The Performance of Two Data-Generation Processes for Data with Specified Marginal Treatment Odds Ratios

Abstract

Monte Carlo simulation methods are increasingly being used to evaluate the property of statistical estimators in a variety of settings. The utility of these methods depends upon the existence of an appropriate data-generating process. Observational studies are increasingly being used to estimate the effects of exposures and interventions on outcomes. Conventional regression models allow for the estimation of conditional or adjusted estimates of treatment effects. There is an increasing interest in statistical methods for estimating marginal or average treatment effects. However, in many settings, conditional treatment effects can differ from marginal treatment effects. Therefore, existing data-generating processes for conditional treatment effects are of little use in assessing the performance of methods for estimating marginal treatment effects. In the current study, we describe and evaluate the performance of two different data-generation processes for generating data with a specified marginal odds ratio. The first process is based upon computing Taylor Series expansions of the probabilities of success for treated and untreated subjects. The expansions are then integrated over the distribution of the random variables to determine the marginal probabilities of success for treated and untreated subjects. The second process is based upon an iterative process of evaluating marginal odds ratios using Monte Carlo integration. The second method was found to be computationally simpler and to have superior performance compared to the first method.

Keywords:

• Average treatment effect
• Data-generating process
• Marginal odds ratios
• Marginal treatment effect
• Monte Carlo simulations
• Simulations

Mathematics Subject Classification:

• 65C05
• 05A15

Acknowledgments

The Institute for Clinical Evaluative Sciences (ICES) is supported in part by a grant from the Ontario Ministry of Health and Long Term Care. The opinions, results, and conclusions are those of the authors and no endorsement by the Ministry of Health and Long-Term Care or by the Institute for Clinical Evaluative Sciences is intended or should be inferred. This research was supported in part by an operating grant from the Natural Sciences and Engineering Research Council (NSERC). Dr. Austin is supported in part by a New Investigator award from the CIHR.