This study incorporated 1,477 participants aged from 60 to 92 years. The mean age of the study population was 69.36 ± 7.46 years. Men and women (56.9% versus 43.1%, respectively) and urban and rural residents (55.5% and 44.5%, respectively) had relatively similar ratios of participation (
Table 1). The majority of participants were retired (79.9%) and had a monthly income of over 800,000 tomans. Married individuals constituted the largest number of participants (76.2%) and the number of household members varied from 1 to 13 persons. Although only 29.9% of the participants had no chronic disease, the proportion of homebound was only 16.4%. Overall, 30.9% of the subjects had mild depression, 2% had moderate depression, and 7.7% had severe depression.
To select the appropriate neural network, we first evaluated all neural network combinations with 2, 3, 4, and 5 nodes and sigmoid and hyperbolic tangent functions in the hidden layer and hyperbolic tangent, linear, and sigmoid functions in the output layer.
Figure 1A depicts the error sum of squares in the training and testing groups for these neural networks. As can be seen, the ANN model with the sigmoid transfer function in both hidden and output layers performed better than all the available models. However, a factor that affects the performance of the neural network is the number of hidden layers. To evaluate this issue in this study, we evaluated all neural networks with two hidden layers having 2, 3, 4, and 5 nodes and sigmoid functions in both hidden and output layers in
Figure 1B. A comparison of the results in
Figures 1A and 1B shows that the increased number of hidden layers could not affect the network fit significantly. Finally, in
Figure 1C, we evaluated the effect of the number of nodes in the hidden layer on the performance of the neural network model. Therefore, a neural network with one hidden, two-node layer, and a sigmoid function in both hidden and output layers was the optimal neural network to predict geriatric depression using factors of age, marital status, number of family members, income, employment status, homebound status, gender, place of residence, number of chronic non-communicable diseases, and ethnicity. This network reduced the error sum of squares in training and testing sets to 290 and 143, respectively.
Figure 2 illustrates the importance of the variables under study in predicting the severity of depression in the optimal network. This figure clearly shows that in the optimal neural network, ethnicity, number of family members, number of chronic diseases, age, and income were five of the most effective variables (74.3%) in predicting geriatric depression, while gender, employment status, and residence were of little impact. To evaluate the neural network performance in predicting the level of geriatric depression, the sensitivity and specificity of this model at each depression level are illustrated in
Figure 3. As the figure indicates, the optimal model could correctly identify healthy individuals with a sensitivity of 71.3% using these variables. The model could also detect different levels of geriatric depression with sensitivity above 62%.