Interpretability and importance of functionals in competing risks and multistate models

The basic parameters in both survival analysis and more general multistate models, including the competing risks model and the illness-death model, are the transition hazards. It is often necessary to supplement the analysis of such models with other model parameters, which are all functionals of the transition hazards. Unfortunately, not all such functionals are equally meaningful in practical contexts, even though they may be mathematically well defined. We have found it useful to check whether the functionals satisfy three simple principles, which may be used as criteria for practical interpretability.

[1]  N. Keiding,et al.  Multi-state models for event history analysis , 2002, Statistical methods in medical research.

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

[3]  Gregg E. Dinse,et al.  A mixture model for the regression analysis of competing risks data , 1985 .

[4]  S. Greenland,et al.  Epidemiologic measures and policy formulation: lessons from potential outcomes , 2005, Emerging themes in epidemiology.

[5]  N R Temkin,et al.  An analysis for transient states with application to tumor shrinkage. , 1978, Biometrics.

[6]  Somnath Datta,et al.  Validity of the Aalen–Johansen estimators of stage occupation probabilities and Nelson–Aalen estimators of integrated transition hazards for non-Markov models , 2001 .

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

[8]  A. Adam Ding,et al.  Regression analysis based on semicompeting risks data , 2007 .

[9]  Ren Johansen An Empirical Transition Matrix for Non-homogeneous Markov Chains Based on Censored Observations , 1978 .

[10]  N Keiding,et al.  Event history analysis and inference from observational epidemiology. , 1999, Statistics in medicine.

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

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

[13]  S Esbjerg,et al.  Multi-state models for bleeding episodes and mortality in liver cirrhosis. , 2000, Statistics in medicine.

[14]  J P Klein,et al.  Plotting summary predictions in multistate survival models: probabilities of relapse and death in remission for bone marrow transplantation patients. , 1993, Statistics in medicine.

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

[16]  J. Fine,et al.  Regression modeling of competing crude failure probabilities. , 2001, Biostatistics.

[17]  J. Klein,et al.  Statistical Models Based On Counting Process , 1994 .

[18]  E. Sverdrup Estimates and test procedures in connection with stochastic models for deaths, recoveries and transfers between different states of health , 1965 .

[19]  Jun Yan,et al.  A regression model for the conditional probability of a competing event: application to monoclonal gammopathy of unknown significance , 2011 .

[20]  K. Dietz,et al.  Daniel Bernoulli's epidemiological model revisited. , 2002, Mathematical biosciences.

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

[22]  Gang Li,et al.  A Bayesian approach to joint analysis of longitudinal measurements and competing risks failure time data , 2007, Statistics in medicine.

[23]  John P Klein,et al.  Regression Modeling of Competing Risks Data Based on Pseudovalues of the Cumulative Incidence Function , 2005, Biometrics.

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

[25]  R. Elashoff,et al.  An approach to joint analysis of longitudinal measurements and competing risks failure time data , 2007, Statistics in medicine.

[26]  M. Noel Karn,et al.  AN INQUIRY INTO VARIOUS DEATH‐RATES AND THE COMPARATIVE INFLUENCE OF CERTAIN DISEASES ON THE DURATION OF LIFE , 1931 .

[27]  Carmen Cadarso-Suárez,et al.  Nonparametric estimation of transition probabilities in a non-Markov illness–death model , 2006, Lifetime data analysis.

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

[29]  Jason P. Fine,et al.  On semi-competing risks data , 2001 .

[30]  M A Nicolaie,et al.  Vertical modeling: A pattern mixture approach for competing risks modeling , 2010, Statistics in medicine.

[31]  Mei-Jie Zhang,et al.  Predicting cumulative incidence probability by direct binomial regression , 2008 .

[32]  John D. Kalbfleisch,et al.  The Statistical Analysis of Failure Data , 1986, IEEE Transactions on Reliability.

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

[34]  Limin Peng,et al.  Regression Modeling of Semicompeting Risks Data , 2007, Biometrics.

[35]  J P Klein,et al.  Multi‐state models and outcome prediction in bone marrow transplantation , 2001, Statistics in medicine.

[36]  Robert Gray,et al.  A Proportional Hazards Model for the Subdistribution of a Competing Risk , 1999 .

[37]  Haesook T. Kim Cumulative Incidence in Competing Risks Data and Competing Risks Regression Analysis , 2007, Clinical Cancer Research.

[38]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data: Kalbfleisch/The Statistical , 2002 .

[39]  A. F. Thomsen,et al.  Increased relative risk of subsequent affective disorders in patients with a hospital diagnosis of obesity , 2006, International Journal of Obesity.

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

[41]  Richard J. Cook,et al.  The Statistical Analysis of Recurrent Events , 2007 .

[42]  Niels Keiding,et al.  Age‐Specific Incidence and Prevalence: A Statistical Perspective , 1991 .

[43]  Michael J. Phelan Estimating the transition probabilities from censored Markov renewal processes , 1990 .