Non-Proportional Hazards and Informative Censoring in a Cancer Trial
A three-centre randomised trial compares a new treatment with standard care in 240 patients with a rare cancer. The primary endpoint is time to progression. Over a median follow-up of 26 months, 168 events are observed and 72 patients are censored. Kaplan–Meier curves separate after 6 months. A Cox model adjusted for age gives a treatment hazard ratio of 0.72 (95% CI 0.55–0.94). The proportional hazards test using Schoenfeld residuals gives p = 0.03 for treatment, with a trend suggesting the hazard ratio moves towards 1 after 18 months. Censoring is 18% in centres A and B but 40% in centre C, where 11 patients withdrew because of toxicity and the remainder were administratively censored at 24 months. Centre C contributes 30% of the sample. The trial statistician must decide whether to report the adjusted hazard ratio as the primary effect measure.
1. Interpret the Schoenfeld test and the trend in the hazard ratio. What should the statistician report as the primary effect measure, and why is the adjusted hazard ratio potentially misleading?
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The Schoenfeld test gives p = 0.03, which is evidence against a constant treatment hazard ratio over time; it is not overwhelming, but the trend towards a hazard ratio of 1 after 18 months is clinically material. Under non-proportional hazards, the Cox hazard ratio is a weighted average of time-specific hazard ratios, with weights determined by the event and censoring distribution. It therefore does not estimate a single constant causal effect and its interpretation depends on the follow-up pattern. Reporting 0.72 as “the” treatment effect would be misleading because much of the apparent benefit may be concentrated before 18 months. Defensible alternatives include a pre-specified time-segmented hazard ratio (for example 0–18 months and after 18 months), a restricted mean survival time difference over a clinically relevant horizon such as 24 or 36 months, or milestone survival differences. The statistician should show the Kaplan–Meier curves, the log-cumulative hazard plot, and a time-varying effect estimate, and should state explicitly that proportional hazards is not supported. The age-adjusted Cox model can remain a secondary analysis, not the primary effect measure.
2. Evaluate the censoring pattern in centre C. Under what assumptions are Kaplan–Meier and Cox estimates valid, and what sensitivity analyses would you request?
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Kaplan–Meier and Cox estimates require censoring to be non-informative after conditioning on covariates in the model: conditional on age and treatment, censored patients should have the same future progression risk as those still at risk. Administrative censoring at 24 months is often plausible if it is unrelated to prognosis. Withdrawal because of toxicity is more suspect, because toxicity may be associated with treatment and with underlying health status, and therefore with progression risk. If those 11 patients had different prognosis from those remaining under observation, the estimates are biased; Kaplan–Meier may overstate survival if higher-risk patients leave early. Centre C also contributes 30% of the sample, so the impact could be material. Requested sensitivity analyses include inverse probability of censoring weighting using a censoring model that includes treatment, age, centre, and toxicity; a joint model or competing-risk-type approach if toxicity is a terminal event for the endpoint definition; best-case and worst-case imputation for the withdrawals; analysis excluding centre C; and a frailty or centre-stratified model to separate centre effects from censoring. Centre-specific results should be reported.
3. Draft a short conclusions paragraph that is defensible given the diagnostics.
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The trial shows an early separation in progression-free survival, with an age-adjusted hazard ratio of 0.72 (95% CI 0.55–0.94), but the proportional hazards assumption is not supported: the treatment effect appears to weaken after about 18 months. The hazard ratio should therefore be interpreted as a time-averaged summary, not a constant effect. Over a 24-month horizon the restricted mean progression-free survival difference is the more interpretable primary measure, supported by the Kaplan–Meier curves and a time-segmented hazard ratio. The centre C censoring pattern is a material sensitivity: the main result should be repeated with inverse probability of censoring weighting and with centre C excluded. If the conclusions are stable across those analyses, the trial provides evidence of a delayed but clinically relevant benefit; if not, the result should be reported as suggestive and the informative censoring should be acknowledged as a limitation.