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
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; G
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%)
Prevalence of disease
Specificity of the test
Sensitivity of the test
External data on sensitivity: 95/100
External data on specificity: 90/100
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 data (multiple lists)
Capture-recapture analysis parameters
Prevalence of PWID or PDU
External data on mortality rate
Number of drug-related deaths
Drug-related mortality rate among PWID/PDU

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

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