Multistate Markov Modelling for Disease Progression of Breast Cancer Patients Based on CA15-3 Marker

  • Gurprit Grover Department of Statistics, University of Delhi, Delhi, India.
  • Prafulla Kumar Swain Department of Statistics, Utkal University, Bhubaneswar, India.
  • Komal Goel Department of Statistics, University of Delhi, Delhi, India.
  • Vikas Singh Department of General Surgery, Institute of Postgraduate Medical Education & Research, Kolkata, India.
Keywords: Multistate model, breast cancer, CA15-3 marker, prognostic factors, Cox PH model


Multi-state models are a flexible tool for analyzing complex time-to-event problems with multiple endpoints, especially in chronic diseases where the patients move through different states. It provides a more detailed insight into the disease process as compared to other statistical models. The primary objective of this paper is to study the significance of CA15-3 as a disease marker in monitoring and evaluating the diseases progression of breast cancer patients using a multistate Markov model. Based on ranges of CA15-3 marker (< 25 U/ml and ≥ 25 U/ml ) states have been defined and transition intensities, transition probabilities and expected state specific survival time have been estimated. Also, the effect of prognostic factors viz. age, tumor size, tumor grade, involve lymph nodes, ER status, PR status etc., on transition intensities have been explored.


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Aalen OO, Farewell VT, De AD, Day NE, Nöel GO. A Markov model for HIV disease progression including the effect of HIV diagnosis and treatment: application to AIDS prediction in England and Wales. Stat Med. 1997; 16: 2191-2210.

Ali I, Wani WA, Saleem K. Cancer scenario in India with future perspectives. Canc Ther. 2011; 8: 56-70.

Andersen PK, Hansen LS, Keiding N. Non-and semi-parametric estimation of transition probabilities from censored observation of a non-homogeneous Markov process. Scand J Stat. 1991; 18: 153-167.

Berruti A, Tampellini M, Tortaa M, Buniva T, Gorzegno G, Dogliotti L. Prognostic value in predicting overall survival of two mucinous markers: CA 15-3 and CA 125 in breast cancer patients at first relapse of disease. Eur J Canc. 1994; 30: 2082-2084.

Broët P, Rochefordière A, Scholl SM, et al. Analyzing prognostic factors inbreast cancer using a multistate model. Breast Canc Res Treat. 1999; 54: 83-89.

Chiang CL. Introduction to stochastic Processes in Biostatistics. New York: John Wiley; 1968.

Colomer R, Ruibal A, Rubio D, et al. Circulating CA 15-3 levels in the postsurgical follow-up of breast cancer patients and in non-malignant diseases. Breast Cancer Res Treat. 1989; 13:123-133.

Cook RJ, Yi GY, Lee KA, Gladman DD. A conditional Markov model for clustered progressive multistate processes under incomplete observation. Biometrics. 2004; 60: 436-443.

Dukic V, Dignam J. Bayesian hierarchical multiresolution hazard model for the study of time-dependent failure patterns in early stage breast cancer. Bayesian Anal. 2007; 2:591-610.

Dnistrian AM, Schwartz MK, Greenberg EJ, Smith CA, Schwartz DC. CA 15-3 and carcinoembryonic antigen in the clinical evaluation of breast cancer. Clin Chim Acta. 1991; 200: 81-93.

Duffy MJ. Serum tumor markers in breast cancer: are they of clinical value?. Clin Chem. 2006; 52: 345-351.

Duffy SW, Day NE, Tabar L, Chen HH, Smith RA. Markov models of breast tumor progression: some age-specific results. J Natl Cancer I Monographs. 1997; 22: 93-97.

Ebeling FG, Stieber P, Untch M, et al. Serum CEA and CA 15-3 as prognostic factors in primary breast cancer.Br J Cancer. 2002; 22: 1217-1222.

Ferlay J, Shin HR, Bray F, Forman D, Mathers C, Parkin DM. Estimates of worldwide burden of cancer in 2008: GLOBOCAN 2008. Int J Canc. 2010; 127: 2893-2917.

Foreman J, Forouzanfar H, Delossantos M, Lazano R, Murray J, Naghavi M. Breast and cervical cancer in 187 countries between 1980 and 2010: a systematic analysis. Lancet. 2011; 378: 1442-1444.

