Determination of Affected Risk Factors on Time to Recurrence and Death in Patients with Postoperative Gastric Cancer using Copula Function

Ghodratollah Roshanaei, Anoshirvan Kazemnejad, Sanambar Sadighi


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.


Parametric survival model; Recurrence time; Gastric cancer; Semi-competing risk; Dependent event; Copula function

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