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.