Household transmissibility of avian influenza A (H7N9) virus, China, February to May 2013 and October 2013 to March 2014

To study human-to-human transmissibility of the avian influenza A (H7N9) virus in China, household contact information was collected for 125 index cases during the spring wave (February to May 2013), and for 187 index cases during the winter wave (October 2013 to March 2014). Using a statistical model, we found evidence for human-to-human transmission, but such transmission is not sustainable. Under plausible assumptions about the natural history of disease and the relative transmission frequencies in settings other than household, we estimate the household secondary attack rate (SAR) among humans to be 1.4% (95% CI: 0.8 to 2.3), and the basic reproductive number R0 to be 0.08 (95% CI: 0.05 to 0.13). The estimates range from 1.3% to 2.2% for SAR and from 0.07 to 0.12 for R0 with reasonable changes in the assumptions. There was no significant change in the human-to-human transmissibility of the virus between the two waves, although a minor increase was observed in the winter wave. No sex or age difference in the risk of infection from a human source was found. Human-to-human transmissibility of H7N9 continues to be limited, but it needs to be closely monitored for potential increase via genetic reassortment or mutation.

Assessing the impact of travel restrictions on international spread of the 2014 West African Ebola epidemic

The quick spread of an Ebola outbreak in West Africa has led a number of countries and airline companies to issue travel bans to the affected areas. Considering data up to 31 Aug 2014, we assess the impact of the resulting traffic reductions with detailed numerical simulations of the international spread of the epidemic. Traffic reductions are shown to delay by only a few weeks the risk that the outbreak extends to new countries.

Randomization and baseline transmission in vaccine field trials

In randomized trials, the treatment assignment mechanism is independent of the outcome of interest and other covariates thought to be relevant in determining this outcome. It also allows, on average, for a balanced distribution of these covariates in the vaccine and placebo groups. Randomization, however, does not guarantee that the estimated effect is an unbiased estimate of the biological effect of interest. We show how exposure to infection can be a confounder even in randomized vaccine field trials. Based on a simple model of the biological efficacy of interest, we extend the arguments on comparability and collapsibility to examine the limits of randomization to control for unmeasured covariates. Estimates from randomized, placebo-controlled Phase III vaccine field trials that differ in baseline transmission are not comparable unless explicit control for baseline transmission is taken into account.

Overview of Vaccine Field Studies: Types of Effects and Designs

Vaccination produces many different types of effects in individuals and in populations. The scientific and public health questions of interest determine the choice of measures of effect and study designs. Here we review some of the various measures and study designs for evaluating different effects of vaccination.

Malaria: living with drug resistance

The epidemiological factors associated with the development and spread of drug-resistant malaria have been recently explored by Wemsdorfer in a paper in which he looked at parasite-drug-human-vector interactions that affect the occurrence and dynamics of drug resistance. The question that decision-makers must be asking themselves, as we face the 21st century, is: how will we live with drug resistance? Allan Schapira, Peter Beales and M. Elizabeth Halloran are ideally placed to consider this question. Extracting lessons from the past, they focus on drug-resistant Plasmodium falciparum in Africa. They propose a mathematical model, which will improve the conceptual basis for policy decisions and which has implications for drug development as well as for malaria-control programmes.

Malaria vaccines: lessons from field trials

Malaria vaccine candidates have already been tested and new trials are being carried out. We present a brief description of specific issues of validity that are relevant when assessing vaccine efficacy in the field and illustrate how the application of these principles might improve our interpretation of the data being gathered in actual malaria vaccine field trials. Our discussion assumes that vaccine evaluation shares the same general principles of validity with epidemiologic causal inference, i.e., the process of drawing inferences from epidemiologic data aiming at the identification of causes of diseases. Judicious exercise of these principles indicates that, for meaningful interpretation, measures of vaccine efficacy require definitions based upon arguments conditional on the amount of exposure to infection, and specification of the initial and final states in which one believes the effect of interest takes place.

Using validation sets for outcomes and exposure to infection in vaccine field studies

Methods of adjusting for bias in estimates due to mismeasured or missing covariates and outcomes through the use of validation sets have been developed in many types of health studies. These methods can be employed for the efficient design and analysis of vaccine studies as well. On the one hand, nonspecific case definitions can lead to attenuated efficacy and effectiveness estimates, but confirmation by culture or a quick test of the infectious agent is also expensive and difficult. On the other hand, data on exposure to infection can influence estimates of vaccine efficacy, but good data on exposure are difficult to obtain. In this paper, the authors show how use of small validation sets can correct the bias of the estimates obtained from a large main study while maintaining efficiency. They illustrate the approach for outcomes using the example of influenza vaccine efficacy and effectiveness trials and illustrate the approach for exposure to infection using the example of a human immunodeficiency virus vaccine trial. The authors discuss challenges posed by infectious diseases in the use of currently available methods. Development of these efficient designs and methods of analysis for vaccine field studies will improve estimation of vaccine efficacy for both susceptibility and infectiousness, as well as estimation of indirect and overall effects of vaccination in community trials.

Design and interpretation of vaccine field studies

There are many different effects to consider when evaluating vaccines in the field. In this review, we have covered some of the various measures and issues related to study design and interpretation of the different measures. We emphasize that in designing and understanding vaccine studies, it is necessary to be specific about what the effect of interest is and about the assumptions underlying the interpretation of the results. Halloran et al. (81) present design, analysis, and interpretation of vaccine studies in more detail.

