The competing risks Cox model with auxiliary case covariates under weaker missing-at-random cause of failure
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In the analysis of time-to-event data with multiple causes using a competing risks Cox model, often the cause of failure is unknown for some of the cases. The probability of a missing cause is typically assumed to be independent of the cause given the time of the event and covariates measured before the event occurred. In practice, however, the underlying missing-at-random assumption does not necessarily hold. Motivated by colorectal cancer molecular pathological epidemiology analysis, we develop a method to conduct valid analysis when additional auxiliary variables are available for cases only. We consider a weaker missing-at-random assumption, with missing pattern depending on the observed quantities, which include the auxiliary covariates. We use an informative likelihood approach that will yield consistent estimates even when the underlying model for missing cause of failure is misspecified. The superiority of our method over naive methods in finite samples is demonstrated by simulation study results. We illustrate the use of our method in an analysis of colorectal cancer data from the Nurses’ Health Study cohort, where, apparently, the traditional missing-at-random assumption fails to hold.
KeywordsCompeting risks Masked cause of failure Missing-at-random Subtype analysis
We thank two anonymous reviewers and the associate editor for insightful comments and suggestions that improved the paper.
- Campbell PT, Jacobs ET, Ulrich CM, Figueiredo JC, Poynter JN, McLaughlin JR, Haile RW, Jacobs EJ, Newcomb PA, Potter JD et al (2010) Case–control study of overweight, obesity, and colorectal cancer risk, overall and by tumor microsatellite instability status. J Natl Cancer Inst 102(6):391–400Google Scholar
- Cancer Genome Atlas Network (2012) Comprehensive molecular characterization of human colon and rectal cancer. Nature 487(7407):330–337Google Scholar
- Hughes LA, Williamson EJ, van Engeland M, Jenkins MA, Giles GG, Hopper JL, Southey MC, Young JP, Buchanan DD, Walsh MD et al (2012) Body size and risk for colorectal cancers showing BRAF mutations or microsatellite instability: a pooled analysis. Int J Epidemiol 41(4):1060–1072Google Scholar
- Kocarnik JM, Shiovitz S, Phipps AI (2015) Molecular phenotypes of colorectal cancer and potential clinical applications. Gastroenterol Rep 3(4):269–276Google Scholar
- Lu W, Liang Y (2008) Analysis of competing risks data with missing cause of failure under additive hazards model. Stat Sin 18(1):219–234Google Scholar
- Ogino S, Nishihara R, VanderWeele TJ, Wang M, Nishi A, Lochhead P, Qian ZR, Zhang X, Wu K, Nan H et al (2016) The role of molecular pathological epidemiology in the study of neoplastic and non-neoplastic diseases in the era of precision medicine. Epidemiology 27(4):602–611Google Scholar
- Wang M, Kuchiba A, Ogino S (2015) A meta-regression method for studying etiological heterogeneity across disease subtypes classified by multiple biomarkers. Am J Epidemiol 182(3):263–270Google Scholar