Estimation of vaccine effectiveness using the screening method.

The screening method provides a simple and rapid way of estimating vaccine effectiveness. This paper discusses the validity of the screening method with particular reference to bias and precision. Methods for correcting confounding, adjusting for covariates and over-dispersion, and deriving confidence limits are discussed in a modelling framework. The methods are illustrated using data on measles and pertussis vaccines.

Is it appropriate to use fixed assay cut-offs for estimating seroprevalence?

Population seroprevalence can be estimated from serosurveys by classifying quantitative measurements into positives (past infection/vaccinated) or negatives (susceptible) according to a fixed assay cut-off. The choice of assay cut-offs has a direct impact on seroprevalence estimates. A time-resolved fluorescence immunoassay (TRFIA) was used to test exposure to human parvovirus 4 (HP4). Seroprevalence estimates were obtained after applying the diagnostic assay cut-off under different scenarios using simulations. Alternative methods for estimating assay cut-offs were proposed based on mixture modelling with component distributions for the past infection/vaccinated and susceptible populations. Seroprevalence estimates were compared to those obtained directly from the data using mixture models. Simulation results showed that when there was good distinction between the underlying populations all methods gave seroprevalence estimates close to the true one. For high overlap between the underlying components, the diagnostic assay cut-off generally gave the most biased estimates. However, the mixture model methods also gave biased estimates which were a result of poor model fit. In conclusion, fixed cut-offs often produce biased estimates but they also have advantages compared to other methods such as mixture models. The bias can be reduced by using assay cut-offs estimated specifically for seroprevalence studies.

Use of the self-controlled case-series method in vaccine safety studies: review and recommendations for best practice.

The self-controlled case-series method was originally developed to investigate potential associations between vaccines and adverse events, and is now commonly used for this purpose. This study reviews applications of the method to vaccine safety investigations in the period 1995-2010. In total, 40 studies were reviewed. The application of the self-controlled case-series method in these studies is critically examined, with particular reference to the definition of observation and risk periods, control of confounders, assumptions and potential biases, methodological and presentation issues, power and sample size, and software. Comparisons with other study designs undertaken in the papers reviewed are also highlighted. Some recommendations are presented, with the emphasis on promoting good practice.

Measures of disassortativeness and their application to directly transmitted infections.

We propose a measure of disassortativeness to summarize contact patterns relevant to the transmission of directly transmitted infections. We discuss the properties of this measure, describe standardization relative to homogeneous mixing, and generalize it to multivariate contact structures. We explore some of its properties and apply our methods to serological surveys of close contact infections and surveys of self-reported social contacts obtained in several European countries.

Epidemiological studies of the non-specific effects of vaccines: II--methodological issues in the design and analysis of cohort studies.

We review sources of bias which can affect non-randomized cohort studies of non-specific effects of vaccines on child mortality. Using examples from the literature on non-specific effects, we describe different sources of selection and information bias, and, where possible, outline analysis strategies to mitigate or eliminate such biases.

Hepatitis B vaccination and first central nervous system demyelinating events: reanalysis of a case-control study using the self-controlled case series method.

The hypothesis that hepatitis B vaccination is a risk factor for multiple sclerosis has been discussed at length. The data from an earlier case-control study were reanalyzed using the self-controlled case series method. Using the matched cases from the case-control study, we found a relative incidence of 1.68, 95% CI (0.77-3.68) for the 0-60-day post-vaccination risk period; this compares to an odds ratio of 1.8, 95% CI (0.7-4.6). When an additional 53 unmatched cases not used in the case-control study were included, the relative incidence was 1.35, 95% CI (0.66-2.79). Our results throw further light on the methodological aspects of the case series method. We recommend that, when case-control studies of vaccination and adverse events are planned, case series analyses based on the cases are also undertaken when appropriate.

Matrix models for childhood infections: a Bayesian approach with applications to rubella and mumps.

Mathematical modelling is an established tool for planning and monitoring vaccination programmes. However, the matrices describing contact rates are based on subjective choices, which have a large impact on results. This paper reviews published models and obtains prior model probabilities based on publication frequency and expert opinion. Using serological survey data on rubella and mumps, Bayesian methods of model choice are applied to select the most plausible models. Estimates of the basic reproduction number R0 are derived, taking into account model uncertainty and individual heterogeneity in contact rates. Twenty-two models are documented, for which publication frequency and expert opinion are negatively correlated. Using the expert prior with individual heterogeneity, R0=6.1 [95% credible region (CR) 4.3-9.2] for rubella and R0=19.3 (95% CR 4.0-31.5) for mumps. The posterior modes are insensitive to the prior for rubella but not for mumps. Overall, assortative models with individual heterogeneity are recommended.