Testing for contributions of mitochondrial DNA mutations to complex diseases

Several complex disorders are suspected of being associated with mitochondrial DNA (mtDNA) mutations. We studied the statistical properties of a test based on proband-relative pairs to identify potential mtDNA mutation involvement in a complex disorder. The test compares the recurrence risk of relatives of probands along the mitochondrial lineage with that of relatives along the nonmitochondrial lineage. If mtDNA mutations are involved, the recurrence risk will be higher among relatives in the mitochondrial lineage. The form of the test is independent of the assumed models of inheritance and interaction of the nuclear autosomal mutations with mtDNA mutations. The power of the test, however, differs among the different models and by the type of proband-relative pairs used in the test. We considered heterogeneity models with and without phenocopies, a three-state heteroplasmic mtDNA transmission model, and a multiplicative epistasis model. Under the heterogeneity model, the power of the test increases as the relationship between the proband and the relative becomes more distant. Under the multiplicative epistasis model, the power of the test decreases as the relationship between the proband and the relative becomes more distant.

Estimation of the efficacy of live, attenuated influenza vaccine from a two-year, multi-center vaccine trial: implications for influenza epidemic control

The authors provide an analysis of data from a two-year (1996-1998), multicenter (ten US cities), double-blinded, placebo-controlled influenza vaccine trial in children. The vaccine was the trivalent cold-adapted influenza vaccine. Estimates are made of the vaccine efficacy for susceptibility to culture-confirmed influenza (VE(S)) while taking inter-center variability in the risk of infection into account. Our overall estimate of VE(S) against influenza is 0.92 (95% confidence interval (CI) 0.89-0.94). In addition, for the second year, although the vaccine contained antigen for A/Wuhan-like (H3N2), the estimated VE(S) for epidemic variant A/Sydney-like (H3N2) was 0.89 (95% CI 0.81-0.94). Thus, the vaccine showed a high degree of protection against a variant not closely matched to the vaccine antigen. With regard to natural immunity, an influenza A infection in the first year reduces the estimated risk of an influenza A infection in the second year by a factor of 0.88 (95% CI 0.21-0.98). When comparing year 1 to year 2, there is a negative correlation of -0.50 in the center-specific attack rates in the placebo groups. This is consistent with the theory that natural immunity provides overall community protection to children. The authors argue that mass vaccination of 70% of the children with the cold-adapted influenza vaccine could provide substantial protection to the community at large.

Efficiency of estimating vaccine efficacy for susceptibility and infectiousness: randomization by individual versus household

In designing vaccine efficacy studies based on the secondary attack rate (SAR) or transmission probability in which both vaccine efficacy for susceptibility, VE(S), and vaccine efficacy for infectiousness, VE(I), are estimated, the allocation of vaccine and placebo within transmission units has an important influence on the efficiency of the study. We compared the following randomization schemes that result in different allocations of vaccine and placebo within two-member households: (1) randomization by individual for a mixed allocation, (2) randomization by transmission unit for concordant allocation, and (3) randomization of only one individual in each transmission unit to either vaccine or placebo. There is a complex interaction among the VE(S), VE(I), and the SAR that determines which allocation of vaccine and placebo within households provides the most information. In general, individual randomization with a mixed allocation of vaccine and placebo is better for estimating both VE(S) and VE(I) than is randomizing by household. However, for estimation of VE(I), at very low SARs and low VE(S), randomization by household is slightly more efficient than randomization by individual.

Semiparametric methods for multiple exposure mismeasurement and a bivariate outcome in HIV vaccine trials

Exposure to infection information is important for estimating vaccine efficacy, but it is difficult to collect and prone to missingness and mismeasurement. We discuss study designs that collect detailed exposure information from only a small subset of participants while collecting crude exposure information from all participants and treat estimation of vaccine efficacy in the missing data/measurement error framework. We extend the discordant partner design for HIV vaccine trials of Golm, Halloran, and Longini (1998, Statistics in Medicine, 17, 2335-2352.) to the more complex augmented trial design of Longini, Datta, and Halloran (1996, Journal of Acquired Immune Deficiency Syndromes and Human Retrovirology 13, 440-447) and Datta, Halloran, and Longini (1998, Statistics in Medicine 17, 185-200). The model for this design includes three exposure covariates and both univariate and bivariate outcomes. We adapt recently developed semiparametric missing data methods of Reilly and Pepe (1995, Biometrika 82, 299 314), Carroll and Wand (1991, Journal of the Royal Statistical Society, Series B 53, 573-585), and Pepe and Fleming (1991, Journal of the American Statistical Association 86, 108-113) to the augmented vaccine trial design. We demonstrate with simulated HIV vaccine trial data the improvements in bias and efficiency when combining the different levels of exposure information to estimate vaccine efficacy for reducing both susceptibility and infectiousness. We show that the semiparametric methods estimate both efficacy parameters without bias when the good exposure information is either missing completely at random or missing at random. The pseudolikelihood method of Carroll and Wand (1991) and Pepe and Fleming (1991) was the more efficient of the two semiparametric methods.

