History Matching of A Complex Epidemiological Model of Human Immunodeficiency Virus Transmission By Using Variance Emulation

R. G. White,R. N. Nsubuga,I. Andrianakis,J. E. Oakley,N. McCreesh,T. J. McKinley,I. Vernon,M. Goldstein

doi:10.1111/rssc.12198

Abstract

SummaryComplex stochastic models are commonplace in epidemiology, but their utility depends on their calibration to empirical data. History matching is a (pre)calibration method that has been applied successfully to complex deterministic models. In this work, we adapt history matching to stochastic models, by emulating the variance in the model outputs, and therefore accounting for its dependence on the model's input values. The method proposed is applied to a real complex epidemiological model of human immunodeficiency virus in Uganda with 22 inputs and 18 outputs, and is found to increase the efficiency of history matching, requiring 70% of the time and 43% fewer simulator evaluations compared with a previous variant of the method. The insight gained into the structure of the human immunodeficiency virus model, and the constraints placed on it, are then discussed.

Highlights

Mathematical modelling has played a large role in informing our understanding of infectious disease transmission and epidemiology
In the field of human immunodeficiency virus (HIV), it has been used to investigate the role of partnership concurrency on HIV transmission (McCreesh et al, 2012), to estimate the contribution of acute, early stage infection to overall transmission (Powers et al, 2013), and to estimate the proportion of transmission that occurs outside cohabiting partnerships (Bellan et al, 2013)
Modelling has been used to predict the effects of making antiretroviral therapy universally available to people living with HIV, regardless of how far their disease has progressed (Granich et al, 2009), and estimating the effects of expanding access to antiretroviral therapy and/or pre-exposure prophylaxis in men who have sex with men in the UK (Punyacharoensin et al, 2016)

Summary

Introduction

Mathematical modelling has played a large role in informing our understanding of infectious disease transmission and epidemiology. We analyse a mathematical model of HIV transmission and partnership concurrency, called Mukwano, developed at the London School of Hygiene and Tropical Medicine. It is an individual-based model with 22 inputs and 18 outputs, and is stochastic, meaning that repeated evaluations for the same input parameters do not return the same output, but rather samples from a distribution with unknown characteristics. The usefulness of this and other models depends on our ability to calibrate them to measured empirical data (Grimm et al, 2006; May, 2004). Poor calibration can result in the amount of uncertainty in future projections being underestimated, leading to overconfident predictions being made, and potentially harmful policy decisions

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