Truncated Estimate in Log-Binomial Model: Algorithm and Simulation

Taisir Taisir

doi:10.3844/amjbsp.2011.20.25

Abstract

Problem statement: Relative risk has concrete meanings of comparing two groups and measuring the association between exposures and outcomes in medical and public health studies. Log-binomial model, using a log link function on binary outcomes, is straightforward to estimate risk ratios, whereas generates boundary problems. When the estimates are located near the boundary of constrained parameter space, common approaches or procedures using software such as R or SAS fail to converge. Approach: In this study we proposed a truncated algorithm to estimate relative risk using the log-binomial model. We used simulation studies on both single and multiple covariates models to investigate its performance and compare with other similar methods. Results: Our algorithm was shown to outperform other methods regarding precision, especially in high dimensional predictor space. Conclusion: The truncated IWLS method solves the slow convergence problem and provides valid estimates when previously proposed methods fail.

Highlights

For datasets with binary responses, there has been tremendous research study done by statisticians on prediction and inference
The logistic model has been among the most popular models and widely used in the fields of medical and public health studies due to its pleasant characteristics linking to estimation of the odds ratio (McCullagh and Nelder, 1999)
We focus on the discussions on COPY and Truncated Iterative Weighted Least Square method (IWLS) methods

Summary

INTRODUCTION

For datasets with binary responses, there has been tremendous research study done by statisticians on prediction and inference. The logistic model has been among the most popular models and widely used in the fields of medical and public health studies due to its pleasant characteristics linking to estimation of the odds ratio (McCullagh and Nelder, 1999). The algorithm of log-binomial models sometimes fails to converge and produces an invalid Maximum Likelihood Estimate (MLE) (Baumgarten et al, 1989; Petersen and Deddens, 2010), attributable to the constrained space of the linear predictors using log link. The methods in favor include: obtained from logistic models to approximate the Maximum Likelihood Estimation; Nonlinear Least relative risks. Squares; Scaling by the Average Prevalence; Duplication of Cases Whereas some of these methods don’t fit in the regression scenario.

MATERIALS AND METHODS

Method

RESULTS

DISCUSSION

CONCLUSION