Based On The Generalized Add - Multiply Risk Cost Saving Experimental Study Of The Model

In epidemiological studies, clinical trials, financial analysis and other scientific investigations, event rate is always low while the cost of covariate assembling for all the subjects is quite huge. Hence, it is hard for researchers to conduct some studies. Cost effective designs are proposed to solve this problem. Under such designs, people only collect covariate histories for the subjects who experience the event of interest (i.e. cases) and a small random subset selected from the cohort. Case-cohort design and nested case control (NCC) design are two commonly used economical designs. Case-cohort design involves the collection of data for a small random sample from the entire cohort called the subcohort and all the cases in the cohort regardless of whether or not they are in the subcohort. Many authors developed statistical methods for fitting case-cohort data with some semipara-metric survival models, such as Cox model, proportional odds model, accelerated failure time model and linear transformation models. In NCC design, controls are sampled from the risk set at event times. Meanwhile, subsequent control sam-plings are independent. The research of NCC design is focused on Cox model and transformation models. In this paper, case-cohort design and the NCC design are applied to general additive-multiplicative hazard model. Additive-multiplicative hazard model is a commonly used hazard model which includes Cox model (mul-tiplicative model) and additive hazard model as special cases. This paper consists of the following three parts:1. Case-cohort analysis with univariate additive-multiplicative hazard model. Because the covariate information can’t be completely observed, new estimating functions are needed. A kind of inverse selection probability weighted estimat-ing function is constructed. Two kinds of typical sampling schemes:independent Bernoulli sampling and stratified simple random sampling are considered. This paper studies the estimating methods and inference procedures respectively under these two kinds of sampling schemes. Monte Carlo studies are used to assess the performance of estimators under finite sample sizes. The NWTSG study is used to illustrate the proposed methods.2. Case-cohort analysis with multivariate additive-multiplicative hazard mod-el. Multivariate failure time data has been more common in economy, finance, biomedical applications and other scientific investigations. It is usually complicat-ed to analyze multivariate failure time data because of the unknown dependence structures and the censoring. Literature on economical design analysis of multi- variate failure time data has been quite limited. This article concentrates on the case-cohort analysis with multivariate failure time data under a class of marginal additive-multiplicative hazard models. Multiple events time data and clustered failure time data are discussed. Estimating methods and inference procedures are provided. Simulation results are used to assess the performance of estimators under finite sample sizes. The Busselton study is used to illustrate the methods.3. NCC analysis with univariate additive-multiplicative hazard model. Inde-pendent Bernoulli sampling and stratified simple random sampling are considered. Under each sampling scheme, a kind of inverse selection probability weighted esti-mating function is constructed. The resulting estimators can be shown to be con-sistent and asymptotically normally distributed. Consistent estimator for baseline hazard functions is also proposed. Simulation results are used to assess the per-formance of estimators under finite sample sizes. The NWTSG study is used to illustrate the methods.The conclusions of this paper provide theoretical and practical guides for clinical researchers.