The iterative bisection procedure: a useful tool for determining parameter values in data-generating processes in Monte Carlo simulations

Abstract

Background: Data-generating processes are key to the design of Monte Carlo simulations. It is important for investigators to be able to simulate data with specific characteristics. Methods: We described an iterative bisection procedure that can be used to determine the numeric values of parameters of a data-generating process to produce simulated samples with specified characteristics. We illustrated the application of the procedure in four different scenarios: (i) simulating binary outcome data from a logistic model such that the prevalence of the outcome is equal to a specified value; (ii) simulating binary outcome data from a logistic model based on treatment status and baseline covariates so that the simulated outcomes have a specified treatment relative risk; (iii) simulating binary outcome data from a logistic model so that the model c-statistic has a specified value; (iv) simulating time-to-event outcome data from a Cox proportional hazards model so that treatment induces a specified marginal or population-average hazard ratio. Results: In each of the four scenarios the bisection procedure converged rapidly and identified parameter values that resulted in the simulated data having the desired characteristics. Conclusion: An iterative bisection procedure can be used to identify numeric values for parameters in data-generating processes to generate data with specified characteristics.