×

Prediction of risks of sequence of events using multistage proportional hazards model: a marginal-conditional modelling approach. (English) Zbl 1436.62463

Summary: In many studies, sequence of events may occur over time that produce repeated measures with censored observations. Multi-state models are commonly used, and the effect of risk factors on the transition from one state to another is assessed using the Cox proportional hazards model. In recent years, there is growing interest to predict the disease status at different stages and endpoints using multi-state models. Because of the complexity of existing methods their applications for prediction is limited. In this paper, a simple alternative method is proposed for risk prediction of the sequence of events using multistage modelling approach. The proposed method of prediction is a new development using a series of events in conditional setting arising from the beginning to the endpoint. The proposed method is based on marginal-conditional approach to link the events occurring in a trajectory. The probability of a trajectory can be calculated easily. The main improvement of proposed method for risk prediction is that it is a simple approach, compared to the existing ones, and this approach can easily be generalized to any number of events in the process to the endpoints. Two examples from real life data is illustrated in this paper using the proposed method for risk prediction.

MSC:

62N02 Estimation in survival analysis and censored data
62M20 Inference from stochastic processes and prediction
62N01 Censored data models
62P25 Applications of statistics to social sciences
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Aalen, OO; Borgan, O.; Gjessing, HK, Survival and event history analysis: a process point of view (2008), New York: Springer Science+Business Media, LLC, New York
[2] Andersen, PK, Competing risks as a multi-state model, Stat Methods Med Res, 11, 203-215 (2002) · Zbl 1121.62567
[3] Andersen, PK; Hensen, LS; Keiding, N., Non- and semi- parametric estimation of transition probabilities from censored observation of a non-homogeneous markov process, Scand J Stat, 18, 153-167 (1991) · Zbl 0735.62079
[4] Andersen, PK; Perme, MP, Inference for outcome probabilities in multi-state models, Stat Methods Med Res, 11, 91-115 (2008)
[5] Arjas, E.; Eerola, M., On predictive causality in longitudinal studies, J Stat Plan Inference, 34, 361-368 (1993) · Zbl 0766.60048
[6] Arriagada, R.; Rutqvist, LE; Kramar, A., Competing risks de- termining event-free survival in early breast cancer, Br J Cancer, 66, 951-957 (1992)
[7] Beyersmann, J.; Schumacher, M.; Allignol, A., Competing risks and multistate models with r (2012), New York: Springer, New York · Zbl 1304.62002
[8] Boracchi, P.; Antolini, L.; Biganzoli, E.; Marubini, E., Competing risks: modelling crude cumulative incidence functions, Statistica Applicata, 17, 25-60 (2005)
[9] Commenges, D., Multi-state models in epidemiology, Lifetime Data Anal, 5, 315-327 (1999) · Zbl 0941.62117
[10] Cox, DR, Regression models and life tables (with discussion), J R Stat Soc B, 34, 187-220 (1972)
[11] Dabrowska, DM; Sun, G.; Horowitz, MM, Cox regression in a Markov renewal model: an application to the analysis of bone marrow transplant data, J Am Stat Assoc, 89, 867-877 (1994) · Zbl 0804.62092
[12] Farewell, VT, An application of Cox’s proportional hazard model to multiple infection data, Appl Stat, 28, 136-143 (1979)
[13] Fine, JP; Gray, RJ, A proportional hazards model for the subdistribution of a competing risk, J Am Stat Assoc, 94, 496-509 (1999) · Zbl 0999.62077
[14] Gail, MA, A review and critique of some models used in competing risk analysis, Biometrics, 31, 209-222 (1975) · Zbl 0312.62075