A Markov model for measuring vaccine efficacy for both susceptibility to infection and reduction in infectiousness for prophylactic HIV vaccines

We use a discrete-time non-homogeneous Markov chain to model data from augmented human immunodeficiency virus (HIV) vaccine trials. For this design, the study population consists of primary participants some of whom have steady sexual partners who are also enrolled to augment the trial. The state space consists of the infection status of primary participants without steady partners and the infection status of both persons in the steady partnerships. The transition probabilities are functions of the two parameters: vaccine efficacy for susceptibility (VES) and infectiousness (VEI). We use likelihood methods to estimate VES and VEI from time-to-event data. We then use stochastic simulations to explore the bias and precision of the estimators under various plausible conditions for HIV vaccine trials. We show that both the VES and VEI are estimable with reasonable precision for the conditions that may exist for planned HIV vaccine trials. We show that exams conducted every six months will likely provide sufficient information to estimate the VE parameters accurately, and that there is little gain in precision for more frequent exams. Finally, we show that joint estimation of the VES and VEI will likely be feasible in a currently planned HIV vaccine trial among injecting drug users in Bangkok, Thailand, if one augments the information about the primary participants in the trial with information about their steady sexual partners.

Semi-parametric models for mismeasured exposure information in vaccine trials

Exposure to infection information is important for estimating vaccine efficacy, but it is difficult to collect and inherently prone to missingness and mismeasurement. It is, therefore, generally not feasible to collect good exposure information on all participants in a large vaccine trial. We discuss study designs that collect detailed exposure information for only a small subset of trial participants, while collecting crude exposure information on all participants, and treat estimation of vaccine efficacy in the missing data/measurement error framework. We demonstrate with the example of an HIV vaccine trial the improvements in bias and efficiency when we combine the different levels of exposure information to estimate vaccine efficacy for reducing both susceptibility and infectiousness. We compare the performance of recently developed semi-parametric missing data methods of Pepe and Fleming and Carroll and Wand, Robins, Hsieh and Newey, and Reilly and Pepe.

Optimal vaccine trial design when estimating vaccine efficacy for susceptibility and infectiousness from multiple populations

Vaccination can have important indirect effects on the spread of an infectious agent by reducing the level of infectiousness of vaccinees who become infected. To estimate the effect of vaccination on infectiousness, one typically requires data on the contacts between susceptible and infected vaccinated and unvaccinated people. As an alternative, we propose a trial design that involves multiple independent and interchangeable populations. By varying the fraction of susceptible people vaccinated across populations, we obtain an estimate of the reduction infectiousness that depends only on incidence data from the vaccine and control groups of the multiple populations. One can also obtain from these data an estimate of the reduction of susceptibility to infection. We propose a vaccination strategy that is a trade-off between optimal estimation of vaccine efficacy for susceptibility and of vaccine efficacy for infectiousness. We show that the optimal choice depends on the anticipated efficacy of the vaccine as well as the basic reproduction number of the underlying infectious disease process. Smaller vaccination fractions appear desirable when vaccine efficacy is likely high and the basic reproduction number is not large. This strategy avoids the potential for too few infections to occur to estimate vaccine efficacy parameters reliably.

Estimation of vaccine efficacy in the presence of waning: application to cholera vaccines

The authors present a nonparametric method for estimating vaccine efficacy as a smooth function of time from vaccine trials. Use of the method requires a minimum of assumptions. Estimation is based on the smoothed case hazard rate ratio comparing the vaccinated with the unvaccinated. The estimation procedure allows investigators to assess time-varying changes in vaccine-induced protection, such as those produced by waning and boosting. The authors use the method to reanalyze data from a vaccine trial of two cholera vaccines in rural Bangladesh. This analysis reveals the differential protection and waning effects for the vaccines as a function of biotype and age.

Population biology, evolution, and immunology of vaccination and vaccination programs

The purpose of prophylactic vaccination is to reduce morbidity and mortality in a population. Many questions related to the design of vaccines and vaccination programs require a population standpoint for their sharp formulation and laboratory and field studies to understand their immunologic background. Practical suggestions of the workshop included increased studies of age-specific immunity, better immunoepidemiologic surveillance, better design of efficacy studies, and more systematic sampling of parasite strains to study the evolutionary pressure exerted by vaccines. Theoretical immunology has much to contribute. One of the realizations of the workshop was the value of a strong interdisciplinary approach in vaccine development, utilizing relevant contributions from immunology, population biology, mathematical modeling, epidemiology, molecular biology, and virology.

Augmented HIV vaccine trial design for estimating reduction in infectiousness and protective efficacy

It is important to design HIV vaccine trials to estimate the efficacy of a vaccine in reducing infectiousness in addition to the protective efficacy. Currently planned phase III HIV vaccine field trials in which at-risk individuals are randomized and followed over time do not permit estimation or testing of the vaccine's effect on reducing infectiousness of vaccinees who become infected. We suggest an augmentation of these field trials that recruits steady sexual partners of the primary participants into the trial as far as they are willing to participate. This study design would allow estimation of the efficacy of the vaccine on reducing infectiousness as well as the protective efficacy. We compare the classical design that does not include partners to two different types of augmented design. In the first type of augmentation, called the non-randomized partner design, the steady sexual partners are not randomized to vaccine or placebo. In the second type of augmentation, called the randomized partner design, the steady sexual partners are also randomized to vaccine or placebo. We present a probability model based on infection status at the end of the trial that provides maximum likelihood estimates of the protective efficacy of the vaccine, VES, and the efficacy of the vaccine on reducing infectiousness, VEI. Wald statistics are used for one degree of freedom tests on VES and VEI. With the augmented design, a likelihood ratio test is used to test whether the vaccine has any effect at all. The randomized partner design has more power and provides narrower confidence intervals than does the non-randomized partner design.

