DISTINGUISHING HIGH-RISK VERSUS LOW-RISK SUBGROUPS IN COMPARTMENTAL EPIDEMIC MODELS: WHERE TO DRAW THE LINE?
Purpose: Economic evaluations of infectious disease control interventions frequently use dynamic compartmental epidemic models. Such models capture heterogeneity in risk of infection by stratifying the population into discrete risk groups, thus approximating what is typically continuous variation in risk with discrete groups. An important open question is whether and how different risk stratification choices influence model predictions.
Method: We developed equivalent Susceptible-Infectious-Susceptible dynamic transmission models: an unstratified model and models stratified into high-risk and low-risk groups. All model parameters other than contact rate(s) were identical. Stratified models differed from one another in terms of the proportion of the population that was high risk (a) and the contact rates in the high- and low-risk groups, though the overall contact rate in all models was equal. Models were equivalent in the sense that absent intervention, they all produced the same overall prevalence of infectious individuals at all times. We introduced a hypothetical intervention that reduced the contact rate and applied it to a proportion of the population, irrespective of risk group in the stratified models. We addressed two questions: 1) Does the choice of where to discretize risk alter the model-predicted effectiveness (cases averted) of an intervention relative to an unstratified model? 2) If so, how are deviations from the unstratified model's predicted effectiveness related to the choice of discretization? To answer these questions, we chose an example set of model parameters and examined model predictions following the discretization of various population distributions of contact rates.
Result: For models that produce equivalent epidemic predictions in the absence of intervention, we find that the predicted number of cases averted depends upon how the population's distribution of contact rates is discretized into high- and low-risk groups (Figure 1, Panel A and B). Additionally, Panel A shows that unstratified models may produce a higher estimate of effectiveness than the stratified models, and the extent of this difference depends on the underlying distribution of risk. Deviation from the prediction of the unstratified model (a = 0) is largest when a takes on intermediate values between 0 and 1 (Panel B).
Conclusion: The choice of how to discretize risk in compartmental epidemic models can influence predicted effectiveness of interventions. Analysts should carefully examine multiple alternatives and report the range of results.