Introducing Two-Way and Three-Way Interactions into the Cox Proportional Hazards Model Using SAS

The Cox proportional hazards model to explore the effect of explanatory variables on survival is by far the most popular and powerful statistical technique. It is used throughout a wide variety of types of clinical studies. However, special techniques are required when multiple interaction terms are introduced into the Cox model. This paper provides an in-depth analysis, with some explanation of the SAS code. It examines two-way and three-way interaction terms into the Cox proportional hazards model using SAS. Examples of using the PHREG procedure are drawn from the recently accepted article in the Journal of American Geriatrics Society (JAGS) (1). CASE STUDY: DEPRESSTION, DIABETES, AND MORTALITY The Prevention of Suicide in Primary Care Elderly: Collaborative Trial (PROSPECT) was a clusterrandomized controlled trial designed to compare an algorithm-based intervention with usual care to reduce major risk factors of suicide (e.g., depression) for older primary care patients (2, 3). The PROSPECT data contain survival times for 1,226 patients in 20 primary care practices. The median follow-up time was 98 months and ranged from 1 to 116 months. The twenty practices were randomly assigned to intervention or usual care. The variables are as follows: time is the time in months from the baseline interview to death. death 1 = dead; 0 = censored. intervention 1 = intervention practices; 0 = usual care practices. practice is the practice number for each patient. major 1 = major depression; 0 = no depression. minor 1 = minor depression; 0 = no depression. diabetes 1 = diabetes; 0 = no diabetes. age is the age in years at baseline. gender 1 = female; 0 = male. education is the number of years of schooling completed. marital 1 = married; 0 = other. smoking 1 = smoker; 0 = non-smoker. cognition is a measure of the cognitive impairment, ranging from 18 to 30 (lower scores indicating greater cognitive impairment). suicidal 1 = suicidal ideation; 0 = no suicidal ideation. charlson is the Charlson comorbidity index at baseline.