[15] Gillam, MH; Ryan, P.; Graves, SE; Miller, LN; de Steiger, RN; Salter, A., Competing risks survival analysis applied to data from the australian orthopaedic association national joint replacement registry, Acta Orthop, 81, 548-555 (2010)
[16] Gray, RJ, A class of K-sample tests for comparing the cumulative incidence of a competing risk, Ann Stat, 16, 1141-1154 (1988) · Zbl 0649.62040
[17] Holt, JD, Competing risk analyses with special reference to matched pair experiments, Biometrika, 65, 159-165 (1978) · Zbl 0421.62079
[18] Hougaard, P., Multi-state models: a review, Lifetime Data Anal, 5, 239-264 (1999) · Zbl 0934.62112
[19] Islam, MA, Multistate survival models for transitions and reverse transitions: an application to contraceptive use data, J Royal Stat Soc Ser A, 157, 441-455 (1994) · Zbl 1001.62527
[20] Islam, MA; Chowdhury, RI, Analysis of repeated measures data (2017), Singapore: Springer, Singapore
[21] Islam, MA; Chowdhury, RI; Chakraborty, N.; Bari, W., A multistage model for maternal morbidity during antenatal, delivery and postpartum periods, Stat Med, 23, 137-158 (2004)
[22] Kalbfleisch, JD; Prentice, RL, The statistical analysis of failure time data (1980), New York: Wiley, New York
[23] Kaplan, EL; Meier, P., Nonparametric estimation from incomplete observations, J Am Stat Assoc, 53, 457-481 (1958) · Zbl 0089.14801
[24] Kay, R., The analysis of transition times in multistate stochastic processes using proportional hazard regression models, Commun Stat, 11, 1743-1756 (1982) · Zbl 0527.62094
[25] Klein, JP; Keiding, N.; Copelan, EA, Plotting sumary predictions in multistate survival models: probabilities of relapse and death in remission for bone marrow transplantation patients, Stat Med, 13, 2315-2332 (1994)
[26] Klein, JP; Moeschberger, ML, Survival analysis: techniques for censored and truncated data (2003), New York: Springer, New York
[27] Kleinbaum, DG; Klein, M., Survival analysis: a self-learling text (2012), New York: Springer, New York
[28] Lunn, M.; Cole, SR; Gange, SJ, Competing risk regression models for epidemiologic data, Am J Epidemiol, 170, 244-256 (2009)
[29] Meira-Machado, L.; Una-Alvarez, J.; Cadarso-Suarez, C.; Andersen, PK, Multi-state models for the analysis of time-to-event data, Stat Methods Med Res, 18, 195-222 (2009)
[30] Moreira, A.; Meira-Machado, L., survivalbiv: estimation of the bivariate distribution function for sequentially ordered events under univariate censoring, J Stat Softw, 46, 1-16 (2012)
[31] Porta N, Gomez G, Calle M L, Maltas N (2007) Competing risks methods. https://upcommons.upc.edu/bitstream/handle/2117/2201/TRCR.pdf. Accessed 20 Jan 2019
[32] Prentice, RL; Kalbfleisch, JD; Peterson, AV; Flournoy, N.; Farewell, VT; Breslow, NE, The analysis of failure times in the presence of competing risks, Biometrics, 34, 541-554 (1978) · Zbl 0392.62088
[33] Putter H (2011) Tutorial in biostatistics: Competing risks and multistate models analyses using the mstate package. http://cran.rproject.org/web/packages/mstate/vignettes/Tutorial.pdf
[34] Putter, H.; Fiocco, M.; Geskus, RB, Tutorial in biostatistics: competing risks and multi-state models, Stat Med, 26, 2389-2430 (2007)
[35] Putter, H.; van der Hage, J.; de Bock, GH; Elgalta, R.; van de Velde, CJH, Estimation and prediction in a multi-state model for breast cancer, Biom J, 3, 366-380 (2006)
[36] Satagopan, JM; Ben-Porat, L.; Berwick, M.; Kutler, D.; Auerbach, AD, A note on competing risks in survival data analysis, Br J Cancer, 91, 1229-1235 (2004)
[37] Tai, BC; Machin, D.; White, I.; Gebski, V., Competing risks analysis of patients with osteosarcoma: a comparison of four different approaches, Stat Med, 20, 661-684 (2001)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.