Monte Carlo Methods in Clinical Research: Applications in Multivariable Analysis

BACKGROUND: Monte Carlo methods use "simulated" analyses with random numbers for solving problems, particularly those that defy solutions using mathematical theory alone. Research using Monte Carlo simulations is very popular in many branches of science and is sometimes done in clinical investigation. The origins and basic strategy of the technique, however, may not be well known to clinical researchers. The purpose of this paper is to describe the history and general principles of Monte Carlo methods and to demonstrate how Monte Carlo simulations were recently applied to examine a phenomenon in multivariable statistical analysis called the number of outcome events per independent variable (EPV). For example, in a cohort of 200 people, with 50 deaths and 5 independent (predictor) variables, EPV = 50/5 = 10. METHODS: The "real-world" data came from a clinical trial of 673 patients in which 7 variables were cogent predictors of 252 deaths, so that EPV = 252/7 = 36. For the Monte Carlo simulations, special models were used while allowing simulations of proportional hazards and logistic regression to maintain the basic relationship of variables and the same size of the original population, at EPV values of 2, 5, 10, 15, 20, and 25. RESULTS: The Monte Carlo simulations confirmed a previously undocumented "rule of thumb" stating that when the EPV is less than 10-20, the algebraic models used in logistic regression and proportional hazards regression may be unreliable, leading to imprecise or spurious results. CONCLUSION: Monte Carlo techniques offer attractive methods for clinical investigators to use in solving problems that are not amenable to customary mathematical approaches.