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<p>Clinical trials often measure recurrent outcomes such as hospitalizations, infections, and drug adherence. Analyzing such events requires accounting for within-subject dependency. Extended Cox models are commonly used, but many assume a continuous risk interval, which may not be valid when risk is temporarily absent, leading to discontinuous risk intervals for repeated events. Ignoring these discontinuities can lead to biased estimates. Different models to account for discontinuities are explored here. Recurrent event analysis can be performed using extended Cox models: Andersen-Gill (AG-CP), Prentice-Williams-Peterson counting process (PWP-CP), PWP gap-time (PWP-GT), and the marginal mean rate model. To demonstrate these models, the analysis of repeated occurrences of drug non-adherence events at each follow-up in a clinical trial. Data from 4000 pregnant women were randomly selected from a double-blinded randomized trial comparing 500 vs. 1500&#xa0;mg daily calcium supplementation to prevent preeclampsia and preterm birth. Participants were followed up every 4&#xa0;weeks and supplement pills provided for next 4&#xa0;weeks until delivery. Adherence was measured using blister pack counts, and non-adherence was treated as a recurrent event. Recurrent events of non-adherence occurred when participants missed visits and uncollected pills, the participants did not have the pills and therefore were considered not at risk of non-adherence until next study visit. This was identified as discontinuous risk interval. The association of wealth index with drug non-adherence was considered for demonstration of the models. Data were structured under both continuous and discontinuous risk assumptions to estimate incidence rates (events per 1000 person-days). Models were compared using AIC, BIC, and log-likelihood. Data from 4000 women (21,156 visits) were analyzed. The incidence of non-adherence was 6.8 events per 1000 person-days (95% CI 6.6–7.0) under continuous risk and higher at 7.5 events per 1000 person-days (95% CI 7.2–7.7) under discontinuous risk. Family wealth index quintiles were significantly associated with recurrent non-adherence. The PWP-GT model was the best fitting model. In recurrent event analysis, excluding risk-free intervals from time to event is essential to estimate accurate and valid event rates. The choice between continuous and discontinuous risk intervals should reflect the follow-up process and clinical nature of the events. The Prentice-Williams-Peterson gap time model fits such data better than other extended Cox models.</p>

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Modeling Recurrent Events in Clinical Trials Using Discontinuous Risk Set: A Comparison of Extended Cox Models

  • 期刊论文

  • 发表日期：

    2026年3月5日

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  • A. John Michael Raj,
  • Tinku Thomas,
  • Pratibha Dwarkanath

摘要

Clinical trials often measure recurrent outcomes such as hospitalizations, infections, and drug adherence. Analyzing such events requires accounting for within-subject dependency. Extended Cox models are commonly used, but many assume a continuous risk interval, which may not be valid when risk is temporarily absent, leading to discontinuous risk intervals for repeated events. Ignoring these discontinuities can lead to biased estimates. Different models to account for discontinuities are explored here. Recurrent event analysis can be performed using extended Cox models: Andersen-Gill (AG-CP), Prentice-Williams-Peterson counting process (PWP-CP), PWP gap-time (PWP-GT), and the marginal mean rate model. To demonstrate these models, the analysis of repeated occurrences of drug non-adherence events at each follow-up in a clinical trial. Data from 4000 pregnant women were randomly selected from a double-blinded randomized trial comparing 500 vs. 1500 mg daily calcium supplementation to prevent preeclampsia and preterm birth. Participants were followed up every 4 weeks and supplement pills provided for next 4 weeks until delivery. Adherence was measured using blister pack counts, and non-adherence was treated as a recurrent event. Recurrent events of non-adherence occurred when participants missed visits and uncollected pills, the participants did not have the pills and therefore were considered not at risk of non-adherence until next study visit. This was identified as discontinuous risk interval. The association of wealth index with drug non-adherence was considered for demonstration of the models. Data were structured under both continuous and discontinuous risk assumptions to estimate incidence rates (events per 1000 person-days). Models were compared using AIC, BIC, and log-likelihood. Data from 4000 women (21,156 visits) were analyzed. The incidence of non-adherence was 6.8 events per 1000 person-days (95% CI 6.6–7.0) under continuous risk and higher at 7.5 events per 1000 person-days (95% CI 7.2–7.7) under discontinuous risk. Family wealth index quintiles were significantly associated with recurrent non-adherence. The PWP-GT model was the best fitting model. In recurrent event analysis, excluding risk-free intervals from time to event is essential to estimate accurate and valid event rates. The choice between continuous and discontinuous risk intervals should reflect the follow-up process and clinical nature of the events. The Prentice-Williams-Peterson gap time model fits such data better than other extended Cox models.