🧭 The Problem at Hand
Parametric and nonparametric duration models assume proportional hazards: the effect of a covariate on the hazard rate remains constant over time. When that assumption fails, a common correction is to interact covariates with some function of time. Including such interactions converts those predictors into time-varying covariates, and the model specification should reflect that change.
🛠️ How Corrections Are Commonly Mis-specified
Many studies that begin with only time-invariant covariates nonetheless continue to estimate models as if all covariates remain time-invariant after adding time interactions. This mismatch between the corrective interaction and the rest of the specification introduces bias, especially for the covariates that are interacted with time.
📚 What Was Reviewed and How
- Reviewed over forty political science articles that use duration models and apply nonproportional-hazards corrections.
- Focused on studies that started with time-invariant covariates and then implemented corrections by interacting covariates with time.
📈 Key Findings
- The majority of such studies suffer from incorrect model specification after applying time interactions.
- Misspecification produces biased estimates, with the largest distortions occurring for covariates interacted with time.
- Properly specifying and estimating models that treat those terms as time-varying typically yields substantively or statistically different results (changes in effect size, significance, or substantive interpretation).
⚖️ Why This Matters
Misapplying nonproportional-hazards corrections undermines inference about duration processes (for example, survival of regimes, policy adoption timing, or event timing analyses). Correct specification is essential to avoid biased estimates and misleading substantive conclusions. The evidence shows that authors and reviewers should treat interactions with time as time-varying covariates and adjust the model specification accordingly.
