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  • All patients who had undergone LC performed between May, 2007 and June, 2009 by any surgeons practicing at two tertiary academic hospitals in southern Taiwan were surveyed by the SF-36 and the Gastrointestinal Quality of Life (GIQLI) instruments. Ethical approval was provided by Institutional Review Board of the Kaohsiung Medical University Hospital (KMUH-IRB-960169). Patients provided written informed consent. Patients with cognitive impairment (n = 1), severe organ disease (n = 4) or psychiatric disease (n = 1) were excluded. Of the 518 eligible subjects who gave written consent and were enrolled in the study at baseline, twelve were excluded due to conversion of LC to open cholecystectomy (OC), and 106 were excluded because they did not undergo postoperative assessments. All 400 of the remaining LC subjects completed the preoperative and 2-year postoperative assessments. The SF-36 (Chinese version) was administered to measure QOL outcomes, and the score was used as a dependent variable. As described in the literature, the physical component summary scale (PCS) and mental component summary scale (MCS) were calculated using norm-based scoring methods to compare QOL in the study population with that of the general Taiwan population [19]. A PCS or MCS value of 50 was considered average for the general Taiwan population. Both PCS and MCS have been widely adopted and were used in the present study to provide an overall QOL index and for further study of longitudinal changes in generic measures as a whole [20]. The GIQLI is recognized as a valid and reliable instrument for measuring functional status, especially in patients undergoing cholecystectomy [13]. Each of its thirty-six items is scored from 0 to 4 with a higher score indicating better health status, and the total GIQLI score ranges from 0 to 144. A Chinese version of the GIQLI has demonstrated validity [2], [13]. The following patient data obtained by records review and questionnaire interview were tested as independent variables in this study: age, gender, body mass index (BMI), education, Charlson co-morbidity index (CCI) score, marital status, previous abdominal surgery, surgical factors, patient referral source, current alcohol or tobacco use, preoperative functional status, operating time, American Society of Anesthesiologist (ASA) score, current complications, operation time, length of stay (LOS) and re-hospitalization within 30 days. The factors used in the MLR model to predict long-term QOL of LC patients included both demographic and clinical characteristics. The MLR model can be formulated as the following linear equation:where is the actual output value, is the intercept, is the model coefficient parameter, is the independent or input variable, is the random error, and m is the number of variables. The SVM model employs non-linear mapping to transform the original training data into higher-dimensional data and searches for the linear optima that define a hyperplane within the new dimension [4]. With appropriate non-linear mapping to a sufficiently high dimension, a decision boundary can separate data into two classes [4]. In the SVM model, this decision boundary is defined by support vectors and margins. The GPR applies a Bayesian approach to nonlinear regression. The Bayesian paradigm provides probabilistic modeling of nonlinear regression. The Bayesian approach to regression specifies a priori probabilities of the parameters to be estimated, and it computes the maximum a posteriori probabilities given the observed data samples. Unlike non-Bayesian schemes, which typically choose a single parameter based on a specified criterion, the Bayesian probabilistic model obtains both the optimal estimated function and the covariance associated with the estimation. Therefore, the Bayesian paradigm provides more information about the estimated parameters compared to non-Bayesian methodology. The GPR is a memory-based method of storing some or all of the training data for use in testing. Therefore, GPR can be quickly trained, which improves the efficiency of the massive-training methodology [7]. The ANN model used in this study was a standard feed-forward, back-propagation neural network with three layers: an input layer, a hidden layer and an output layer. The multilayer perceptron (MLP) network is an emerging tool for designing special classes of layered feed-forward networks [21]. Its input layer consists of source nodes, and its output layer consists of neurons; these layers connect the network to the outside world. In addition to these two layers, the MLP usually has one or more layers of neurons referred to as hidden neurons because they are not directly accessible. The hidden neurons extract important features contained in the input data. The dataset was divided randomly into two sets, one set of 320 cases (80% of the overall dataset) for training the model and another set of eighty cases for testing the model. The model was built using the training set. Demographic and clinical characteristics were the independent variables, and the outcome (QOL) was the dependent variable. The SVM, GPR, MLR and ANN models were then tested using the eighty cases in the testing dataset. The model fit and prediction accuracy of the system models were measured in terms of mean square error (MSE) and mean absolute percentage error (MAPE), respectively. The MSE, which is computed between the desired and predicted values and then averaged across all data, is used as an indicator of goodness of fit. The MAPE indicates the average deviation from the desired value and is usually expressed as a percentage [22]. The prediction accuracy of a model is considered excellent if its MAPE value is lower than 10%. Values between 10% and 20%, between 20% and 50%, and higher than 50% are considered indicators of high, average, and low prediction accuracy, respectively [22]. The formulas for calculating MSE and MAPE are andwhere n is the number of observations, is the desired (target) value of the ith observation, and is the actual output value of the ith observation. The change rates are also given. The optimal number of neurons in the hidden layer and the activation functions are iteratively determined by comparing the MSE index of the output error among several neural networks. The network training process continues as long as training and test errors decrease. That is, training stops when the training error rate and test error rate no longer change or when they begin increasing. The prediction accuracy of the model is then judged by computing the MAPE value. The change rate is also used to compare model performance between the training and test sets. This criterion is used to calculate the difference in MSE index between the test and the training sets so that the better model can be identified. Absolute value was defined as [(the MSE value from test set – the MSE value from training set)/(the MSE value from training set)] ×100%. The lower the change rate and the lower the MSE value are, the better the model performs. The unit of analysis in this study was the individual LC surgery patient. The data analysis was performed in several stages. Firstly, continuous variables were tested for statistical significance by one-way analysis of variance (ANOVA), and categorical variables were tested by Fisher exact analysis. Univariate analyses were applied to identify significant predictors (P<0.05). Secondly, STATISTICA 10.0 (StatSoft, Tulsa, OK) software was used to construct the MLP network model, the SVM model, the GPR model and the MLR model of the relationship between the identified predictors and QOL. Finally, sensitivity analysis was performed to assess the importance of variables in the fitted models. To simplify the training process, key variables were introduced, and unnecessary variables were excluded. A global sensitivity analysis was also performed to assess the relative significance of input parameters in the system model and to rank the variables in order of importance. The global sensitivity of the input variables against the output variable was expressed as the ratio of the network error (variable sensitivity ratios, VSR) with a given input omitted to the network error with the input included. A ratio of 1 or lower indicates that the variable degrades network performance and should be removed.
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