Does concurrent prescription of selective serotonin reuptake inhibitors and non-steroidal anti-inflammatory drugs substantially increase the risk of upper gastrointestinal bleeding?

BACKGROUND: A 15-fold increased risk of gastrointestinal bleeding has been reported with concurrent use of selective serotonin reuptake inhibitors and non-steroidal anti-inflammatory drugs. Recent guidance cautions against concurrent prescription, particularly in older people. AIM: To quantify the risk of gastrointestinal bleeding associated with current exposure to non-steroidal anti-inflammatory drugs, selective serotonin reuptake inhibitors, and both drugs concurrently. METHODS: We conducted a case-control analysis of 11,261 cases with upper gastrointestinal bleeding and 53,156 controls matched by gender, age and general practice from computerized primary care data. We coupled this with self-controlled case series analysis. RESULTS: Both drugs were associated with a twofold increased risk of gastrointestinal bleeding (odds ratio =2.38, 95% confidence interval 2.08-2.72 for selective serotonin reuptake inhibitors and odds ratio = 2.15, 95% confidence interval 2.02-2.28 for non-steroidal anti-inflammatory drugs). This increased risk was marginally higher for concurrent prescription (odds ratio = 2.93, 95% confidence interval 2.25-3.82). The self-controlled analysis showed a greater incidence rate ratio for gastrointestinal bleeding with non-steroidal anti-inflammatory drugs (2.71, 95% confidence interval 2.51-2.91) and lower incidence rate ratio with selective serotonin reuptake inhibitors (1.71, 95% confidence interval 1.48-1.98). The incidence rate ratio when both drugs were combined was 3.25, 95% confidence interval 1.95-5.42. Estimates were similar after restricting to people over 80 years of age. Increased risk of gastrointestinal bleeding was not specifically related to class of non-steroidal anti-inflammatory drugs and was similar when we looked at tricyclic anti-depressants. CONCLUSIONS: Our study suggests that the risk of gastrointestinal bleeding is not substantially increased when non-steroidal anti-inflammatory drugs and selective serotonin reuptake inhibitors are prescribed together, compared with their use alone.

Infections with varying contact rates: application to varicella.

We develop methods for the analysis of infectious disease data when age-specific contact rates vary over time. Our methods are valid when contact rates vary slowly on the time scale of the infection process, and are applicable to a variety of data types including serial seroprevalence surveys and case reports. The methods exploit approximate endemic equilibria, and require numerical solution of an associated integral equation in age and time. We also estimate summary statistics such as time-dependent analogs of the basic reproduction number and critical immunization threshold. We illustrate the methods with data on varicella (chickenpox) in the United Kingdom.

Estimation of infectious disease parameters from serological survey data: the impact of regular epidemics.

Serological surveys are a useful source of information about epidemiological parameters for infectious diseases. In particular they may be used to estimate contact rates, forces of infection, the reproduction number and the critical vaccination threshold. However, these estimation methods require the assumption that the infection is in endemic equilibrium. Such equilibria seldom exist in practice: for example, many common infections of childhood exhibit regular epidemic cycles. In this paper, we investigate whether ignoring such cycles produces biased estimates. We apply the methods to data on mumps and rubella in the U.K. prior to the introduction of the combined measles, mumps, rubella (MMR) vaccine. We conclude that past epidemics have only a marginal effect on estimates, and that standard methods that do not adjust for regular epidemics are valid.

Control without separate controls: evaluation of vaccine safety using case-only methods.

Epidemiological methods involving only cases are reviewed in the context of vaccine safety studies. These methods include some ecological methods, case-coverage methods, case-crossover and self-controlled case series methods. The properties of the methods are described using examples from the literature. It is argued that such methods, and in particular the self-controlled case series method, are powerful epidemiologic tools meriting the same attention as more traditional cohort and case-control methods.

Parvovirus B19 viraemia in Dutch blood donors.

Blood, donated by asymptomatic donors, may contain and transmit parvovirus B19. To investigate the dynamics of parvovirus viraemia in asymptomatic blood donors, we studied the amounts of parvovirus DNA in pools of donor plasma, the prevalence of parvovirus antibodies among blood donors in relation to age, and the seasonal and year-to-year variation of the incidence of parvovirus infection in The Netherlands. The incidence of parvovirus infection follows a seasonal cycle and a cycle of several years. Among Dutch blood donors the incidence was estimated to be 0.56% per year. Forty seven out of 100 pools of 5000 plasma donations tested positive for parvovirus DNA. We inferred that the course of viraemia in asymptomatic donors shows a short peak (> 10(9) copies parvovirus DNA/ml), followed by viraemia below 10(6) copies/ml for about 2 weeks.

Estimation of effective reproduction numbers for infectious diseases using serological survey data.