Study designs for evaluating different efficacy and effectiveness aspects of vaccines

Vaccine efficacy and effectiveness (VE) are generally measured as 1 minus some measure of relative risk (RR) in the vaccinated group compared with the unvaccinated group (VE = 1 - RR). In designing a study to evaluate vaccination, the type of effect and the question of interest determine the appropriate choice of comparison population and parameter. Possible questions of interest include that of the biologic effect of vaccination on susceptibility, on infectiousness, or on progression to disease in individuals. The indirect effects, total effects, and overall public health benefits of widespread vaccination of individuals within the context of a vaccination program might also be of primary concern. The change in behavior induced by belief in the protective effects of vaccination might influence the estimates of these effects or might itself be of interest. In this paper, the authors present a framework of study designs that relates the scientific question of interest to the choice of comparison groups, the unit of observation, the level of information available for analysis, and the parameter of effect.

A case-control study of the effectiveness of BCG vaccine for preventing leprosy in Yangon, Myanmar

BACKGROUND

Five randomized trials, a follow-up study, and six case-control investigations of BCG vaccine's effectiveness (VE) for preventing leprosy have been conducted internationally, with widely varying estimates of VE. Because of the difficulty of generalizing from disparate results, local estimates of VE are needed for health planning purposes and are currently particularly relevant, given the World Health Organization's (WHO) goal to eliminate leprosy by the year 2000.

METHODS

We conducted a case-control study in Yangon, Myanmar. Residents of Yangon between the ages of 6 years and 24 years who were listed in the National Leprosy Registry as being on active treatment for leprosy between December 1992 and April 1993 were eligible to participate in the study as cases. Control subjects were matched to the cases on age, sex, and neighbourhood.

RESULTS

One or more doses of BCG were associated with a VE of 66%. The results show a significant trend of increasing VE with increasing number of BCG doses (one dose, VE = 55%; two doses, VE = 68%; three doses, VE = 87%). One dose of BCG vaccine appeared to provide protection substantially higher than that found in an earlier vaccine trial in Myanmar, but consistent with results from case-control studies in other countries.

CONCLUSIONS

These data suggest that BCG reduces the risk of leprosy in Myanmar, and that BCG vaccination of infants, along with early case-finding and treatment, should be considered an important part of the leprosy intervention strategy.

Measuring vaccine efficacy for both susceptibility to infection and reduction in infectiousness for prophylactic HIV-1 vaccines

Current Phase III trials are designed to assess only a vaccine candidate's ability to reduce susceptibility to infection or disease, that is, vaccine efficacy for susceptibility (VES). Human immunodeficiency virus (HIV) vaccination, however, may reduce the level of infectiousness of vaccinees who become infected, producing an important indirect reduction in HIV transmission even if the vaccine confers only modest protection against infection. We propose two approaches for augmenting the information of a classic trial for estimating protective efficacy that enable the additional estimation of the vaccine's effect on infectiousness, that is, vaccine efficacy for infectiousness (VEI). In the first augmentation, steady sexual partners of trial participants are recruited but not randomized to vaccine or placebo. Their infection status is monitored throughout the trial. In the second augmentation, the sexual partners are randomized. Through computer simulations and analytic methods, we investigate the feasibility and statistical properties of the augmented designs. Phase III prophylactic HIV-1 vaccines trials are currently being planned. Employment of the augmented designs described in this paper would not only provide estimation of VEI but also increase the precision of the VES estimator and the power to reject the null hypothesis of no vaccine effect.

Predictors of Chlamydia trachomatis infection among female adolescents: a longitudinal analysis

Screening guidelines recommend testing all sexually active female adolescents for Chlamydia trachomatis during a pelvic examination at each clinic visit. Such criteria have been based on cross-sectional studies; new evaluations should take into account multiple clinic visits and assess whether criteria are appropriate when a prior test is negative and risk factors are absent. Because repeated observations on an individual may be correlated, the authors used the generalized estimating equation method. Little information exists on subsequent risk of infection; as control programs develop, approaches targeting high-risk populations for recurrent infections are needed. Using data on females aged 15-19 years who visited family planning clinics more than once from 1988 to 1992 (n = 26,921) in Region X (Alaska, Idaho, Oregon, and Washington), the authors constructed a retrospective cohort. Teens with chlamydia at their first visit were at high risk for subsequent infection (odds ratio = 1.6, 95% confidence interval 1.4-1.7). Among teens uninfected at the first visit and without risk factors at the second, prevalence at the second visit was 6%. When intervisit correlations using the generalized estimating equation method were taken into account, predictors of chlamydial infection were consistent with those in previous cross sectional studies cervicitis, friable cervix, and multiple, new, or symptomatic sex partner(s). These findings support screening sexually active female adolescents at each visit, even if prior tests results are available.

