The Competing Risks Cox Model When Failure Type Is Missing Not at Random

• Activity Number: 286 - Missing Data Methods
• Type: Contributed
• Date/Time: Wednesday, August 11, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Biometrics Section
• Author(s): Benjamin W Langworthy* and Tomotaka W Ugai and Shuji Ogino and Molin Wang
• Companies: Harvard University and Harvard University and Harvard University and Harvard T.H. Chan School of Public Health
• Keywords: Competing risks; Cox Model; Non-ignorable missingness; Cause specific hazard; Partial likelihood

Abstract

When time-to-event data has multiple potential causes, a competing risks Cox model is frequently used to estimate cause specific hazard ratios. For many data sets the cause of failure may be missing for many subjects. Existing methods assume either missing-completely-at-random or missing-at-random where the missingness is independent of failure type conditional on observed variables. We develop a method that can consistently estimate cause specific hazard ratios even when failure type is missing-not-at random. By assuming a parametric form for the missingness model, we derive a joint partial likelihood for the missingness model and the cause specific hazard ratios. When the missingness model is correctly specified this likelihood-based approach leads to consistent estimates of the cause specific hazard ratios and missing model parameters. We compare our method to existing methods that assume failure type is missing-at-random in simulation studies. To illustrate our method we use a prospective cohort study, the Nurses’ Health Study and the Health Professionals Follow-up Study, to estimate the association of smoking with the incidence of colorectal cancer molecular subtypes.