A mathematical modeling framework for tuberculosis burden estimation and economic evaluation of pharmaceutical interventions

Tuberculosis (TB) is a major cause of disease and death globally. In 2015, WHO estimated there were 9.6 million TB cases and 1.5 TB deaths. Nearly 500,000 of these cases were resistant to two or more of the main drugs used to treat TB. New drugs, and combinations of drugs, are being developed to treat tuberculosis, as are new vaccines that may protect against disease in adults.

Quantifying the burden of TB is fundamental to understanding its global epidemiology and for making appropriate resource allocation decisions. Most estimates of new TB case numbers each year rely strongly on the number of cases reported by countries in that year to WHO. Unfortunately, one in three TB cases are thought to go either undetected or unreported, so the number of cases reported underestimates the number of new cases. While one can correct for this, it is hard to know exactly how much to adjust the reported numbers. Some countries have good systems for recording causes of deaths, which can be used to estimate the number of deaths caused by TB. Increasingly, large and expensive prevalence surveys are being used to estimate the number of people with active disease in a population. These estimates are less subject to bias, but measure a different quantity. Little work has explored the best way of combining these three data sources.

A major goal of this work is to use mathematical transmission models for burden estimation and provide a unified framework for all data. These models yield the number of new cases, deaths, and also the prevalence of disease. They explicitly represent disease transmission and so introduce a dependence between the number of new cases in different years. These models involve parameters evidenced from previous epidemiological work, but must be calibrated to learn from data on TB reports, deaths and prevalence. Calibration means adjusting imperfectly known model parameters in order to match observed model outputs to the data. This process provides a model that may be used to make predictions about burden, but may also teach us something about the underlying processes. Many of the parameters concerning the epidemiology and disease course of TB are quite uncertain, and this uncertainty is rarely represented fully in models needing calibration, but will be done in this project using statistical techniques that also allow comparison of different models' performance.

TB burden estimation and calibration of transmission models are almost always carried out on a country-by-country basis. Many parameters describing disease progression are likely to be similar in different countries, even if their exact values differ for unknown reasons. Hierarchical modelling techniques allow such parameters to be correlated between countries. This can improve precision, particularly for countries with little data, as estimates can be informed by data from neighbouring countries. I will explore these techniques for the transmission model, and also in statistical modelling aiming to account for the observed patterns of drug-resistance. The transmission model will ultimately be extended to include different types of drug resistance.

As new treatments and vaccines emerge, those with responsibility for public health will want to understand the potential impact these new technologies can have in terms of gains in health, and changes in spending. Producing cost-effectiveness and budget impact evidence requires a model that includes transmission, in order to account for indirect benefits accrued by avoiding secondary cases. We will use our model to provide guidance to decision-makers seeking to maximise health gain with limited resources. We will also analyse sources of uncertainty in the model to identify future research that would have most value in increasing the precision of burden estimates and in reducing decision uncertainty around the introduction of new interventions.

The aim of this study is to develop methods to better understand the global burden of tuberculosis (TB), patterns of drug-resistance to TB, and the cost-effectiveness of new pharmaceutical interventions. I will build on my age- and gender-structured model of TB transmission, including HIV/ART, coded in fortran and R, and publicly available as a package. I will use a fully Bayesian inference framework, to calibrate the model to data including notification and vital registration data, and prevalence survey data, integrating over uncertainty in poorly identified parameters. Alternative models, including regression and time-series models of the temporal autocorrelation in incidence will be considered under the same model assumptions relating incidence to measured data. Bayesian model comparison techniques will be used to formally compare the fit of alternative models, and the potential benefit of model averaging in terms of improved out-of-sample predictive accuracy assessed. The model will be fitted in a hierarchical framework and any gains in performance assessed. The relative contribution of different data sources to estimates will be analysed and value-of-information analysis undertaken to identify data types and locations that would most reduce (decision) uncertainty. I will develop Bayesian hierarchical ecological multinomial regression models of the patterns and trends in all types of drug-resistance, having compiled a database of relevant country-level variables. I will incorporate drug-resistance in our transmission model, exploring emulation techniques and pragma-based use of accelerators to make this tractable. I will apply hierarchical regression techniques to cost data and extend our model to calculate disability adjusted life years and costs. I will perform cost-effectiveness, budget impact and health impact analyses of emerging pharmaceutical interventions for TB.

Outputs on the burden of TB are likely to be of interest to a wide range of stakeholders. Methodology and results are likely to be directly useful to organizations involved in similar areas, namely WHO, Avenir Health and the Institute for Health Metrics and Evaluation. Burden results will be of interest to major donors in prioritising investment decisions, and to the countries themselves in identifying any reporting or performance gaps, in preparing concept notes for donors such as the Global Fund, and, potentially, for presenting additional evidence against results. Burden results will be of potential interest to advocates for TB or advocates for particular subgroups identified as receiving less attention. Work prioritising data collection for TB burden estimation will be of interest to those involved in coordinating such efforts at an international level. Understanding patterns of TB drug-resistance, their trends and determinants, will be of interest to epidemiologists, TB programme managers, as well as the manufacturers of anti-TB drugs and diagnostics capable of drug-sensitivity testing.

Results from cost-effectiveness analyses will be of interest to major donors, and national tuberculosis programme managers and Ministries of Health, but also to pharmaceutical companies developing such interventions, and advocates concerned with promoting research and development and market access for such products. Results from cost-effectiveness analyses in specific settings should inform decision-making, and have the potential for impact on the health and productivity of wider society through improved healthcare resource allocation.

The scientific advisory board for this project will include representation from bodies including the WHO and TB Alliance, ensuring that key stakeholders are aware of results arising from the study. Where possible, output data from the study will be made publicly available, and software implementing methods and the model will be made publicly available.

As a result of this project, I will further my skills in the epidemiology of TB and drug-resistant TB in particular, and model implementation and calibration. Through a mixture of formal training and learning-by-doing, I will also develop skills in hierarchical modelling, systematic review, and health economic evaluation, giving me a unique combination of skills for undertaking modelling and analysis to inform TB policy. I will also have developed a platform that can be updated and applied to the economic evaluation of interventions emerging from the pipeline, and further adapted to address additional questions. Interacting with and organising the scientific advisory board will enhance my professional and academic networks, and develop inter-personal and organizational skills. Planning and implementing a complex and long-term piece of work will strengthen my strategic thinking and project management skills, as will specific training courses planned in this area. I intend to develop PhD studentships, potentially in collaboration with the Wellcome Trust Doctoral Training Centre in ScHARR.