Epidemiologic effects of varicella vaccination

For a plausible range of values for the different efficacy characteristics of the live varicella (Oka) vaccine at different levels of coverage, modeling results suggest that routine immunization of preschool children would greatly reduce the number of primary varicella cases, whereas the shift in age distribution of cases would not result in increased overall morbidity as measured by number of hospitalizations. Although information about some of the vaccine assumptions is scanty, the combinations of assumptions leading to an increase in morbidity seem unlikely. A catch-up program in older children who have not yet had chickenpox will be important. The number and age distribution of the cases in vaccinees are sensitive to assumptions about the vaccine, especially the degree and distribution of partial protection against infection, relative residual infectiousness, and waning of immunity. Responsiveness to boosting by wild-type VZV infection was especially important in reducing the number of older cases. The advantage conferred by responsiveness to boosting depends on the level of transmission. The direct and indirect effects of vaccines and vaccination programs interact. Understanding how a vaccine works at the individual level is important for the vaccinated individual, but it also influences the overall public health benefits of an immunization programs. Lieu et al based a cost-effectiveness analysis of varicella vaccines on this model of varicella dynamics and assumptions about how the vaccines work. Models cannot replace biologic understanding. The purpose of such models is not to predict the number of cases of varicella, but to examine some possible consequences of introducing a vaccine into the routine immunization schedule of preschool children in the United States, effects of different vaccination strategies, and the benefits of a temporary catch-up program for older children. Modeling exercises of this sort force us to formalize our thinking, for instance about the vaccine mechanisms, and to admit our uncertainties, such as about the vaccine efficacy assumptions. Such models also show where more data need to be collected, for example, on boosting and waning of immunity and relative residual infectiousness. Improvements in the design of vaccine efficacy studies are necessary to provide the input to these models for looking at the long-term effects of vaccination programs. Frailty models can be used to analyze the data in the presence of heterogeneities in susceptibility. Waning can also be estimated using appropriate methods. Relative infectiousness of vaccinees with breakthrough cases can be measured by comparing the relative secondary attack rates when the index infected person is vaccinated and when the index infected person is unvaccinated. More studies are needed to understand how to evaluate responsiveness to boosting. Vaccine efficacy studies in the field should be designed to obtain better estimates of residual susceptibility, residual infectiousness, duration of protection, and the effects of boosting by reinfection with wild-type VZV.

Recent developments in theories of pathogenesis of AIDS

Experimental and theoretical progress in HIV research includes an improved resolution of the spatial heterogeneity and the dynamics (time course and turnover rates) of virus and CD4+ cells. Some of these advances have resulted from the joint work of experimental and theoretical groups, demonstrating that interdisciplinary research can be fruitful.

Estimability and interpretation of vaccine efficacy using frailty mixing models

The authors consider estimability and interpretation of vaccine efficacy based on time to event data, allowing that some of the population might have a very low probability of acquiring disease, and the rest have partial, possibly continuously distributed, susceptibility. The efficacy parameters of interest in the frailty mixing model include the fraction highly unlikely to acquire the infection or disease due to the vaccine, the degree of partial protection in those still susceptible, and the average protection or summary measure of efficacy under heterogeneity. The efficacy estimates can still be usefully interpreted when the heterogeneity results from heterogeneity in contact patterns, contact rates, or infectiousness of the contacts, as long as these are equal in the vaccinated and unvaccinated groups. A likelihood-based method allows estimation of the efficacy parameters of interest from grouped time to event data. Simulated vaccine studies assuming different levels and distributions of efficacy demonstrate that ignoring heterogeneity in susceptibility or exposure to infection generally results in underestimation of vaccine efficacy as well as incorrect interpretation of the estimates. The approach is also applicable to other covariates affecting susceptibility or exposure to infection in infectious diseases. Exploitation of the dependent happening structure of infectious diseases to obtain a shape for the baseline hazard may help identifiability. The authors recommend fitting several models to time to event data in vaccine studies.

On individual and population effectiveness of vaccination

BACKGROUND

The protective effect of a vaccine following an outbreak is often measured by the vaccine efficacy statistic, namely one minus the ratio of attack rates in vaccinees and non-vaccinees. This quantity is not an adequate measure of the population-level benefits of the vaccine.

METHODS

We discuss two measures of the effectiveness of a vaccination programme. The first is the commonly used vaccine efficacy statistic. This is called here the individual vaccination effectiveness. The second measure, called the population effectiveness, is defined as one minus the ratio of the overall (or average) attack rate in the population when the vaccination programme is implemented to the expected attack rate in the same population without vaccination. We outline a method for computing the population effectiveness following an outbreak of a directly transmitted acute infectious disease in a closed heterogeneous population. We then explore and compare the behaviour of the two measures of vaccination effectiveness under various conditions.

RESULTS

The population vaccination effectiveness is more robust than individual effectiveness to factors that may interfere with the evaluation of the performance of vaccination. Such factors are non-uniform vaccination, changes in contact patterns by vaccinees, and the ability of the vaccine to reduce infectiousness.

CONCLUSION

The population vaccination effectiveness is a more adequate measure of the population-level benefits of a vaccination programme. The main disadvantage of this measure is that it cannot be readily calculated from observed attack rates.

