Generalized Method Of Moments Estimation For Additive Hazard Model And Cox Model With Length-Biased Right-Censored Data

In survival analysis,real data are often censored or truncated.The length-biased data appears when the truncated variable in the left-truncated data follows a uniform distribution.This paper considers the length-biased and right-censored data which ex-ists in both censored and truncated cases.It has attracted the attention of many scholars because of its characteristics conforming to the distribution of actual experimental data.And it is of great significance to estimate and solve the model of the length-biased and right-censored data.Existing research focuses more on the construction of estimated equations,but ignores the optimal solution of them.In order to improve the estima-tion efficiency of additive hazard model and Cox proportional hazard model based on the length-biased and right-censored data,this paper takes advantage of the generalized methods of moments estimation on the basis of previous research.Then the general-ized composite estimators of two kinds of semiparametric models can be given by the construct of different moment conditions.The advantage of the generalized method of moments estimation is that it is only affected by the construction of moment conditions or estimation equations.So there is no need to know the distribution of research data in advance,which also makes the generalized composite estimator have a wider range of application and more simple calculation.At the theoretical level,this paper proves the consistency and asymptotic normal-ity of the two generalized composite estimators based on additive hazard model and Cox proportional hazard model adding the method of generalized moments.Further,we prove the consistent convergence of the corresponding cumulative hazard functions and survival functions of the two models.The results of numerical simulation and example analysis also confirmed the theoretical conclusions.In the numerical simulation part,this paper respectively fits the estimation results from different data volumes,different censoring rates,different models and different true values of parameter settings.In or-der to illustrate the excellent properties of generalized composite estimators,we contrast the difference between the generalized composite estimation method proposed in this paper with the general composite estimation and single estimation method.It can be ob-tained that the generalized composite estimator developed based on the additive hazard model has achieved an improvement in the estimated performance compared with the previous two estimation methods of the estimation of length-biased right-censored data and left-truncated right-censored data.Although the new estimator developed on the basis of Cox model also improves the variance estimation,the improved effect is lim-ited.As an example application,this paper applies the proposed generalized composite estimator to the analysis of Channing House data and Oscar data to study the effect of different covariates on the survival time of individuals.From the estimation results of parameters,it can be obtained that both the generalized composite estimator under the additive hazard model and the Cox model can achieve better estimation results.