A review of the existing methodology in competing-risk theory☆

Abstract The theory of competing risks is concerned with assessing a specific risk in the complicating presence of other risks. This paper reviews existing methods for dealing with the problem. Much of the existing methodology (both parametric and nonparametric) involves the assumption of independent risks. This situation receives most of the attention in this paper, although a brief discussion summarizing attempts to deal with the complicated problem of dependent risks is given. Adaptations of methods used to incorporate concomitant information in survival analyses are discussed. Brief reference is made to the most relevant graphical methods that have been proposed. The review tends to be verbal in nature, leaving the interested reader to check out mathematical details in the references.

[1]  R. J. Herman,et al.  Maximum Likelihood Estimation For Multi-Risk Model , 1971 .

[2]  Letter to the Editor—A Note on Conditional Probability of Failure When Hazards are Proportional , 1963 .

[3]  H. A. David,et al.  The Theory of Competing Risks. , 1979 .

[4]  P. Clifford.  Nonidentifiability in stochastic models of illness and death. , 1977, Proceedings of the National Academy of Sciences of the United States of America.

[5]  D. Cox,et al.  THE ANALYSIS OF EXPONENTIALLY DISTRIBUTED LIFE-TIMES WITH Two TYPES OF FAILURE , 1959 .

[6]  F. Downton.  Bivariate Exponential Distributions in Reliability Theory , 1970 .

[7]  R. Doll.  The Age Distribution of Cancer: Implications for Models of Carcinogenesis , 1971 .

[8]  D. Cox.  Regression Models and Life-Tables , 1972 .

[9]  D G Hoel,et al.  Statistical analysis of survival experiments. , 1972, Journal of the National Cancer Institute.

[10]  H. A. David,et al.  Life Tests under Competing Causes of Failure and the Theory of Competing Risks , 1971 .

[11]  J. Neyman,et al.  A simple stochastic model of recovery, relapse, death and loss of patients. , 1951, Human biology.

[12]  Joseph Berkson,et al.  Competing Exponential Risks, with Particular Reference to the Study of Smoking and Lung Cancer , 1960 .

[13]  C. L. Chiang,et al.  Introduction to stochastic processes in biostatistics. , 1968 .

[14]  I. Olkin,et al.  A Multivariate Exponential Distribution , 1967 .

[15]  Vern T. Farewell,et al.  A Study of Distributional Shape in Life Testing , 1977 .

[16]  ON A CHARACTERIZATION OF THE THREE LIMITING TYPES OF THE EXTREME. , 1965 .

[17]  T. Boardman,et al.  Estimation In Compound Exponential Failure Models , 1970 .

[18]  J. Boag,et al.  Maximum Likelihood Estimates of the Proportion of Patients Cured by Cancer Therapy , 1949 .

[19]  Simeon M. Berman,et al.  Note on Extreme Values, Competing Risks and Semi-Markov Processes , 1963 .

[20]  S. I. Rubinow,et al.  Compartment analysis: An inverse problem , 1971 .

[21]  Regina C. Elandt-Johnson,et al.  Conditional failure time distributions under competing risk theory with dependent failure times and proportional hazard rates , 1976 .

[22]  M. R. Sampford,et al.  The Estimation of Response-Time Distributions. II. Multi-Stimulus Distributions , 1952 .

[23]  J. Kalbfleisch,et al.  Marginal likelihoods based on Cox's regression and life model , 1973 .

[24]  Survival time analysis for treatment evaluation in cancer therapy. , 1961, Cancer research.

[25]  P. Lee,et al.  Weibull distributions for continuous-carcinogenesis experiments. , 1973, Biometrics.

[26]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[27]  A. Nadas,et al.  The Distribution of the Identified Minimum of a Normal Pair Determines the Distribution of the Pair , 1971 .

[28]  Douglas R. Miller.  A Note on Independence of Multivariate Lifetimes in Competing Risks Models , 1977 .

[29]  Pike Mc,et al.  A method of analysis of a certain class of experiments in carcinogenesis. , 1966 .

[30]  R. Albert,et al.  Considerations relating to the formulation of limits for unavoidable population exposures to environmental carcinogens , 1972 .

[31]  B. Turnbull.  Nonparametric Estimation of a Survivorship Function with Doubly Censored Data , 1974 .

[32]  M. L. Moeschberger,et al.  Life Tests Under Dependent Competing Causes of Failure , 1974 .

[33]  R. E. Barlow,et al.  Total time on test processes and applications to failure data , 1975 .

[34]  D G Hoel,et al.  A representation of mortality data by competing risks. , 1972, Biometrics.

[35]  H. A. David.  The theory of competing risks , 1980 .

[36]  A. W. Kimball.  MODELS FOR THE ESTIMATION OF COMPETING RISKS FROM GROUPED DATA , 1969 .

[37]  Z. W. Birnbaum,et al.  Origins and fundamental concepts of the competing-risks problem , 1978 .

[38]  C. L. Chiang.  A STOCHASTIC STUDY OF THE LIFE TABLE AND ITS APPLICATIONS III. THE FOLLOW-UP STUDY WITH THE CONSIDERATION OF COMPETING RISKS"'2 , 1961 .

[39]  M. Sampford.  The Estimation of Response-Time Distributions. I. Fundamental Concepts and General Methods , 1952 .

[40]  P N Lee,et al.  Statistical Analysis of the Bio-assay of Continuous Carcinogens , 1972, British Journal of Cancer.