Nonparametric estimation of transition probabilities in the non-Markov illness-death model: A comparative study

Biometrics

Volumn 71, Issue 2, 2015, Pages 364-375

  de Uña Álvarez, Jacobo ^a   Meira Machado, Luís ^b  

^a UNIVERSITY OF VIGO   (Spain)

^b UNIVERSITY OF MINHO   (Portugal)

Author keywords

Aalen Johansen estimator; Kaplan Meier; Markov condition; Multi state model; Survival analysis

Indexed keywords

SAMPLING;

AALEN-JOHANSEN ESTIMATOR; COMPARATIVES STUDIES; KAPLAN-MEIER; MARKOV CONDITION; MARKOV ESTIMATORS; MODEL COMPLEXES; MULTI-STATE MODEL; NON-PARAMETRIC ESTIMATIONS; SURVIVAL ANALYSIS; TRANSITION PROBABILITIES;

DISEASES;

CANCER; COMPARATIVE STUDY; MARKOV CHAIN; PREDICTION; PROBABILITY; SURVIVAL;

ALGORITHM; BIOMETRY; COLONIC NEOPLASMS; COMPARATIVE STUDY; COMPUTER SIMULATION; HUMAN; KAPLAN MEIER METHOD; MARKOV CHAIN; MORTALITY; NONPARAMETRIC TEST; PROBABILITY; STATISTICAL MODEL; SURVIVAL ANALYSIS;

ALGORITHMS; BIOMETRY; COLONIC NEOPLASMS; COMPUTER SIMULATION; HUMANS; KAPLAN-MEIER ESTIMATE; MARKOV CHAINS; MODELS, STATISTICAL; PROBABILITY; STATISTICS, NONPARAMETRIC; STOCHASTIC PROCESSES; SURVIVAL ANALYSIS;

EID: 84931562530     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/biom.12288     Document Type: Article

References (28)

1. Aalen, O. and Johansen, S. (1978). An empirical transition matrix for nonhomogeneous Markov chains based on censored observations. Scandinavian Journal of Statistics 5, 141-150.
2. Allignol, A., Beyersmann, J., Gerds, T., and Latouche, A. (2014). A competing risks approach for nonparametric estimation of transition probabilities in an non-Markov illness-death model. Lifetime Data Analysis 20, 495-513.
3. Amorim, A. P., de Uña-Álvarez, J., and Meira-Machado, L. (2011). Presmoothing the transition probabilities in the illness-death model. Statistics & Probability Letters 81, 797-806.
4. Andersen, P. K., Esbjerg, S., and Sorensen, T. I. A. (2000). Multistate models for bleeding episodes and mortality in liver cirrhosis. Statistics in Medicine 19, 587-599.
5. Andersen, P. K., Hansen, L. S., and Keiding, N. (1991). Nonparametric and semiparametric estimation of transition probabilities from censored observations of a non-homogeneous Markov process. Scandinavian Journal of Statistics 18, 153-167.
6. Borgan, O. (2002). Estimation of covariate-dependent Markov transition probabilities from nested case-control data. Statistical Methods in Medical Research 11, 183-202.
7. Commenges, D. (1999). Multi-state models in epidemiology. Lifetime Data Analysis 5, 315-327.
8. Datta, S. and Satten, G. A. (2001). Validity of the Aalen-Johansen estimators of stage occupancy probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models. Statistics & Probability Letters 55, 403-411.
9. Datta, S. and Satten, G. A. (2002). Estimation of integrated transition hazards and stage occupation probabilities for non-Markov systems under dependent censoring. Biometrics 58, 792-802.
10. de Uña-Álvarez, J. (2010). Recent developments in censored, non-Markov multi-state models. In Combining Soft Computing and Statistical Methods in Data Analysis (Borgelt et al. Eds.), Advances in Intelligent and Soft Computing, 173-179. Berlin: Springer.
11. Frydman, H., Gerds, T., Gron, R., and Keiding, N. (2013). Nonparametric estimation in a Markov 'illness-death' model when all transition times are interval censored. Biometrical Journal 55, 823-843.
12. Frydman, H. and Szarek, M. (2009). Nonparametric estimation in a Markov 'illness-death' process from interval censored observations with missing intermediate transition status. Biometrics 65, 143-151.
13. Glidden, D. (2002). Robust inference for event probabilities with non-Markov event data. Biometrics 58, 361-368
14. Hougaard, P. (1999). Multi-state models: A review. Lifetime Data Analysis 5, 239-264.
15. Hougaard, P. (2000). Analysis of Multivariate Survival Data. New York, New York: Springer.
16. Lan, L. and Datta, S. (2010). Non-parametric estimation of state occupation, entry and exit times with multistate current status data. Statistical Methods in Medical Research 19, 147-165.
17. Meira-Machado, L. F., de Uña-Álvarez, J., and Cadarso-Suárez, C. (2006). Nonparametric estimation of transition probabilities in a non-Markov illness-death model. Lifetime Data Analysis 12, 325-344.
18. Meira-Machado, L., de Uña-Álvarez, J., Cadarso-Suárez, C., and Andersen, P. K. (2009). Multi-state models for the analysis of time to event data. Statistical Methods in Medical Research 18, 195-222.
19. Meira-Machado, L., Roca-Pardiñas, J., Van Keilegom, I., and Cadarso-Suárez, C. (2013). Bandwidth selection for the estimation of transition probabilities in the location-scale progressive three-state model. Computational Statistics 28, 2185-2210.
20. Moreira, A., de Uña-Álvarez, J., and Machado, L. (2013). Presmoothing the Aalen-Johansen estimator in the illness-death model. Electronic Journal of Statistics 7, 1491-1516.
21. Moertel, C. G., Fleming, T. R., Macdonald, J. S., Haller, D. G., Laurie, J. A., Goodman, P. J., Ungerleider, J. S., Emerson, W. A., Tormey, D. C., Glick, J. H., Veeder, M. H., and Mailliard, J. A. (1990). Levamisole and fluorouracil for adjuvant therapy of resected colon carcinoma. New England Journal of Medicine 332, 352-358.
22. Mostajabi, F. and Datta, S. (2013). Nonparametric regression of state occupation, entry, exit, and waiting times with multistage right-censored data. Statistics in Medicine 32, 3006-3019.
23. Pepe, M. S. (1991). Inference for events with dependent risks in multiple end-point studies. Journal of the American Statistical Association 86, 770-778.
24. Pepe, M. S., Longton, G., and Thornquist, M. (1991). A qualifier Q for the survival function to describe the prevalence of a transient condition. Statistics in Medicine 10, 413-421.
25. Satten, G. A. (1999). Estimating the extent of tracking in interval-censored chain-of-events data. Biometrics 55, 1228-1231.
26. Spitoni, C., Verduijn, M., and Putter, H. (2012). Estimation and asymptotic theory for transition probabilities in Markov renewal multi-state models. International Journal of Biostatistics 8, 23.
27. Stute, W. (1993). Consistent estimation under random censorship when covariables are present. Journal of Multivariate Analysis 45, 89-103.
28. Stute, W. (1996). Distributional convergence under random censorship when covariables are present. Scandinavian Journal of Statistics 23, 461-471.