Best method to analyze reasons for discontinuation of treatment

Question

To evaluate my hypothesis that females have worse treatment effectiveness compared to males in patients with axial spondyloarthritis, I wish to investigate reasons for discontinuation in addition to treatment retention rates.

First, I used Kaplan-Meier plots to investigate treatment survival and stratified by sex. This resulted in a highly significant and clinically relevant result. Second, I quantified this risk through univariable and multivariable Cox proportional-hazards model and assessed females' HR risk for discontinuation of treatment.

Now I wish to investigate my following outcome: reasons for discontinuation of treatment, classified as lack of efficacy (LE), adverse events (AE), other, and remission (RE).

Approach 1: Recode reasons for discontinuation into a new variable, with LE as 1 rest as 0. Similarly, recode a new variable with AE as 1 and the rest as 0. Use logistic regression (2x) to evaluate the probability of having AE/LE, compare between sexes, and calculate relative risk and risk difference.

Approach 2: Use the Cox proportional-hazards model with the same variable "time" as in the first analysis, but now recode "event AE" as 1 and censor observations as 0 if it is other than AE. Similarly, the same for LE. Then calculate females' risk for adverse events and lack of efficacy (i.e., HR) compared to males.

Which approach is more sensible? Is another approach better?

Answer 1

Your situation calls for a competing-risks model, in which a terminal event (discontinuation of treatment in this case) can occur for a set of mutually exclusive reasons (LE, AE, RE here). As the "Multi-state models and competing risks" vignette notes (page 8):

A common mistake with competing risks is to use the Kaplan-Meier separately on each event type while treating other event types as censored.

That "common mistake" is, unfortunately, pretty much what you propose to do.

The way to proceed is to code your event marker as a factor coding the reason for discontinuation, with its reference level representing right censoring. That allows both for Kaplan-Meier displays and Cox models, as explained in the vignette. For Cox models you will have to make choices about whether the different event types share baseline hazards, covariates, and coefficient values for shared covariates.