Premium
Further results on the non‐parametric linear regression model in survival analysis
Author(s) -
Aalen Odd O.
Publication year - 1993
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780121705
Subject(s) - covariate , statistics , mathematics , regression analysis , proportional hazards model , parametric statistics , econometrics , martingale (probability theory) , linear regression , goodness of fit , linear model , random effects model , kernel density estimation , medicine , estimator , meta analysis
This paper gives further developments of a non‐parametric linear regression model in survival analysis. Three subjects are studied. First, martingale residuals, originally developed for the Cox model, are introduced for our linear model. Their theory is developed and they are shown to be useful for judging goodness of fit. The second focus of the paper is on the use of bootstrap replications to judge which features of the cumulative regression plots are likely to reflect real phenomena and not merely random variation. In particular, this is applied to judging whether the effect of a covariate disappears over time, a problem for which no formal test exists. The third subject is density type, or kernel, estimation of the regression functions themselves. This might give more direct information than the cumulative plots. The approaches are illustrated by data from a clinical trial of carcinoma of the oropharynx, and by survival times of grafts in renal patients.