Survival › Time-to-event

Cox PH with time-varying covariates

Cox regression with time-varying covariates models predictors that change during follow-up, supplied in (start, stop, event) counting-process format.

What is Cox PH with time-varying covariates?

When a covariate's value changes during follow-up (e.g. cumulative dose, biomarker measured at multiple visits), the standard fixed-covariate Cox model misrepresents the timing. The counting-process format expresses each subject as one row per time interval during which the covariates were constant, with a (start, stop) window and an event flag for whether the event happened at stop.

Different from coxph_tt: coxph_tv handles covariates whose values actually change; coxph_tt handles covariates whose *effect* (β) changes with time on a fixed baseline value.

When should I use Cox PH with time-varying covariates?

  • Cumulative-exposure covariates (e.g. dose over time).
  • Time-updated biomarkers from longitudinal measurements.
  • Adverse events whose effect on subsequent survival you want to model.

What data does it need?

Start, stop, event + one or more predictors (some varying within subject).

What does it report?

HR table with robust SEs (clustered on subject) + concordance + LR test.

What does it assume?

  • PH (constant HR over time for any fixed covariate value).
  • Independent subjects.
  • No carry-over confounding from time-varying covariate.

How do I interpret the result?

HRs from time-varying Cox describe the instantaneous hazard ratio at the current covariate value — not a cumulative-exposure summary.

See also

References

  • Therneau & Grambsch (2000). Modeling Survival Data: Extending the Cox Model.