Gasparini G. Prognostic variables in node-negative and node-positive breast cancer. Breast Canc Res Treat. 1998; 52:321-31.

Grover G, Gadpayle A, Swain PK, Deka B. A Multistate Markov Model Based on CD4 Cell Count for HIV/AIDS. Int J Stat Med Res. 2013; 2: 144-1451.

Grover G, Seth D, Vjala R, Swain PK. A multistate Markov model for the progression of liver cirrhosis in the presence of various prognostic factors. Chilean Journal of Statistics. 2014; 5: 15-27.

Hendriks JCM, Satten GA, Ameijden EJCV, Druten HAMV, Coutinho RA, Griensven GJP V. The incubation period to AIDS injecting drug users estimated from prevalent cohort data, accounting for death prior to an AIDS diagnosis. AIDS. 1998; 12: 1537-1544.

Jackson CH. Multistate Models for Panel Data: The msm Package for R. J Statist Software. 2011; 38: 1-28.

Joly P, Commenges D, Helmer C, Letenneur L. A penalized likelihood approach for an illness-death model with interval‐censored data: Application to age-specific incidence of dementia. Biostatistics. 2002; 3: 433-443.

Kalbfleisch JD, Lawless JF. The analysis of panel data under a Markov assumption. J Am Statist Assoc. 1985; 80: 863-871.

Kay R. A Markov model for analysing cancer markers and disease states in survival studies. Biometrics. 1986; 42: 855-865.

Lamerz R, Reithmeier A, Stieber P, Eiermann W, Fatehmoghadam A. Role of Blood Markers in the Detection of Metastases from Primary Breast-Cancer. Diagnostic Oncology. 1991; 1: 88-97.

Longini IW, Clark S, Byers R, et al. Statistical analysis of the stages of HIV infection using a Markov model. Stat Med. 1989; 8: 851-843.

Marshall G, Jones RH. Multi‐state models and diabetic retinopathy. Stat Med. 1995; 14: 1975-1983.

O’Keeffe AG, Tom BD, Farewell VT. A case‐study in the clinical epidemiology of psoriatic arthritis: multistate models and causal arguments. J Roy Stat Soc C Appl Stat. 2011; 60: 675-699.

Putter H, Hage J, Elgalta R. Estimation and Prediction in a Multi-State Model for Breast Cancer. Biom J. 2006; 48: 366-380.

Robertson JF, Pearson D, Price MR, Selby C, Blamey RW, Howell A. Objective measurement of therapeutic response in breast cancer using tumour markers. Br J Canc. 1991; 64: 757-63.

Safi F, Kohler I, Beger HG, Röttinger E. The value of the tumor marker CA 15‐3 in diagnosing and monitoring breast cancer. A comparative study with carcinoembryonic antigen. Cancer. 1991; 68: 574-582.

Taghipour S, Banjevic D, Miller A, Montogomery N, Jardine A, Harvey B. Parameter estimates for invasive breast cancer progression in the Canadian National Breast Screening Study. Br J Canc. 2013; 108: 542-548.

Tomlinson IP, Whyman A, Barrett JA, Kremer JK. Tumour marker CA15-3: possible uses in the routine management of breast cancer. Eur J Cancer. 1995; 31: 899-902.

Tondini C, Hayes DF, Gelman R, Henderson IC, Kufe DW. Comparison of CA15-3 and carcinoembryonic antigen in monitoring the clinical course of patients with metastatic breast cancer. Cancer Res. 1988; 48: 4107-4112.

Ventura L, Carreras G, Puliti D, Paci E, Zappa M, Miccinesi G. Comparison of multi-state Markov models for cancer progression with different procedures for parameters estimation. An application to breast cancer. J Epidemiol Biostat Public Health. 2014; 11: 1-10.

Vizcarra E, Lluch A, Cibrian R, Jarque F, Garcia CJ. CA15. 3, CEA and TPA tumor markers in the early diagnosis of breast cancer relapse. Oncology. 1994; 51: 491-496.

Webb PM, Cummings MC, Bain CJ, Furnival CM. Changes in survival after breast cancer: improvements in diagnosis or treatment?. Breast. 2004; 13: 7-14.