Development and application of semi-parametric survival analysis for time dependent non-linear prognostic factors

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1. Considering the situation that (i) the proportional hazard assumption employed in the Cox regression analysis does not hold, (ii) Covariates depend on time and the relationship between survival time and prognostic factors are non-linear, we developed a flexible method of the analysis of survival data based on the following ideas; (a) employed the first order Spline regression function for modeling the relationship of survival time and prognostic factors, (b) introduced tensor product to take into account the interaction of prognostic factors, and c introduced new algorithm for selecting to meaningful interaction terms and knots. Those theoretical problems that are arisen in the development are attacked by investigators under the leadership of the head investigator. The results are published in those papers listed below.2. We developed a computer program for the new method and applied it to the data from the Hisayama cohort study to explore the relationship between stroke and covari … More ates. It is shown that the risk factors of the stroke that had non-linear relationship with survival time are detected in addition to the known risk factors. Also their risks on the stroke are assessed. Papers demonstrating the usefulness of the method were presented at several international meetings, and a paper submitted for publication, accepted and in press in the Statistics in Medicine.3. The method above is for the survival data. But it is also useful for studying non-linear relationship of response variable and covariates in non-survival data. To demonstrate it the method was applied to the dada from male junior high school students for elucidate linear and non-linear relationships between reduced visual acuity and its contributing factors including living habits and environment. A paper summarizing the results is submitted for publication in a journal.4. At least one international conference was held in a year to publicize the results that we obtained and had critical review of our research by world leading scientists. Less