous, except confounders are also controlled for in Cox model.

Plotting results

density_plots_estimates.R imports the outputs from do files 2, 3 and 4 are imported and plotted