The effective reproduction number of an infection, denoted Re, may be used to monitor the impact of a vaccination programme. If Re is maintained below 1, then sustained endemic transmission of the infection cannot occur. In this paper we discuss methods for estimating Re from serological survey data, allowing for age and individual heterogeneity. We describe semi-parametric and parametric models, and obtain an upper bound on Re when vaccine coverage and efficacy are not known. The methods are illustrated using data on mumps and rubella in England and Wales.

Branching process models for surveillance of infectious diseases controlled by mass vaccination.

Mass vaccination programmes aim to maintain the effective reproduction number R of an infection below unity. We describe methods for monitoring the value of R using surveillance data. The models are based on branching processes in which R is identified with the offspring mean. We derive unconditional likelihoods for the offspring mean using data on outbreak size and outbreak duration. We also discuss Bayesian methods, implemented by Metropolis-Hastings sampling. We investigate by simulation the validity of the models with respect to depletion of susceptibles and under-ascertainment of cases. The methods are illustrated using surveillance data on measles in the USA.

On vaccine efficacy and reproduction numbers.

We consider the impact of a vaccination programme on the transmission potential of the infection in large populations. We define a measure of vaccine efficacy against transmission which combines the possibly random effect of the vaccine on individual susceptibility and infectiousness. This definition extends some previous work in this area to arbitrarily heterogeneous populations with one level of mixing, but leads us to question the usefulness of the concept of vaccine efficacy against infectiousness. We derive relationships between vaccine efficacy against transmission, vaccine coverage and reproduction numbers, which generalize existing results. In particular we show that the projected reproduction number RV does not depend on the details of the vaccine model, only on its overall effect on transmission. Explicit expressions for RV and the basic reproduction number R0 are obtained in a variety of settings. We define a measure of projected effectiveness of a vaccination programme PE=1-(RV/R0) and investigate its relationship with efficacy against transmission and vaccine coverage. We also study the effective reproduction number Re(t) at time t. Monitoring Re(t) over time is an important aspect of programme surveillance. Programme effectiveness PE is less sensitive than RV or the critical vaccination threshold to model assumptions. On the other hand Re(t) depends on the details of the vaccine model.

Deaths from variant Creutzfeldt-Jakob disease in the UK.

In 2002, 17 people died from variant CJD (vCJD) in the UK, compared with 20 in 2001 and 28 in 2000. We analysed data for deaths from vCJD since 1995 and estimated the underlying trend in mortality. The trend had a quadratic component (p=0.005), suggesting that the increase was not exponential, and that the previously increasing trend is slowing down. The death rate peaked in 2000. These findings are encouraging, but mortality might increase again in the future.

Interval estimation for Poisson capture-recapture models in epidemiology.

Capture-recapture studies in epidemiology are frequently undertaken to adjust underlying rates for underreporting. This contrasts with applications in ecology, in which the aim is to estimate population size. In consequence, the Poisson model provides a more appropriate framework than the multinomial in some epidemiological applications. A method for constructing profile Poisson likelihood interval estimates using log-linear modelling, avoiding the need for constrained optimization, is described for several relevant parameters, including the unobserved disease rate, the total disease rate, and the case ascertainment probability. Asymptotic properties of these estimates are studied and contrasted with those derived from the multinomial model. The method is illustrated with a published data set on spina bifida.

Changes in age related seroprevalence of antibody to varicella zoster virus: impact on vaccine strategy.

AIM: To study changes in the seroprevalence of varicella zoster virus (VZV) antibody over the past 25 years with a view to determining the target age group for any future vaccination strategy. METHODS: Stored sera collected from different age groups over a period of 25 years were tested by a commercial VZV IgG enzyme immunoassay at a four year time interval. Data were analysed by logistic regression to investigate the evidence for changes in incidence and hence seroprevalence over that period. RESULTS: There was a significant rise in VZV antibody prevalence in the 1-4 year age group during the study period. CONCLUSIONS: A universal childhood VZV vaccination strategy will need to take account of the increase in incidence of VZV infection in children under the age of 4 years; hence, the suggested target age would be between 12 and 18 months---soon after the disappearance of maternal antibody.

Within-subject exposure dependency in case-crossover studies.

In the case-crossover design, only cases are sampled and the hazard ratio is estimated from within-subject comparisons of exposures at the event time and in M control periods prior to the event. We consider the effect of within-subject dependence of exposures in successive time periods. We show that estimates obtained from the conditional logistic model are biased. This bias disappears if the distribution of exposures in the M+1 successive time intervals is exchangeable. In contrast, the Mantel-Haenszel estimator for the odds ratio is approximately unbiased provided that exposures are stationary. Suitable methods of analysis of case-crossover designs using maximum likelihood may be derived from cohort rather than case-control models.