title: Assessing the effect of quantitative and qualitative predictors on gastric cancer individuals survival using hierarchical artificial neural network models.
abstract: BACKGROUND
  There are numerous unanswered questions in the application of artificial neural network models for analysis of survival data. In most studies, independent variables have been studied as qualitative dichotomous variables, and results of using discrete and continuous quantitative, ordinal, or multinomial categorical predictive variables in these models are not well understood in comparison to conventional models.
  
  
  OBJECTIVE
  This study was designed and conducted to examine the application of these models in order to determine the survival of gastric cancer patients, in comparison to the Cox proportional hazards model.
  
  
  METHODS
  We studied the postoperative survival of 330 gastric cancer patients who suffered surgery at a surgical unit of the Iran Cancer Institute over a five-year period. Covariates of age, gender, history of substance abuse, cancer site, type of pathology, presence of metastasis, stage, and number of complementary treatments were entered in the models, and survival probabilities were calculated at 6, 12, 18, 24, 36, 48, and 60 months using the Cox proportional hazards and neural network models. We estimated coefficients of the Cox model and the weights in the neural network (with 3, 5, and 7 nodes in the hidden layer) in the training group, and used them to derive predictions in the study group. Predictions with these two methods were compared with those of the Kaplan-Meier product limit estimator as the gold standard. Comparisons were performed with the Friedman and Kruskal-Wallis tests.
  
  
  RESULTS
  Survival probabilities at different times were determined using the Cox proportional hazards and a neural network with three nodes in the hidden layer; the ratios of standard errors with these two methods to the Kaplan-Meier method were 1.1593 and 1.0071, respectively, revealed a significant difference between Cox and Kaplan-Meier (P < 0.05) and no significant difference between Cox and the neural network, and the neural network and the standard (Kaplan-Meier), as well as better accuracy for the neural network (with 3 nodes in the hidden layer). Probabilities of survival were calculated using three neural network models with 3, 5, and 7 nodes in the hidden layer, and it has been observed that none of the predictions was significantly different from results with the Kaplan-Meier method and they appeared more comparable towards the last months (fifth year). However, we observed better accuracy using the neural network with 5 nodes in the hidden layer. Using the Cox proportional hazards and a neural network with 3 nodes in the hidden layer, we found enhanced accuracy with the neural network model.
  
  
  CONCLUSIONS
  Neural networks can provide more accurate predictions for survival probabilities compared to the Cox proportional hazards mode, especially now that advances in computer sciences have eliminated limitations associated with complex computations. It is not recommended in order to adding too many hidden layer nodes because sample size related effects can reduce the accuracy. We recommend increasing the number of nodes to a point that increased accuracy continues (decrease in mean standard error), however increasing nodes should cease when a change in this trend is observed.
authors.affiliation: Department Of Basic Sciences, National Nutrition and Food Technology Research Institute, Faculty of Nutrition Sciences and Food Technology, Shahid Beheshti University of Medical Sciences, Tehran, IR Iran.
authors.forename: Zohreh
authors.initials: Z
authors.lastname: Amiri
authors.forename: Kazem
authors.initials: K
authors.lastname: Mohammad
authors.forename: Mahmood
authors.initials: M
authors.lastname: Mahmoudi
authors.forename: Mahbubeh
authors.initials: M
authors.lastname: Parsaeian
authors.forename: Hojjat
authors.initials: H
authors.lastname: Zeraati
keywords: Life Expectancy; Neural Networks; Proportional Hazards Model; Survival