Advances in Artificial Intelligence

Volume 2015, Article ID 270165, 7 pages

http://dx.doi.org/10.1155/2015/270165

## Two Artificial Neural Networks for Modeling Discrete Survival Time of Censored Data

^{1}Department of Mathematics and Statistics, University of South Florida, 4202 E. Fowler Avenue, CMC 342, Tampa, FL 33620, USA^{2}Department of Mathematics and Statistics, University of South Florida, 4202 E. Fowler Avenue, CMC 366, Tampa, FL 33620, USA

Received 17 September 2014; Revised 17 February 2015; Accepted 23 February 2015

Academic Editor: Jun He

Copyright © 2015 Taysseer Sharaf and Chris P. Tsokos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Artificial neural network (ANN) theory is emerging as an alternative to conventional statistical methods in modeling nonlinear functions. The popular Cox proportional hazard model falls short in modeling survival data with nonlinear behaviors. ANN is a good alternative to the Cox PH as the proportionality of the hazard assumption and model relaxations are not required. In addition, ANN possesses a powerful capability of handling complex nonlinear relations within the risk factors associated with survival time. In this study, we present a comprehensive comparison of two different approaches of utilizing ANN in modeling smooth conditional hazard probability function. We use real melanoma cancer data to illustrate the usefulness of the proposed ANN methods. We report some significant results in comparing the survival time of male and female melanoma patients.

#### 1. Introduction

Artificial neural network (ANN) is becoming one of the most popular alternatives to conventional statistical modeling. It is actually conceived as an advanced generalized linear model. We have seen various applications of ANN utilized in different scientific subjects like engineering, economics, environment, and health, among others. For example, van Hinsbergen et al. 2009 [1] applied artificial neural networks to short-term time prediction of traffic travel time. Kingston et al. 2005 [2] proposed ANN to model water resources. In economics, Baesens et al. 2005 [3] used ANN to predict survival time of personal loan data. Baesens et al. compared the ANN model used with other survival analysis models like logistic regression and Cox PH and the results came in favor of the ANN.

In the medical sciences, most of the proposed applications of ANN were on prognostic models. For example, one of the most paramount research entities is cancer. Classifying a tumor as malignant or benign is important in cancer research. Chen et al. in 2002 used ANN to diagnose breast cancer tumors [4]. Ercal et al. in 1994 presented an ANN model to distinguish between three benign skin cancer categories and malignant melanoma [5]. But fitting a complex nonlinear modeling such as ANN in regression problems is less prevalent. Determining the risk factors that cause cancer or modeling the survival time of a patient once he/she is diagnosed with cancer using ANN is less common.

In this present study, we are interested in utilizing ANN in survival time modeling of skin cancer (melanoma) patients. Soong et al. [6] in 2010 developed a statistical model to predict the survival time of localized melanoma patients. They used the proportional hazard model developed by Cox [7], but the assumptions of hazard function proportionality may not be applicable to a different set of data. Moreover, they did not study the effect of interaction terms. Thus, applying ANN is more applicable and efficient, especially when the data does not satisfy Cox PH assumptions. ANN does not require any assumptions that need to be justified, and it is more precise in fitting nonlinear models [8–10]. One of the basic approaches in utilizing ANN in survival analysis is by classification, whether a patient will survive over a fixed time interval or not [11]. However, the latter classification method lacks the information about the survival probability function estimates. In 1995, Lapuerta et al. proposed the use of multiple neural networks one for each time interval [12]. This model predicts the survival probability of each time period based on a neural network trained on the observations of the same time period only. The pitfall of this approach is the large number of networks that will be trained if one studies the survival time over immense time intervals.

Other methods of ANN applied to survival time were proposed by Faraggi and Simon in 1995 [8] and by Ohno-Machado in 1996 [13]. We consider in this study the approach represented by Biganzoli et al. in 1998 [9], which was a modification of a study done by Ravdin and Clark in 1992 [14], in addition to the approach represented by Mani et al. in 1999 [10]. Thus, in this study a comparison between the two methods Biganzoli and Mani is given. Also, we study the difference between the survival time of male and female melanoma patients.

In the following section, we discuss the data used to perform our comparison, along with significant results exhibiting the differences between male and female melanoma patient survival times. In the third section we discuss briefly the two methods emphasizing the differences, advantages, and disadvantages of both. In the fourth section we present our results and identify the model that gave the best performance in estimating the survival probability function with less error.

#### 2. Materials and Methods

##### 2.1. Data

We have 130,006 patients diagnosed with melanoma between the years 2000 and 2009 in the USA. Data accumulated from 13 registers of the Surveillance, Epidemiology, and end results program (SEER) [15]. We filter out this large dataset to contain only consummate information with respect to the patient’s age at diagnosis, tumor thickness, stage of cancer, and ulceration. Soong et al. [6] in 2010 used these four variables, but their study did not consider the difference between male and female survival. We found that there exists a significant difference between the median survival time of males and females based on a 5% level of significance using the Kruskal-Wallis test. Thus, studying the effect of gender on survival time by making one model for both males and females is not statistically correct, as the survival time for male and females does not have the same distribution. Figure 1 represents a schematic diagram of the distribution of the complete data with respect to gender and cancer stage.