Abstract
The control and treatment of dyslipidemia is a major public health challenge, particularly for patients with coronary heart diseases. In this paper we propose a framework for survival analysis of patients who had a major cardiac event, focusing on assessment of the effect of changing LDL-cholesterol level and statins consumption on survival. This framework includes a Cox PH model and a Markov chain, and combines their results into reinforced conclusions regarding the factors that affect survival time. We prospectively studied 2,277 cardiac patients, and the results show high congruence between the Markov model and the PH model; both evidence that diabetes, history of stroke, peripheral vascular disease and smoking significantly increase hazard rate and reduce survival time. On the other hand, statin consumption is correlated with a lower hazard rate and longer survival time in both models. The role of such a framework in understanding the therapeutic behavior of patients and implementing effective secondary and primary prevention of heart diseases is discussed here.
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References
Aalen OO, Johansen S (1978) An empirical transition matrix for non-homogeneous Markov chains based on censored observations. Scand J Stat 5: 141–150
Agresti A (2002) Categorical data analysis. Wiley, New York
Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6): 716–723
Andersen PK, Borgan O, Gill RD, Keiding N (1993) Statistical models based on counting processes. Springer, New York
Anderson TW, Goodman LA (1957) Statistical inference about Markov chains. Ann Math Stat 28: 89–110
Beck JR, Pauker SG (1983) The Markov process in medical prognosis. Med Decis Making 3: 419–458
Collins R, Armitage J, Parish S, Sleight P, Peto R (2002) MRC/BHF Heart Protection Study of cholesterol lowering with simvastatin in 20,536 high-risk individuals: a randomised placebo-controlled trial. Lancet 360: 7–22
Collins R, Armitage J, Parish S, Sleight P, Peto R (2004) Effects of cholesterol-lowering with simvastatin on stroke and other major vascular events in 20,536 people with cerebrovascular disease or other high-risk conditions. Lancet 363: 757–767
Cox DR (1972) Regression models and life tables. J R Stat Soc B 34(2): 187–220
Cox DR, Snell EJ (1968) A general definition of residuals (with discussion). J R Stat Soc B 30: 248–275
Eckman MH, Levine HJ, Salem DN, Pauker SG (1998) Making decisions about antithrombotic therapy in heart disease: decision analytic and cost-effectiveness issues. CHEST 114: 699–714
Feely J (1999) The therapeutic gap—compliance with medication and guidelines. Atherosclerosis 147(1): S31–S37
Frieden BR (2004) Science from Fisher information. Cambridge University Press, Cambridge
Gilutz H, Novack L, Shvartzman P, Zelingher J, Bonneh DY, Henkin Y, Maislos M, Peleg R, Liss Z, Rabinowitz G, Vardy D, Zahger D, Ilia R, Leibermann N, Porath A (2009) Computerized community cholesterol control (4C): meeting the challenge of secondary prevention. Isr Med Assoc J 11(1): 23–29
Grambsch P, Therneau T (1994) Proportional hazards tests and diagnostics based on weighted residuals. Biometrika 81: 515–526
Heron M, Hoyert DL, Murphy SL, Xu J, Kochanek KD, Tejada-Vera B (2009) Deaths: final data for 2006. National Vital Statistics Reports. http://www.cdc.gov/nchs/data/nvsr/nvsr57/nvsr57_14.pdf
Israel Central Bureau of Statistics (2009) Death causes in Israel—2007. Announcement for the Press, 18 August 2009. http://www.cbs.gov.il/reader/newhodaot/hodaa_template.html?hodaa=200905179
Kemeny JG, Snell JL (1976) Finite Markov chains. Springer, New York
Pliskin JS, Steinman TI, Lowrie EG, Beck JR (1976) Hemodialysis—projecting future bed needs: deterministic and probabilistic forcasting. Comput Biomed Res 9: 317–336
R Development Core Team (2009) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, http://www.R-project.org
Schwarz GE (1978) Estimating the dimension of a model. Ann Stat 6(2): 461–464
Smith SC Jr, Allen J, Blair SN, Bonow RO, Brass LM, Fonarow GC, Grundy SM, Hiratzka L, Jones D, Krumholz HM, Mosca L, Pasternak RC, Pearson T, Pfeffer MA, Taubert KA (2006) AHA/ACC guidelines for secondary prevention for patients with coronary and other atherosclerotic vascular disease: 2006 update: endorsed by the National Heart, Lung, and Blood Institute. Circulation 113: 2363–2372
Sonnenberg FA, Beck JR (1993) Markov models in medical decision making: a practical guide. Med Decis Making 13: 322–338
Tuma NB, Hannan MT, Groeneveld LD (1979) Dynamic analysis of event histories. Am J Sociol 84: 820–854
Vashitz G, Meyer J, Parmet Y, Peleg R, Goldfarb D, Porath A, Gilutz H (2009) Defining and measuring physicians’ responses to clinical reminders. J Biomed Inform 42: 317–326
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Shauly, M., Rabinowitz, G., Gilutz, H. et al. Combined survival analysis of cardiac patients by a Cox PH model and a Markov chain. Lifetime Data Anal 17, 496–513 (2011). https://doi.org/10.1007/s10985-011-9196-y
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DOI: https://doi.org/10.1007/s10985-011-9196-y