Statistical Methods in Medical Research

Capture—recapture (C—RC) using four data sources, one of which accounted for 81% of captured injectors, and multiple indicator methods (MIM) were used to obtain national, regional and local estimates of the prevalence of injecting drug use among opiate and/or crack cocaine users in England. Persons aged 15 to 64 years, in contact with health and/or criminal justice services during 2005/2006, and known to be using opiates and/or crack cocaine and injecting drugs were included in the C—RC analysis. The MIM analysis included indicators relating to drug treatment, drug-related deaths, population density and drug offences.

There were an estimated 130,000 opiate and/or crack cocaine users who injected drugs in 2005/06 (95% confidence interval 125,800 to 137,000), corresponding to 3.9 per thousand of the population aged 15 to 64 years (95% confidence interval 3.8—4.1). Regional variation in the prevalence of injecting was evident, ranging from 6.1 per thousand of the population aged 15 to 64 years in Yorkshire and the Humber (95% confidence interval 5.6 to 6.6) to 2.3 per thousand in the East of England (95% confidence interval 1.8 to 2.9). Application of gender and age-group distributions for treated injecting drug users (IDUs) to the prevalence estimates suggested that there were 97,200 male injectors (95% confidence interval 94,000 to 102,500) and 63,600 female injectors aged 25 to 34 years (95% confidence interval 61,500 to 67,000).

The prevalence estimates provide a basis from which numbers of current IDUs infected with hepatitis C virus (HCV) can be approximated.

Using Bayesian capture—recapture methods, we estimate current injectors in Scotland in 2003, and, thereby, injectors' drug-related death rates for the period 2003—2005. Four different data sources are considered [Hepatitis C Virus (HCV) database, hospital admissions, social enquiry reports, and drug misuse database reports by General Practices or Drug Treatment Agencies] which provide covariate information on sex, region (Greater Glasgow versus elsewhere in Scotland) and age group (15—34 years and 35+ years).

We quantified Scotland's current injectors in 2003 at 27,400 (95% highest probability density interval: 20,700—32,100) by incorporating underlying model uncertainty in terms of the possible interactions present between data sources and/or covariates. The posterior probability was 72% that Scotland had more current injectors in 2003 than in 2000. Detailed comparison with 2000 gave evidence of importantly changed numbers of current injectors for different covariate classes.

In addition, and of particular social interest, is the estimation of injectors' drug-related death rates. Expert information was used to construct upper and lower bounds on the number of drug-related deaths pertaining to injectors, which were then used to provide bounds on injectors' drug-related death rates. Failure to incorporate expert information could result in over-estimation of drug-related death rates for subclasses of injectors.

In England and Wales, routine monitoring has been consistently showing an increase in mortality and morbidity due to infection with the Hepatitis C Virus (HCV). However, the magnitude of the underlying epidemic is still the subject of debate. In this paper we present estimates of the number of individuals aged 15—59 chronically infected with HCV in 2003, derived from a Bayesian synthesis of information available from multiple sources on the size of the groups at risk for HCV and the risk specific anti-HCV prevalence. Results show that the number of chronic infections is of the order of 142,000 (95% CrI: 90,000, 231,000), with the majority (85%, 95% CrI: 74%, 93%) in injecting drug users and about 80% (95% CrI: 74%, 84%) in the age group 15—44.

Injecting drug use is the main route of transmission for the hepatitis C virus in the developed world. Knowledge about the characteristics of the past and current injecting drug user (IDU) population is therefore vital in order to understand the epidemiology of hepatitis C. The IDU population is `hard to reach' and hence most epidemiological studies have concentrated on estimating current IDU prevalence, whilst little is known about the potentially large pool of ex-injectors. We demonstrate a method for estimating the proportion of ex-users in the population, by considering injecting drug use as a time-to-event process. We show how unbiased estimates of injecting duration and historical patterns in injecting initiation can be derived from a sample of ex-IDUs obtained from a population survey, and how such data lead to estimates of the proportion of ex-IDUs in the population. Finally, we show how to obtain estimates of the prevalence of ex-IDUs by using additional information on the prevalence of current IDUs.

Many studies on optimal designs for linear mixed model analysis of repeated measures data have focussed on estimating the fixed effects. The present study investigates the optimal number of time points and subjects in case random effects have to be estimated. Linear mixed models with a linear or quadratic trend across equidistant time points are studied. Given a particular cost function, we examine which designs minimise the expected average squared prediction error. Robustness of the optimal design, important when one does not know the underlying model, is also treated.

The objectives of this study were to establish and describe a database of Cochrane and non-Cochrane meta-analyses of safety data and to determine under what conditions exact methods differ from asymptotic methods in meta-analyses of safety data. A sample of Cochrane (n = 500) and non-Cochrane (n = 200) systematic reviews was randomly selected and a database of safety meta-analyses established. Point estimates and confidence intervals for each meta-analysis were recalculated using exact methods and compared to the results of asymptotic methods. Cochrane reviews were nearly four times as likely as non-Cochrane reviews to contain meta-analyses of safety data (35% compared to 9%). More than 50% of safety meta-analyses contained an outcome with a rare event rate (<5%) and 30% contained at least one study with no events in one arm of the study. For rare event meta-analyses, exact point estimates differed substantially from asymptotic estimates 46% of the time, compared to 17% for those without rare events. Exact confidence intervals differed substantially from asymptotic ones 67% of the time compared to only 19% for those without rare events. The magnitude of differences was also correlated with the number of studies and the summary statistic used to combine the data. Asymptotic methods will not always be a good approximation for exact methods in safety meta-analyses. Event rates and number of studies should be closely examined when choosing the statistical method for combining rare event data.