Assessment of the direct effectiveness of BC meningococcal vaccine in Rio de Janeiro, Brazil: a case-control study

BACKGROUND

Meningococcal disease is still a serious public health problem in many countries. A vaccine produced by Cuba was the first product against B meningococcus available on a large scale. In an attempt to control the increasing incidence of this serogroup in greater Rio de Janeiro, Brazil, the vaccine was used in 1990 in children aged 6 months-9 years. About 1.6 million children were vaccinated.

METHODS

In order to assess the direct effectiveness of the vaccine in preventing disease, we conducted a case-control study during the first year after vaccination. Using a hospital-based census, we selected all children hospitalized with meningococcal disease and sampled the control group among children hospitalized with other types of meningitis. Vaccine effectiveness was estimated from the relationship, 1-OR, where OR (odds ratio) was the exponential of the logistic regression coefficient for the association between meningococcal disease and previous vaccination.

RESULTS

A total of 275 cases and 279 controls were selected between September 1990 and October 1991. The summary adjusted measure of protection against serogroup B was 54% (95% confidence interval [CI]: 20-74%). Estimated protection varied among different age strata and place of residence, being high among children aged > or = 4 years, 71% (95% CI: 34-87%), and among those who lived in the City of Rio de Janeiro, 74% (95% CI: 42-89%).

CONCLUSIONS

The results suggest that the vaccine produced by Cuba may offer protection against serogroup B meningococcal disease, but its effects may not be homogeneous.

The effect of disease prior to an outbreak on estimates of vaccine efficacy following the outbreak

A common source of bias in evaluating vaccine efficacy following a disease outbreak is the presence of persons who had the disease prior to the outbreak. This paper examines the effects of including and excluding pre-outbreak disease cases from the calculation of vaccine efficacy based on the cumulative incidence at the end of an outbreak. Using a five-stage model, the effects of the following factors on the bias of vaccine efficacy estimates are examined: the true protective efficacy of the vaccine, the prevaccination infection rate, differences in vaccine uptake among the previously diseased and nondiseased, differences in pre-outbreak exposure to infection between vaccinees and nonvaccinees, and differences in exposure during the outbreak between vaccinees and nonvaccinees. Numerical calculations of the bias are performed for a hypothetical outbreak of measles in a developing country. Exclusion of pre-outbreak disease cases requires accurate data on disease rates prior to the outbreak, and such data are often unreliable or nonexistent. Inclusion of pre-outbreak cases contributes to the bias of the estimated vaccine efficacy, especially when there is a high prevaccination infection rate and vaccine uptake among the previously diseased is considerably lower than that among the nondiseased. In most practical cases, however, this bias is not very large.

Causal inference in infectious diseases

Since the 1970s, Rubin has promoted a model for causal inference based on the potential outcomes if individuals received each of the treatments under study. Commonly, the assumption is made that the outcome in one individual is independent of the treatment assignment and outcome in other individuals. In infectious diseases, however, whether one person become infected is quite often dependent on the infection outcome in other individuals, a situation known as dependent happenings. Here, we review the model proposed by Rubin for the example of infectious disease. Consequences of the violation of the stability assumption include the need for an expanded representation of outcomes, and the existence of different kinds of effects, such as direct and indirect effects. Effects of interest include changes in susceptibility as well as changes in infectiousness. We define the transmission probability formally as an average causal parameter of effect in a population by conditioning on exposure to infection. Unconditional indirect and total effects are difficult to define formally using this model for causal inference. The assignment mechanism can influence the sampling mechanism when it determines who is exposed to infection, raising problems that require further inquiry. We conclude by contrasting the role of differential exposure to infection in direct and indirect effects.

Empirical Bayes methods for stabilizing incidence rates before mapping

The epidemiologic utility of mapping and ranking incidence rates is often questioned owing to instability of the observed incidence values in areas with small populations. Spurious fluctuations in the observed rates caused by this instability can mask true spatial and temporal trends in risk. To produce maps with the required level of geographic resolution, yet based on reliable estimates, it is desirable to reduce the random variation in the observed rates before mapping. In this paper, we describe the empirical Bayes approach for obtaining stabilized incidence estimates. We begin by deriving Bayes rate estimators and then illustrate how using the observed rates to estimate unknown distributional information leads to the empirical Bayes formulation. A drawback of the approach is that the histogram of the empirical Bayes rate estimates may be narrower than the true distribution of risk. We outline a constrained empirical Bayes approach that produces improved estimators for the true distribution of the unknown rates. We include discussions of relevant previous applications of empirical Bayes methods to rate mapping problems and an evaluation of the strengths and weaknesses of the approach.

Theoretical epidemiologic and morbidity effects of routine varicella immunization of preschool children in the United States

The authors studied the effects of routine varicella immunization of US preschool children and of implementation of a catch-up program in older children on the age distribution of cases and on overall morbidity, with emphasis on the sensitivity of the results to level of vaccine coverage, duration of protection, responsiveness to boosting, relative residual susceptibility and infectiousness, and degree of morbidity among vaccine breakthrough cases. An age-structured theoretical transmission model was used, with values for vaccine efficacy based on a review of the literature by an expert panel. Although implementation of a vaccination program resulted in a shift in the age distribution of remaining varicella cases toward older ages with higher complication rates, the overall reduction in cases resulted in decreased morbidity as measured by overall number of hospitalizations and number of primary cases. Routine immunization with live-virus varicella vaccine would probably result in a substantial reduction in the number of uncomplicated primary cases of chickenpox, as well as a decreased number of complicated cases requiring hospitalization. The number and age distribution of vaccinated cases would depend strongly on the characteristics of the vaccine. Vaccine efficacy studies in the field should be designed to obtain better estimates of residual susceptibility, residual infectiousness, duration of protection, and effects of boosting by wild-type reinfection.

