Biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates

SUMMARY: Certain important nonlinear regression models lead to biased estimates of treatment effect, even in randomized experiments, if needed covariates are omitted. The asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates. The asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential, and, in regular cases, this is a necessary condition for zero bias. Many commonly used models do have such exponential regressions; thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models. For moderately censored exponential survival data, analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of Cox, if needed covariates are omitted. Simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size.