Bayesian ‘multi-parameter evidence synthesis’ in addictions research

1. Bayesian ‘multi-parameter evidence synthesis’ in addictions research Lisbon Addictions, October 2017 Hayley E Jones Population Health Sciences, Bristol Medical School, University of Bristol, UK

2. Aims and Acknowledgements Aims: • To communicate the basic concepts – what does MPES allow us to do? • Showcase a few examples in addictions research Acknowledgements: • A E Ades and Matt Hickman, Population Health Sciences, University of Bristol, UK • Daniela De Angelis, MRC Biostatistics Unit, University of Cambridge, UK • Funding from the Medical Research Council (MRC), UK: M014533/1; G1000021 I have no conflicts of interest related to this presentation

3. Introduction Meta-analysis: “A statistical analysis which combines the results of several independent studies considered by the analyst to be ‘combinable’” (Huque, 1988) Multi-parameter evidence synthesis (MPES): “Statistical combination of information on different functions of parameters that are related within a mathematical model” (Ades et al, 2008) When might this be useful in addictions research? To date, applications have been to estimate the prevalence of PDU / PWID or of drug-related harms. Why? • Lack of information telling us directly about these quantities – need to use indirect evidence; • Can include multiple types of information and check their consistency

4. Characteristics of MPES Many data sources – but each is only one part of the jigsaw • Account for fact that a data source estimates a function of the quantity of interest (e.g. prevalence) rather than the quantity itself • Basically, ‘indirect estimation’, just done in a slightly different way • Simultaneously model ‘all available data’ • A generalised version of meta-analysis • Allows us to check consistency of different evidence sources

5. Simple example of (1) • Data source estimates a function of the quantity of interest, rather than the quantity itself • Suppose we want to know the prevalence of a condition. In a sample of 1500 people, 180 test positive (hypothetical data) Observed prevalence is therefore 180/1500 = 12% • But the test isn’t perfect! i.e. it doesn’t have 100% sensitivity or specificity • Then 12% is not a direct estimate of the prevalence. Instead, it is an estimate of:

6. Estimating prevalence, adjusting for sensitivity and specificity Corrected estimate of prevalence, fully accounting for uncertainty in all three data sources = 3.1% (95% Cr-I 0.2, 8.0%) Sensitivity of the test Specificity of the test Prevalence of disease External data on specificity: 90/100 External data on sensitivity: 95/100 Data: 180/1500 = 12% test positive

7. Fitting an MPES model • We use Bayesian Markov chain Monte Carlo (MCMC) software such as WinBUGS / OpenBUGS / JAGS / Stan. • Need to: • Write down the likelihood of all the different types of data • Specify prior distributions for the parameters • Specify the actual function of parameters that each data source provides an estimate of, and how these relate to each other (the ‘model’) • Make sure we have at least as many data sources as parameters

8. (2) Combining multiple data sources • E.g. estimating the prevalence of PDU / PWID • Capture-recapture (CRC) estimation is widely recommended, but also relies on some strong assumptions – and can lead to very biased estimates if these assumptions are violated (*) • Important to check that CRC estimates are consistent with other evidence – e.g. number of drug-related deaths • But rather than just checking this – ideally we want to estimate prevalence based on both sources of information simultaneously Refs: King et al 2005 (AJE), 2009 (Stat Methods Med Res), 2014 (J Roy Stat Soc Ser A) (*) More on this in my talk tomorrow in Paper Session 32

9. Estimating the prevalence of PWID/PDU Estimate of prevalence is revised given the additional data Capture-recapture analysis parameters Prevalence of PWID or PDU Drug-related mortality rate among PWID/PDU Capture-recapture data (multiple lists) Number of drug-related deaths External data on mortality rate

10. Example: PWID in Bristol, UK, 2011 • Estimate from CRC: • 2 models with joint best fit gave estimates of 2960 (95% Cr-I 2430, 3890) or 2530 (2210, 2980) PWID • Additional evidence from mortality data: • 15 drug-related poisonings (DRPs) • Estimated rate of DRPs among PWID = 5.7 (3.9, 8.3) per 1000 person years • Implies estimate of 15/0.0057 = 2630 or, more formally (from a simple Bayesian model), 2570 (1330, 4730) PWID • Estimate from a Bayesian model formally combining CRC and mortality data: 2770 (2570, 3110) Jones, HE. et al (2016). Problem drug use prevalence estimation revisited: heterogeneity in capture–recapture and the role of external evidence. Addiction

