Biased Estimates of Treatment Effect in Randomized Experiments with Nonlinear Regressions and Omitted Covariates
研究了随机实验中，若遗漏必要协变量，某些非线性回归模型会导致处理效应估计有偏，并给出了渐近偏差的条件，发现线性或指数回归可保证无偏，且对删失生存数据，指数模型比Cox比例风险模型偏差更小。
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.