Simulation analysis of an adjusted gravity model for hospital admissions robust to incomplete data

Abstract

Background: Gravity models are often hard to apply in practice due to their data-hungry nature. Standard implementations of gravity models require that data on each variable is available for each supply node. Since these model types are often applied in a competitive context, data availability of specific variables is commonly limited to a subset of supply nodes.

Methods: This paper introduces a methodology that accommodates the use of variables for which data availability is incomplete, developed for a health care context, but more broadly applicable. The study uses simulated data to evaluate the performance of the proposed methodology in comparison with a conventional approach of dropping variables from the model.

Results: It is shown that the proposed methodology is able to improve overall model accuracy compared to dropping variables from the model, and that model accuracy is considerably improved within the subset of supply nodes for which data is available, even when that availability is sparse.

Conclusion: The proposed methodology is a viable approach to improve the performance of gravity models in a competitive health care context, where data availability is limited, and especially where a the supply nodes with complete data are most relevant for the practitioner.

Keywords: Gravity model; Healthcare planning; Hospital admissions estimation; Huff Model.

Fig. 1

The graph shows the relationship between $\alpha$ and the balancing parameter BM across all experiments: 5 runs for 7 effect sizes, and 19 sample sizes (increments of 0.05 starting at 0.05 up to 0.95), yielding 665 observations

Fig. 2

For different effect sizes, the figure shows the estimated effect size by the model. P is the proportion of facilities for which reputation data is made available to the model

Fig. 3

The figure shows four scatterplots of different data availability scenarios that compare the estimated effect size of the reputation parameter and its value as introduced in the generated dataset

Fig. 4

The figure on the left shows the relationship between the most important error metric, the Mean Average Percentage Error (MAPE), and data availability for effect sizes 0.9 and 0.3. The figure on the right shows the average MAPE for different data availabilities plotted against the effect size

Fig. 5

The figure shows the in-group MAPE for different reputation data availability levels given an effect size of 0.5. A right-tailed student’s T distribution with 4 degrees of freedom was used to calculate the t-value=2.13, on the 5% significance level. The upper bound for $p=0.05$ is 0.20, which is out of the range of the y-axis