On the estimation of survival time of cardio-vascular disease patients with random number of myocardial infarctions using parametric and semi-parametric methods

Abstract

Cardiovascular disease (CVD) is the leading cause of mortality in developing countries.  CVD  studies that involve the recording  of  two  or  more distinct and well-defined  myocardial infarctions (MI) occurring  over  time  in   the  same  patient  give rise to recurrent  event  data. In  recent  years  a  variety  of  fruitful   statistical   methods    have  been proposed for the analysis of recurrent events  in  medical  areas. The  present  article  is  concerned  with   the  estimation   of   the  survival  time   of    CVD   patients,  in   the  presence   of   recurrent    myocardial infarctions followed  by  a  terminal event    death, under    three    different   possibilities,  i.e., the inter-event times between heart attacks follow gamma distribution,    the  number   of    heart attacks for   an individual   occur   with  time   independent   constant   intensity   λ ,  which   is    varying   across   individuals,   and  the hazard  rates  for   the   recurrent heart attacks  vary  from  different  attacks  for  the  same  individual. Cox's proportional hazard model has also been applied to study the effect of age at the time of first MI  and the number of MI's experienced by the patient, on the survival time of CVD patients. Prior to that proportionality assumption has been tested. The methods  are   applied  to  a CVD  patients data    set  obtained  from  Dr.Ram  Manohar  Lohia  (R.M.L)  Hospital,   Delhi. The major advantage  of   developing   models    for  estimating the survival time of CVD patients is that the  treatment comparisons  can  be  designed so  that  the  expected   survival time of new CVD patients   can  be   predicted   and   improved  after the first MI. Also it can be used as a baseline for further studies.