CoxRegressionII.pptVIP

Satistics 262 Cox Regression II Monday “Gut Check” Problem… Write out the likelihood for the following data, with weight as a time-dependent variable: SAS code for a time-dependent variable… proc phreg data=example; model time*censor(0) = weight; if time3 then weight=w0; if time=3 and time6 then weight=w3; if time=6 and time9 then weight=w6; if time=9 then weight=w9; run; Model results Using baseline weight: HR=2.8 Using weight as time-changing variable: HR=9.3    Males: 1, 3, 4, 10+, 12, 18 (subjects 1-6) Females: 1, 4, 5, 9+ (subjects 7-10) The PL  Age is a common confounder in Cox Regression, since age is strongly related to death and disease. You may control for age by adding baseline age as a covariate to the Cox model. A better strategy for large-scale longitudinal surveys, such as NHANES, is to use age as your time-scale (rather than time-in-study). You may additionally stratify on birth cohort to control for cohort effects. Age as time-scale The risk set becomes everyone who was at risk at a certain age rather than at a certain event time. The risk set contains everyone who was still event-free at the age of the person who had the event. Requires enough people at risk at all ages (such as in a large-scale, longitudinal survey). The likelihood with age as time 3. Residuals Residuals are used to investigate the lack of fit of a model to a given subject. For Cox regression, there’s no easy analog to the usual “observed minus predicted” residual of linear regression Martingale residual ci (1 if event, 0 if censored) minus the estimated cumulative hazard to ti (as a function of fitted model) for individual i: ci-H(ti,Xi,??i) E.g., for a subject who was censored at 2 months, and whose predicted cumulative hazard to 2 months was 20% Martingale=0-.20 = -.20 E.g., for a subject who had an event at 13 months, and whose predicted cumulative hazard to 13 months was 50%: Martingale=1-.50 = +.50 Gives excess failures. Martingale residuals are not s