Model choices to obtain adjusted risk difference estimates from a binomial regression model with convergence problems: An assessment of methods of adjusted risk difference estimation

Background

Risk Difference (RD) is becoming the measure of choice for estimating effect size in antimalarial drug efficacy trials. Calculating RD using binomial regression is prone to model nonconvergence. Cheung’s modified ordinary least squares (OLS) method is a proven technique for handling non-convergence when estimating RD. Other promising methods include the Poison, Additive Binomial Regression and binary regression models fitted using the statistical package R. (Deddens’) Copy method that was primarily developed to overcome non-convergence of log-binomial regression models when estimating risk ratios is another potential method. Simulations were conducted to compare the performance of the Copy method against four alternatives (Cheung’s modified OLS method, the Additive Binomial Regression Model fitted with the blm algorithm, the binary regression model fitted with the glm2 algorithm, and the Poisson model with identity link and robust standard errors fitted with the glm algorithm) for obtaining RD estimates when a binomial model fails to converge.

Methods

We computed estimates of efficiency and bias with treatment arm efficacies of (a) 60% vs. 85%, (b) 95% vs. 90%, (iii) 95% vs. 98% using simulation studies. A total of 5,000 datasets were simulated under each of these three scenarios.

Results

The modified OLS method and the binary regression model fitted using the glm2 algorithm in R provided unbiased, efficient estimates of RD across all assessed scenarios. In contrast, the Copy method yielded biased estimates of RD even when 100% convergence was achieved. The Poisson and Additive Binomial Regression models had 100% and almost 100% convergence rates respectively, but both produced very slightly biased RD estimates.

Conclusion

The Copy method is not suitable for estimating RD when binomial regression model fitting fails to converge. Cheung’s modified OLS or the binary regression model fitted using the glm2 algorithm in R should be the method of choice to overcome non-convergence with binomial models for calculating adjusted RD estimates.