Abstract: In this paper,the comparison is qiven between the random simulation of the maximum likelihood estimators and the quasi-maximum likelihood estimators of the population-averaged treatment effects in the one-dimensional structural regression models with one covariate and the measurement errors.It is found that one of the formulae can be replaced by the other,and they are not influenced by the measurement errors.When the other errors(that is,they are different from the measurement errors)are little,the results are similar when using the two formulae,but the use of the quasi-maximum likelihood estimators is better than the use of the maximum likelihood estimators.On the contrary,when the other errors are large,the use of the maximum likelihood estimators is better than that of the quasi-maximum likelihood estimators. 

Key words: population-averaged treatment effects； maximum likdlihood estimators； quasi-maximum likelihood estimators； random sampling； measurement error； random simulation； comparison；