11. Wastewater-based epidemiology Jones et al (2014) Science of the Total Environment Excretion profile of drug: what proportion is excreted as the metabolite? Total daily consumption of drug by a population Size of population using sewerage system Proportion of all drug consumed by each route of administration Stability of the metabolite in wastewater Total volume of wastewater passing through system Concentration of metabolite of drug in wastewater sample

12. Wastewater – contribution to MPES? Frequency of use Typical dose Prevalence of drug use Purity Total daily consumption of drug by a population Excretion profile Population Volume Route Stability Concentration of metabolite of drug in wastewater sample Drug-related poisonings CRC Surveys

13. Case study: estimation of HCV prevalence • Available data: seroprevalence studies in different populations: • PWID attending treatment clinics • Genitourinary medicine (GUM) clinic attenders • Women attending antenatal clinics • Individuals donating blood • But none of these are representative samples of whole population • Each estimates prevalence of HCV in a mixture of: • Current PWID • Ex PWID • Non PWID Sweeting et al, 2008

14. Estimation of HCV prevalence To use these data sources to estimate overall prevalence, need also: • Data on relative size of each of the 3 sub-populations (current PWID, ex PWID, non PWID) in each data source. e.g. survey data on proportion of pregnant women with injecting history • Data on relative size of each of the 3 sub-populations in the whole population • Capture-recapture study tells us about prevalence of current PWID • Prevalence of ex PWID estimated based on number of current PWID, survey data on age, duration of injecting etc, and assumptions Sweeting et al, 2008

15. Estimation of HCV prevalence Sweeting et al, 2008; Hickman et al, 2013

16. Estimation of HIV prevalence • MPES has been basis of official UK estimates of HIV prevalence since 2004 • Similarly, model splits population into risk groups (13) and jointly estimates: • Size of each risk group (including, again, prevalence of current & ex PWID…) • HIV prevalence in each group • Probability of an infected individual in each group being diagnosed • Data sources include: • Various seroprevalence surveys • Census • National Survey of Sexual Attitudes and Lifestyles (NATSAL) • Survey of Prevalent HIV Diagnosed (SOPHID) • Challenges around inconsistency of evidence

17. Discussion (1/2): advantages • MPES modelling allows multiple data sources to be synthesised to estimate a quantity / quantities of interest, even if no direct estimates exist • Fully accounts for uncertainty in each data source • If more data sources than parameters, can investigate inconsistencies between evidence (‘triangulation’) and explicitly model biases • Can update MPES model as additional data are identified / become available

18. Discussion (2/2): is it too difficult? • Requires: • Statistical expertise and programming in Bayesian software • Epidemiological expertise – a clear understanding of the data sources, how they were generated and potential biases • The HCV and HIV models were developed over a number of years through a collaboration between expert epidemiologists and statisticians - don’t be intimidated by the complexity of these models! • Simpler but also very useful applications of MPES include: • Estimating prevalence of PWID/PDU using a combination of CRC and drug-related mortality data • Essentially any kind of ‘indirect estimation’ translates to an MPES (as data informs function of parameters) if it is done ‘properly’, i.e. fully accounting for uncertainty

19. References & further reading Overviews: • Hickman, M et al. (2013). Multiple parameter evidence synthesis—a potential solution for when information on drug use and harm is in conflict. Addiction • Ades, AE et al. (2008). Multiparameter evidence synthesis in epidemiology and medical decision-making. Journal of Health Services Research & Policy HCV model: • Sweeting, MJ et al. (2008). Estimating hepatitis C prevalence in England and Wales by synthesizing evidence from multiple data sources. Assessing data conflict and model fit. Biostatistics • Harris, RJ et al. (2011). Hepatitis C prevalence in England remains low and varies by ethnicity: an updated evidence synthesis. European Journal of Public Health HIV model: • Goubar, A. et al (2008). Estimates of human immunodeficiency virus prevalence and proportion diagnosed based on Bayesian multiparameter synthesis of surveillance data. J Roy Statist Soc: Series A