# Predicting family doctor contract fulfillment propensity using the FA-GA-BP model and per capita household expenditures

## TL;DR

This study develops a model to predict how likely people are to fulfill family doctor contracts based on household spending data.

## Contribution

The FA-GA-BP model combines factor analysis and genetic algorithm optimization to improve prediction accuracy of contract fulfillment.

## Key findings

- The FA-GA-BP model achieved an R² of 0.9223, indicating high prediction accuracy.
- The model's root mean square error was 0.0618 and relative error was 9.20%.
- The model's coefficient of determination exceeded 0.8138 across different community classifications.

## Abstract

This study aimed to identify the propensity to fulfill family doctor contract services (FDCS) among community residents and to develop a low-error, high-precision inversion model. The development of this model is crucial for monitoring the quality of FDCS and advancing basic community health services.

Based on a survey of a typical urban community, this study used average per capita household living expenditure as the primary input parameter. Data on FDCS fulfillment frequency from six consecutive quarters across communities were analyzed. The study combined factor analysis (FA) with genetic algorithm (GA) optimization of the backpropagation (BP) neural networks to simulate fulfillment tendencies for FDCS. The model's accuracy and applicability were then evaluated. FA of per capita household living expenditure identified two principal factors significantly influencing FDCS fulfillment propensity: “Quality of Life Factor” and the “Rigid Demand Factor.” Extracting these factors from per capita expenditure via FA and then employing the BP algorithm for simulation significantly improved estimation accuracy relative to conventional BP models using unsimplified parameters.

The prediction values obtained from the combined FA and GA–BP method yielded a coefficient of determination RGA_BP2=0.9223 with the measured values. The root mean square error and RE relative error of the fitted model were 0.0618 and 9.20%, respectively. Communities were classified by fulfillment rates and subjected to FA–GA–BP simulation predictions to meet management needs. The simulated coefficient of determination for all classifications exceeded 0.8138.

The findings indicate that the FA–GA–BP model provides reliable and generalizable predictions of the propensity to fulfill FDCS among residents. This robust inversion model, developed by optimizing the BP algorithm with FA and GA, exhibits high accuracy, low error, and good compatibility with data from diverse community datasets. The results have significant implications for the dynamic monitoring of FDCS fulfillment status.