Epidemiologic effects of vaccines with complex direct effects in an age-structured population

Vaccines can alter the dynamic interaction of an infectious agent with a host in complex ways. The effect of routine childhood immunization on age-specific cases was studied in an age-structured population, assuming different vaccine effects at the individual level. Assumptions about vaccine efficacy include partial protection to infection and disease, reduction in infectiousness, waning of protection, and boosting of the level and duration of protection by natural infection. The concept of relative pathogenicity is introduced to describe the effect of a vaccine on the development of disease conditional on being infected. The concepts of the immunologically naive susceptible, naive susceptible equivalent, and relative residual infection potential are introduced in the context of defining the reproduction number of a population vaccinated with a partially protective vaccine. Sensitivity to boosting has a particularly pronounced effect in reducing the number of older vaccinated cases. Near the threshold for eliminating transmission, the dynamic behavior and number as well as age distribution of cases is very sensitive to the degree of protection and relative residual infectiousness. The number of unvaccinated cases is more sensitive to the level of coverage than to the type of vaccine, while the number of vaccinated cases is very sensitive to assumptions about vaccine efficacy.

Exposure efficacy and change in contact rates in evaluating prophylactic HIV vaccines in the field

Field studies of the efficacy of prophylactic vaccines in reducing susceptibility rely on the assumption of equal exposure to infection in the vaccinated and unvaccinated groups. Differential exposure to infection could, however, be the goal of other types of intervention programme, or it could occur secondary to belief in the protective effects of a prophylactic measure, such as vaccination. We call this differential exposure the exposure efficacy, or behaviour efficacy. To study the relative contribution of unequal exposure to infection and differential susceptibility to the estimate of vaccine efficacy, we formulate a simple model that explicitly includes both susceptibility and exposure to infection. We illustrate this on the example of randomized field trials of prophylactic human immunodeficiency virus vaccines. Increased exposure to infection in the vaccinated group may bias the estimated reduction in susceptibility. The bias in the estimate depends on the choice of efficacy parameter, the amount of information used in the analysis, the distribution and level of protection in the population, and the imbalance in exposure to infection. Sufficient increase in contacts in the vaccinated could result in the vaccine being interpreted as having an immunosuppressive effect. Estimates of vaccine efficacy are generally more robust to imbalances in exposure to infection when the detailed history of exposure to infection can be used in the analysis or at high levels of protection. The bias also depends on the relationship between the distribution of vaccine protection and the distribution of behaviour change, which could differ between blinded and unblinded trials.

Cost-effectiveness of a routine varicella vaccination program for US children

OBJECTIVE

To evaluate the economic consequences of a routine varicella vaccination program that targets healthy children.

METHODS

Decision analysis was used to compare the costs, outcomes, and cost-effectiveness of a routine vaccination program with no intervention. Clinical outcomes were based on a mathematical model of vaccine efficacy that relied on published and unpublished data and on expert opinion. Medical utilization rates and costs were collected from multiple sources, including the Kaiser Permanente Medical Care Program and the California Hospital Discharge Database.

RESULTS

A routine varicella vaccination program for healthy children would prevent 94% of all potential cases of chickenpox, provided the vaccination coverage rate is 97% at school entry. It would cost approximately $162 million annually if one dose of vaccine per child were recommended at a cost of $35 per dose. From the societal perspective, which includes work-loss costs as well as medical costs, the program would save more than $5 for every dollar invested in vaccination. However, from the health care payer's perspective (medical costs only), the program would cost approximately $2 per chickenpox case prevented, or $2500 per life-year saved. The medical cost of disease prevention was sensitive to the vaccination coverage rate and vaccine price but was relatively insensitive to assumptions about vaccine efficacy within plausible ranges. An additional program for catch-up vaccination of 12-year-olds would have high incremental costs if the vaccination coverage rate of children of preschool age were 97%, but would result in net savings at a coverage rate of 50%.

CONCLUSIONS

A routine varicella vaccination program for healthy children would result in net savings from the societal perspective, which includes work-loss costs as well as medical costs. Compared with other prevention programs, it would also be relatively cost-effective from the health care payer's perspective.

Estimation of vaccine efficacy from epidemics of acute infectious agents under vaccine-related heterogeneity

A stochastic epidemic model is formulated for the study of the protective effects of vaccination in a population that is stratified by vaccine-related factors. The epidemic model is transformed into a counting process, and then martingale-based methods are used to provide estimators of vaccine efficacy and their variances. Following an example, various extensions of the model are discussed.

