Statistical methods for dependent competing risks

Many biological and medical studies have as a response of interest the time to occurrence of some event,X, such as the occurrence of cessation of smoking, conception, a particular symptom or disease, remission, relapse, death due to some specific disease, or simply death. Often it is impossible to measureX due to the occurrence of some other competing event, usually termed a competing risk. This competing event may be the withdrawal of the subject from the study (for whatever reason), death from some cause other than the one of interest, or any eventuality that precludes the main event of interest from occurring. Usually the assumption is made that all such censoring times and lifetimes are independent. In this case one uses either the Kaplan-Meier estimator or the Nelson-Aalen estimator to estimate the survival function. However, if the competing risk or censoring times are not independent ofX, then there is no generally acceptable way to estimate the survival function. There has been considerable work devoted to this problem of dependent competing risks scattered throughout the statistical literature in the past several years and this paper presents a survey of such work.

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

[2]  John P. Klein,et al.  Some recent results in competing risks theory , 1982 .

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

[4]  Related Topics,et al.  Survival analysis : state of the art , 1992 .

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

[6]  D. Cox,et al.  Analysis of Survival Data. , 1985 .

[7]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

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

[9]  M Gail,et al.  A review and critique of some models used in competing risk analysis. , 1975, Biometrics.

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

[11]  J. Klein,et al.  Independent or dependent competing risks: does it make a difference , 1987 .

[12]  Rupert G. Miller,et al.  Survival Analysis , 2022, The SAGE Encyclopedia of Research Design.

[13]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[14]  J Benichou,et al.  Estimates of absolute cause-specific risk in cohort studies. , 1990, Biometrics.

[15]  S. Lagakos,et al.  Models for censored survival analysis: Constant-sum and variable-sum models , 1977 .

[16]  R. Gray.  A Class of $K$-Sample Tests for Comparing the Cumulative Incidence of a Competing Risk , 1988 .

[17]  Consequences of Departures From Independence in Exponential Series Systems , 1984 .

[18]  A. V. Peterson,et al.  Bounds for a joint distribution function with fixed sub-distribution functions: Application to competing risks. , 1976, Proceedings of the National Academy of Sciences of the United States of America.

[19]  M S Pepe,et al.  Kaplan-Meier, marginal or conditional probability curves in summarizing competing risks failure time data? , 1993, Statistics in medicine.

[20]  E. Slud,et al.  How dependent causes of death can make risk factors appear protective. , 1988, Biometrics.

[21]  J. Klein,et al.  Estimating Random Effects In the Framingham Heart Study , 1992 .

[22]  William A. Link,et al.  A Model for Informative Censoring , 1989 .

[23]  Margaret S. Pepe,et al.  Inference for Events with Dependent Risks in Multiple Endpoint Studies , 1991 .

[24]  J P Klein,et al.  Bounds on net survival probabilities for dependent competing risks. , 1988, Biometrics.

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

[26]  Eric V. Slud,et al.  Dependent competing risks and summary survival curves , 1983 .

[27]  S. Lagakos,et al.  Models for censored survival analysis: A cone class of variable-sum models , 1978 .

[28]  James J. Heckman,et al.  The identifiability of the competing risks model , 1989 .

[29]  Martin Crowder,et al.  On the Identifiability Crisis in Competing Risks Analysis , 1991 .

[30]  John P. Klein,et al.  Estimates of marginal survival for dependent competing risks based on an assumed copula , 1995 .

[31]  F. Guess,et al.  Response linked censoring: Modelling and estimation , 1990 .

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

[33]  C. L. Chiang,et al.  Competing Risks and Conditional Probabilities , 1970 .

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

[35]  G. Enderlein,et al.  Chiang, Ch. L.: Introduction to Stochastic Processes in Biostatistics. Wiley, & Sons, Inc., New York, London, Sydney 1968. 301 S., 1 Abb., 25 Tab., Preis 131 s , 1970 .

[36]  D P Byar,et al.  Dependent competing risks and the latent-failure model. , 1988, Biometrics.

[37]  M. Fréchet.  Sur les tableaux de correlation dont les marges sont donnees , 1951 .

[38]  John P. Klein,et al.  The Independence Assumption for a Series or Parallel System When Component Lifetimes Are Exponential , 1986, IEEE Transactions on Reliability.

[39]  J. Klein,et al.  Identifiability and Estimation of Marginal Survival Functions for Dependent Competing Risks Assuming the Copula is Known , 1996 .

[40]  D. Clayton.  A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence , 1978 .

[41]  Jeffrey J. Gaynor,et al.  On the Use of Cause-Specific Failure and Conditional Failure Probabilities: Examples from Clinical Oncology Data , 1993 .

[42]  J. Klein,et al.  A self-consistent estimator of marginal survival functions based on dependent competing risk data and an assumed copula , 1994 .

[43]  Lagakos Sw.  General right censoring and its impact on the analysis of survival data. , 1979 .

[44]  L. Weissfeld,et al.  Methods for bounding the marginal survival distribution. , 1995, Statistics in medicine.

[45]  J. Robins.  Estimation of the time-dependent accelerated failure time model in the presence of confounding factors , 1992 .

[46]  E L Korn,et al.  Applications of crude incidence curves. , 1992, Statistics in medicine.

[47]  E. Slud,et al.  Nonparametric Identifiability of Marginal Survival Distributions in the Presence of Dependent Competing Risks and a Prognostic Covariate , 1992 .

[48]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

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

[50]  Frank Proschan,et al.  Reliability and Biometry: Statistical Analysis of Lifelength , 1974 .

[51]  D. Oakes,et al.  A concordance test for independence in the presence of censoring. , 1982, Biometrics.

[52]  V T Farewell,et al.  The analysis of failure times in the presence of competing risks. , 1978, Biometrics.

[53]  Odd Aalen,et al.  Nonparametric Estimation of Partial Transition Probabilities in Multiple Decrement Models , 1978 .

[54]  P. Hougaard.  A class of multivanate failure time distributions , 1986 .