Application of Observed and Simulated Data on Log-Binomial and Similar Models

• Activity Number: 42
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Shailendra Banerjee*+
• Companies: CDC
• Keywords: Log-Binomial Model ; Logistic Regression Model ; Numerical Optimization Procedure

Abstract

Relative risk can be directly estimated from log-binomial model to assess risk in a binary outcome data. But, log-binomial model has some inherent estimating problems. Its log-likelihood function produces score function which typically will have dominating term for large probability of event. In this situation, we might get false convergence, non-convergence, or out-of bounds estimated probabilities. But, for logistic regression model, large value of probability of event can not make any dominating term . Thus, the log binomial model has some constraints on the coefficients in order for the estimated probabilities to be between 0 and 1. Maximum likelihood estimate from log-binomial model can be obtained from score equation by solving for the parameters. However, in complicated situations, a numerical solution is obtained through Newton-Raphson algorithm based on a probable starting value. Clearly, in all numerical optimization procedure, starting values seem to be very important in terms of convergence and number of iterations it requires. In this study, we tested the effect of starting values on the convergence of log-binomial model using simulated data.