Family history of the cancer on the survival of the patients with gastrointestinal cancer in northern Iran, using frailty models

Abstract

Background: Gastrointestinal (GI) tract cancer is one of the common causes of the mortality due to cancer in most developing countries such as Iran. The digestive tract is the major organ involved in the cancer. The northern part of the country, surrounded the Caspian Sea coast, is well known and the region with highest regional incidence of the GI tract cancer. In this paper our aim is to study the most common risk factors affecting the survival of the patients suffering from GI tract cancer using parametric models with frailty.

Methods: This research was a prospective study. Information of 484 cases with GI cancer was collected from Babol Cancer Registration Center during 1990-1991. The risk factors we studied are age, sex, family history of cancer, marital status, smoking status, occupation, race, medication status, education, residence (urban, rural), type of cancer, migration status (indigenous, non-native). The studied cases were followed up until 2006 for 15 years. Hazard ratio was used to interpret the death risk. The effect of the factors in the study on the patients survival are studied under a family of parametric models including Weibull, Exponential, Log-normal, and the Log-logistic model. The models are fitted using with and without frailty. The Akaike information criterion (AIC) was considered to compare between competing models.

Results: Out of 484 patients in the study, 321 (66.3%) were males and 163 (33.7%) were females. The average age of the patient at the time of the diagnosis was 59 yr and 55 yr for the males and females respectively. Furthermore, 359 (74.2%) patients suffered from esophageal, 110 (22.7%) patients recognized with gastric, and 15 (3.1%) patients with colon cancer. Survival rates after 1, 3, and 5 years of the diagnosis were 24%, 16%, and 15%, respectively. We found that the family history of the cancer is a significant factor on the death risk under all statistical models in the study. The comparison of AIC using the Cox and parametric models showed that the overall fitting was improved under parametric models (with and without frailty). Among parametric models, we found better performance for the log-logistic model with gamma frailty than the others. Using this model, gender and the family history of the cancer were found as significant predictors.

Conclusions: Results suggested that the early preventative care for patients with family history of the cancer may decrease the risk of the death in the patients with GI cancer. The gender appeared to be an important factor as well so that men experiencing lower risk of death than the women in the study. Since the proportionality assumption of the Cox model was not held (p = 0.0014), the Cox regression model was not an appropriate choice for analysing our data.

Figure 1

Survival curve of GI tract cancer patients using Kaplan-Meier method. (a), (b) Kaplan-Meier estimates of the survival curves for GI tract cancer data separated by family history of cancer and gender, respectively. (c) Kaplan-Meier overall survival curves.

Figure 2

Deviance residuals to evaluate model fit of parametric models. In this plot, the deviance residual is large for short survival times and then decreases with time. This pattern suggests that the log normal and log logistic models with gamma frailty are better than other both models (The log logistic model has the lowest mean deviance residual with respect to other models).

Figure 3

Cox-Snell residuals obtained from fitting various survival models with gamma frailty to the GI tract cancer data. The panels indicate the Cox-Snell residuals (together with their cumulative hazard function) obtained from fitting different parametric models to the same data via maximum likelihood estimation.