The Quantile Regression And Its Application In Diabetes Care

Generally we take advantage of regression analysis to study relationshipbetween one random variable and one or more controllable variables when wemodel to survival data. For censored data, we common use Cox proportionalhazard model which is ?exible and received many attentions. However, thismodel places significant assumptions on the behavior of conditional survivalfunctions and sometimes the assumptions is unfounded. Censored quantileregression proposed this paper is a more ?exible alternative approach thanCox proportional hazard model. Especially, the regression quantile coe?cientsare interpretable as direct regression e?ects on the survival times. It mayestimate the quantile function of the conditional distribution and representthe conditional distribution with the di?erent quantile estimate function inthe di?erent position, thus we can obtain the more information about theconditional distribution.Censored quantile regression can be viewed as generalizations to thequantile regression, so the paper firstly introduce the theory of quantileregression including the calculation about quantile regression and propertiesand the the asymptotic of quantile regression estimators. Secondly, thetheory of survival analysis is described, involving to theory of Cox regressionin survival data and details of censored quantile regression. At last we applycensored quantile regression to censored data of diabetes and obtain di?erentregression functions in di?erent quantile point of survival time which givesome prevention and treatment proposals for diabetes patients.