Robust Treatment Comparison Based on Utilities of Semi-Competing Risks in Non-Small-Cell Lung Cancer

Thomas A. Murray, Peter F. Thall, Ying Yuan, Sarah McAvoy, Daniel R. Gomez

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


A design is presented for a randomized clinical trial comparing two second-line treatments, chemotherapy versus chemotherapy plus reirradiation, for treatment of recurrent non-small-cell lung cancer. The central research question is whether the potential efficacy benefit that adding reirradiation to chemotherapy may provide justifies its potential for increasing the risk of toxicity. The design uses two co-primary outcomes: time to disease progression or death, and time to severe toxicity. Because patients may be given an active third-line treatment at disease progression that confounds second-line treatment effects on toxicity and survival following disease progression, for the purpose of this comparative study follow-up ends at disease progression or death. In contrast, follow-up for disease progression or death continues after severe toxicity, so these are semi-competing risks. A conditionally conjugate Bayesian model that is robust to misspecification is formulated using piecewise exponential distributions. A numerical utility function is elicited from the physicians that characterizes desirabilities of the possible co-primary outcome realizations. A comparative test based on posterior mean utilities is proposed. A simulation study is presented to evaluate test performance for a variety of treatment differences, and a sensitivity assessment to the elicited utility function is performed. General guidelines are given for constructing a design in similar settings, and a computer program for simulation and trial conduct is provided. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)11-23
Number of pages13
JournalJournal of the American Statistical Association
Issue number517
StatePublished - Jan 2 2017

Bibliographical note

Publisher Copyright:
© 2017 American Statistical Association.


  • Bayesian analysis
  • Group sequential
  • Piecewise exponential model
  • Radiation oncology
  • Randomized comparative trial
  • Utility elicitation


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