Nonparametric Estimation of Cumulative cause Specific Reversed Hazard Rates under Masked Causes of Failure
01 Jun 2017-Vol. 2, Iss: 1
TL;DR: This paper considers the nonparametric estimation of cumulative cause specific reversed hazard rates for left censored competing risks data under masked causes of failure with maximum likelihood estimators and least squares type estimators.
Abstract: In the analysis of competing risks data, it is common that the exact cause of failure for certain study subjects is missing. This problem of missing failure type may be due to inadequacy in the diagnostic mechanism or reluctance to report the exact cause of failure. In the present paper, we consider the nonparametric estimation of cumulative cause specific reversed hazard rates for left censored competing risks data under masked causes of failure. We first develop maximum likelihood estimators of cumulative cause specific reversed hazard rates. We then consider the least squares type estimators for cumulative cause specific reversed hazard rates, when the information about the conditional probability of exact failure type given a set of possible failure types is available. Simulation studies are conducted to assess the performance of the proposed estimators. We illustrate the applicability of the proposed methods using a data set. Abstract
References
More filters
49,597 citations
TL;DR: Generalized Estimating Equations is a good introductory book for analyzing continuous and discrete correlated data using GEE methods and provides good guidance for analyzing correlated data in biomedical studies and survey studies.
Abstract: (2003). Statistical Analysis With Missing Data. Technometrics: Vol. 45, No. 4, pp. 364-365.
6,960 citations
"Nonparametric Estimation of Cumulat..." refers background in this paper
...…gi), where ti, δi, gi are the observed values of T, δ, G respectively for i = 1, 2...n. Assume that the missing at random assumption for observing gi ( Little and Rubin (1987)) that is given failure time and failure type, probability of observing g is same for all the types contained in g…...
[...]
TL;DR: This book complements the other references well, and merits a place on the bookshelf of anyone concerned with the analysis of lifetime data from any eld.
Abstract: (2003). The Statistical Analysis of Failure Time Data. Technometrics: Vol. 45, No. 3, pp. 265-266.
4,600 citations
TL;DR: In this paper, the EM algorithm converges to a local maximum or a stationary value of the (incomplete-data) likelihood function under conditions that are applicable to many practical situations.
Abstract: Two convergence aspects of the EM algorithm are studied: (i) does the EM algorithm find a local maximum or a stationary value of the (incomplete-data) likelihood function? (ii) does the sequence of parameter estimates generated by EM converge? Several convergence results are obtained under conditions that are applicable to many practical situations Two useful special cases are: (a) if the unobserved complete-data specification can be described by a curved exponential family with compact parameter space, all the limit points of any EM sequence are stationary points of the likelihood function; (b) if the likelihood function is unimodal and a certain differentiability condition is satisfied, then any EM sequence converges to the unique maximum likelihood estimate A list of key properties of the algorithm is included
3,414 citations
"Nonparametric Estimation of Cumulat..." refers background in this paper
...Thus the EM algorithm mentioned above converges to this unique maximum (Dempster et al. (1977), Wu (1983)) [33,34]....
[...]
TL;DR: "Statistical Models Based on Counting Processes" may be viewed as a research monograph for mathematical statisticians and biostatisticians, although almost all methods are given in sufficient detail to be used in practice by other mathematically oriented researchers studying event histories.
Abstract: Modern survival analysis and more general event history analysis may be effectively handled in the mathematical framework of counting processes, stochastic integration, martingale central limit theory and product integration. This book presents this theory, which has been the subject of an intense research activity during the past one-and-a-half decades. The exposition of the theory is integrated with the careful presentation of many practical examples, based almost exlusively on the authors' experience, with detailed numerical and graphical illustrations. \"Statistical Models Based on Counting Processes\" may be viewed as a research monograph for mathematical statisticians and biostatisticians, although almost all methods are given in sufficient detail to be used in practice by other mathematically oriented researchers studying event histories (demographers, econometricians, epidemiologists, actuariala mathematicians, reliability engineers, biologists). Much of the material has so far only been available in the journal literature (if at all), and a wide variety of researchers will find this an invlauable survey of the subject.
2,852 citations