Using Discrete-Time Survival Analysis to Examine Hazard Estimates of Biochemical Failure Among Prostate Cancer Patients

Abstract

To research and explicate under what conditions the discrete-time survival method is comparable with Cox regression model respect to hazard estimation. A medical research prostate cancer data in Michigan largest health care system was used. The survival and hazard functions of biochemical failure were tested under both Cox regression and discrete-time survival models. Data were restructured from “Person-Level” to “Person-Period” before testing in the discrete-time survival model. This study was undertaken to examine the effect of four different sample sizes and two different time periods to investigate their corresponding impact survival and hazard estimation and goodness of fit statistics between Cox regression and discrete-time survival models. The univariate analysis was tested for each individual factor for different sample size n=1577, n=1213, n=809, and n=422 under both Cox regression and discrete-time survival models. All single covariates were strong predictors of biochemical failure in the univariate analysis. In the Cox regression under sample size n=1577, the patient in high-risk group, with nadir time less than 2 years, or with no hormone treatment before RT had 2.541, 3.947, or 4.974 times more likely to have biochemical failure than the patient in the intermediate-risk group, nadir time greater than 2 year, or with hormone treatment before RT. In the discrete-time survival model with 10 time periods, the hazard estimates were 2.717 times for high-risk patient group, 5.457 times for no hormone receiver before RT, and 4.161 times higher for patients with less than 2 year nadir time. Similarly, in the discrete-time model with 5 time periods, the hazard estimates were 3.242, 5.150 and 3.303 times higher correspondingly. Both discrete-time survival model and Cox regression model provided similar hazard estimations. Sample size had an impact on survival analysis and hazard estimates. Small sample size had larger hazard estimation in general.Abstract 2999VariableCox Regression ModelDiscrete-time Survival Model5 Time PeriodsDiscrete-time Survival Model10 Time PeriodsN=1577N=6041N=9692HZ95% CIHZ95% CIHZ95% CIHigh Risk2.541∗∗∗2.141 - 3.0173.242∗∗∗2.474 - 4.2472.717∗∗∗2.262 - 3.265Nadir Time < 2 yrs3.947∗∗∗3.242 – 4.8053.303∗∗∗2.463 – 4.4294.161∗∗∗3.389 – 5.109No HT before RT4.974∗∗∗3.856 – 6.4165.150∗∗∗3.493 – 7.5945.457∗∗∗4.183 – 7.120Goodness-of-fit-2LL7106.81787.93825n parameters3813AIC7166.81803.93851BIC7182.91857.63944.3 Open table in a new tab