Nonparametric maximum likelihood estimation for competing risks survival data subject to interval censoring and truncation. (English) Zbl 1209.62049

Summary: We derive the nonparametric maximum likelihood estimate (NPMLE) of the cumulative incidence functions for competing risks survival data subject to interval censoring and truncation. Since the cumulative incidence function NPMLEs give rise to an estimate of the survival distribution which can be undefined over a potentially larger set of regions than the NPMLE of the survival function obtained ignoring failure type, we consider an alternative pseudolikelihood estimator. The methods are then applied to data from a cohort of injecting drug users in Thailand susceptible to infection from HIV-1 subtypes B and E.


62G05 Nonparametric estimation
62N02 Estimation in survival analysis and censored data
62N01 Censored data models
62P10 Applications of statistics to biology and medical sciences; meta analysis
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[1] Aalen, Nonparametric inference in connection with multiple decrement models, Scandanavian Journal of Statistics 3 pp 15– (1976) · Zbl 0331.62030
[2] Fletcher, Practical Methods of Optimization (1987) · Zbl 0905.65002
[3] Frydman, A note on nonparametric estimation of the distribution function from interval censored and truncated observations, Journal of the Royal Statistical Society, Series B 56 pp 71– (1994) · Zbl 0800.62223
[4] Frydman, Nonparametric estimation of a Markov ’illness-death’ process from interval censored observations, with application to diabetes survival data, Biometrika 82 pp 773– (1995) · Zbl 0899.62103
[5] Gentleman, Maximum likelihood for interval censored data: Consistency and computation, Biometrika 81 pp 618– (1994) · Zbl 0825.62434
[6] Groeneboom, Information Bounds and Nonparametric Maximum Likelihood Estimation (1992) · Zbl 0757.62017
[7] Hudgens , M. G. 2000 HIV, interval censoring, and competing risks Emory University
[8] Kalbfleisch, The Statistical Analysis of Failure Time Data (1980) · Zbl 0504.62096
[9] Pan, A note on inconsistency of NPMLE of the distribution function for left truncated and case I interval censored data, Lifetime Data Analysis 5 pp 281– (1999) · Zbl 0934.62032
[10] Peto, Empirical survival curves for interval censored data, Applied Statistics 22 pp 86– (1973)
[11] Turnbull, The empirical distribution function with arbitrarily grouped, censored and truncated data, Journal of the Royal Statistical Society, Series B 52 pp 290– (1976) · Zbl 0343.62033
[12] Vanichseni, Continued high HIV-1 incidence in a vaccine trial preparatory cohort of injecting drug users in Bangkok, Thailand, AIDS (2001)
[13] Wellner, A hybrid algorithm for computation of the nonparametric maximum likelihood estimator from censored data, Journal of the American Statistical Association 92 pp 945– (1997) · Zbl 0889.62026
[14] Yu, Asymptotic variance of the GMLE of a survival function with interval censored data, Sankhyā 60 pp 184– (1998) · Zbl 1058.62556
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