title: Determination of affected risk factors on time to recurrence and death in patients with postoperative gastric cancer using copula function.
abstract: BACKGROUND
  In survival studies when the event times are dependent, performing of the analysis by using of methods based on independent assumption, leads to biased. In this paper, using copula function and considering the dependence structure between the event times, a parametric joint distribution has made fitting to the events, and the effective factors on each of these events would be determined.
  
  
  METHODS
  This retrospective cohort study was conducted from March 2003 to March 2007. The data collected from 256 patients with gastric cancer who underwent surgery and that the event time of the two outcomes of death and recurrence for them was recorded. Akaike Information Criterion (AIC) was used to determine of suitable parametric models. Moreover, applying copula function with regard to the relationships between the events, the effect of the risk factors of each of the two outcomes was determined. The data analysis was done using R2.12.1 software.
  
  
  RESULTS
  According to the AIC criterion, the Weibull distribution had the best fitting in both of the event times. The median times for recurrence and survival of the patients were estimated 20.2 and 28.1 months respectively. Furthermore, with a fitting of Weibull distribution to the two event times using Clayton copula function, the variables of gender, tumor size and tumor pathological stage on survival, and tumor size and tumor pathological stage on recurrence were significant (P<0.001).
  
  
  CONCLUSIONS
  Applying copula function for determining specific risk factors of the semi-competing events produces suitable results opposite the common methods which are based on independent assumption of the events.
authors.affiliation: Research Center for Health Sciences and Department of Biostatistics and Epidemiology, Hamadan University of Medical Sciences, Hamadan, Iran. gh.roshanaei@umsha.ac.ir.
authors.forename: Ghodratollah
authors.initials: G
authors.lastname: Roshanaei
authors.affiliation: Department of Biostatistics, Faculty of Medical Sciences, Tarbiat Modares University, Tehran, Iran. kazem_an@modares.ac.ir.
authors.forename: Anoshirvan
authors.initials: A
authors.lastname: Kazemnejad
authors.affiliation: Department of Medical Oncology, Cancer Research Center, Cancer Institute. Imam Khomeini Hospital, Tehran, Iran.
authors.forename: Sanambar
authors.initials: S
authors.lastname: Sadighi
mesh_terms: D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D009364:Neoplasm Recurrence, Local / Q000401:mortality*; D009367:Neoplasm Staging; D011184:Postoperative Period; D012189:Retrospective Studies; D018570:Risk Assessment / Q000379:methods; D012307:Risk Factors; D017678:Sex Distribution; D013274:Stomach Neoplasms / Q000401:mortality* / Q000473:pathology* / Q000601:surgery; D015996:Survival Rate; D013997:Time Factors; D016896:Treatment Outcome
keywords: Copula function; Dependent event; Gastric cancer; Parametric survival model; Recurrence time; Semi-competing risk