Tutorial: Survival Estimation for Cox Regression Models with Time-Varying Coefficients UsingSASandR

Abstract

Survival estimates are an essential compliment to multivariable regression models for time-to-event data, both for prediction and illustration of covariate effects. They are easily obtained under the Cox proportional-hazards model. In populations defined by an initial, acute event, like myocardial infarction, or in studies with long-term followup, the proportional-hazards assumption of constant hazard ratios is frequently violated. One alternative is to fit an interaction between covariates and a prespecified function of time, implemented as a time-dependent covariate. This effectively creates a time-varying coefficient that is easily estimated in software such as SAS and R. However, the usual programming statements for survival estimation are not directly applicable. Unique data manipulation and syntax is required, but is not well documented for either software. This paper offers a tutorial in survival estimation for the time-varying coefficient model, implemented in SAS and R. We provide a macro coxtvc to facilitate estimation in SAS where the current functionality is more limited. The macro is validated in simulated data and illustrated in an application.

Pseudomonas aeruginosa and acute rejection independently increase the risk of donor-specific antibodies after lung transplantation

“…Of the 147 recipients, 87 (59%) who had Pseudomonas aeruginosa isolation after transplantation did not have Pseudomonas aeruginosa isolation before transplantation. Although the DSA appeared before Pseudomonas isolation in 10.7% of our cohort, these cases were excluded from the time‐dependent Cox proportional hazards analyses and did not contribute to the risk conferred by Pseudomonas isolation on DSA development . Gram‐negative bacilli other than Pseudomonas aeruginosa were isolated at least once in 182 (40%) recipients, and gram‐positive cocci were isolated in 103 (22%) recipients.…”

“…In such analyses (say, for the development of DSA), the “time to outcome” was identified as occurring when the first DSA was detected, and the risk factor was treated in a time‐dependent manner by selecting the first time after transplant that Pseudomonas was isolated in the bronchial wash, BAL, or sputum. Therefore, in all cases in these analyses, the explanatory variables occurred before the outcome …”

Association between oral leukoplakia and risk of upper gastrointestinal cancer death: A follow‐up study of the Linxian General Population Trial

“…Hazard ratios (HRs) and 95% CIs were calculated using standard Cox proportional hazard models (PHMs) and proportional subdistribution hazard models (PSHMs), adjusting for age at baseline (continuous variable), gender (men vs. women), BMI (continuous variable), smoking (yes/no), alcohol consumption (yes/no), tooth loss (yes/no), family cancer history (yes/no), and commune (Yaocun, Rencun, Donggang, and Hengshui [as a reference]). The proportionality assumption was examined using models that allowed time‐dependent HRs; no differences in time variables were observed . A possible interaction between OL and basic characteristics was determined using stratified models, such as age at baseline (<52 and ≥52, based on the median age), gender (men vs. women), smoking (yes/no), and alcohol consumption (yes/no).…”

Optimal Timing of Anticoagulant Treatment After Intracerebral Hemorrhage in Patients With Atrial Fibrillation

“…For a given set of patient characteristics (ie, the high-and lowrisk patients), the cause-specific hazards were combined to compute the thrombotic event, hemorrhagic event, and the combined CIF. 22 Thus, the effect of the treatment starting times could be assessed for each event separately and for the combined events. The main results were stratified by sex and patient risk status.…”