On the distribution of vaccine protection under heterogeneous response

We assume that individuals in a vaccinated cohort respond heterogeneously and acquire a continuous spectrum of effective protection against an environmental exposure to infection that can be varying in time. The notion of dynamical invariants is applied to a proportional hazard model with an unvaccinated or placebo cohort as baseline. The hazard is expressed as a susceptibility factor times a measure of environmental exposure to infection. Using the time-evolving information for the aggregated vaccinated cohort and the unvaccinated cohort, it is possible to reconstruct the distribution of effective protection imparted by the vaccination at the beginning of observation. Efficacy is defined in terms of the hazard ratio at the beginning of observation.

Measuring vaccine efficacy from epidemics of acute infectious agents

A good measure of field vaccine efficacy should evaluate the direct protective effect of vaccination on the person who receives the vaccine. The conventional estimator for vaccine efficacy depends on population level factors that are either unrelated or indirectly related to the direct biological action of the vaccine on persons, including population structure, duration of the study, the fraction vaccinated, and herd immunity, that is, indirect effects. Indirect effects can cause the conventional vaccine efficacy estimator to be inaccurate. We review alternative vaccine efficacy estimators that control for indirect effects at the population level. Thus, they are more accurate than the conventional estimator. We use epidemic simulations to explore the robustness of the conventional and proposed estimators under different field conditions. In addition, we apply the different vaccine efficacy estimators to data from a measles epidemic in Muyinga, Burundi.

Interpretation and estimation of vaccine efficacy under heterogeneity

Interpretation and estimation of vaccine efficacy is complicated when the vaccine effect is heterogeneous across vaccinated strata. If a person has a certain susceptibility, or probability of becoming infected conditional on a specified exposure to infection, then one effect of a vaccine would be to reduce that susceptibility, possibly to zero. Vaccine efficacy is a function of the relative susceptibilities in the vaccinated and unvaccinated persons. Under heterogeneity of vaccine effect, a general expression for a summary vaccine efficacy parameter is a function of the vaccine efficacy in the different vaccinated strata weighted by the fraction of the vaccinated subpopulations in each stratum. Interpretation and estimability of the summary vaccine efficacy parameter depends on whether the strata are identifiable, and whether the heterogeneity is host- or vaccine-related. Bounds are derived for the summary vaccine efficacy when the strata are not identifiable for the case of an outbreak of an acute infectious disease. The upper bound assumes that everyone is equally affected by the vaccine, and the lower bound assumes that some are completely protected while others have no protection. The biologic interpretation of the two bounds is different.

Modeling transmission dynamics of stage-specific malaria vaccines

Population effects of malaria vaccination programs will depend on a complex interaction of the stage specificity of the vaccine, its duration of effectiveness, whether it is responsive to natural boosting, the strategy implemented, the proportion vaccinated and the pre-existing endemic conditions. In this article, Elizabeth Halloran and Claudio Struchiner review models of malaria transmission that incorporate aspects of immunity relevant to studying the effects of stage-specific malaria vaccination programs. They discuss the difference in the assumptions and applicability of the models and compare their predictions. Experience with malaria has demonstrated the difficulty in eliminating transmission, so emphasis needs to be on the new host-parasite balance that will be induced by the vaccination program. Although Halloran and Struchiner advise caution in interpreting the results of such models, they conclude that quantitative and theoretical analysis will be important in planning and evaluating interventions with malaria vaccines.

Modeling AIDS vaccines: the cellular level

This paper discusses current strategies for the development of AIDS vaccines which allow immunization to disturb the natural course of HIV at different detailed stages of its life cycle. Mathematical models describing the main biological phenomena (i.e. virus and vaccine induced T4 cell growth; virus and vaccine induced activation of latently infected T4 cells; incremental changes in immune response as infection progresses; antibody dependent enhancement and neutralization of infection) and allowing for different vaccination strategies serve as a background for computer simulations. The mathematical models reproduce updated information on the behavior of immune cells, antibody concentrations and free viruses. The results point to some controversial outcomes of an AIDS vaccine such as an early increase in virus concentration among vaccinated when compared to nonvaccinated individuals.

Estimation of vaccine efficacy in outbreaks of acute infectious diseases

In a previous paper we defined the efficacy of a vaccine as 1-beta 1/beta 0, where beta 0 is the instantaneous probability of transmission of infection to an unvaccinated person exposed to a single infectious person, and beta 1 is similarly defined for a vaccinated person. We showed that under the conditions of an outbreak of an acute, directly transmitted infectious disease in a homogeneous and randomly mixing population, an estimate of this measure of vaccine efficacy is 1-[1n(1-A1)/1n(1-A0)], where A0 and A1 are the observed final attack rates among unvaccinated and vaccinated persons, respectively. In the present work we present an approximation for the standard error of this estimator, accounting for both the sampling and process variation. We extend the results of our previous paper to a stratified population, where the strata correspond to different levels of susceptibility and may have different vaccination coverage. We also consider populations that consist of small units (for example, households) where individuals mix primarily in these units. In this case, definition of vaccine efficacy is in terms of the within-unit transmission probabilities and is estimable by using transmission models for infectious diseases. We apply the estimation methods described above to data from influenza and measles outbreaks. We also examine, via a stochastic simulation study, the robustness of the vaccine efficacy estimators under various population structures and mixing patterns.

Study designs for dependent happenings

In 1916, Sir Ronald Ross defined "dependent happenings" as events where the number affected in a unit of time depends on the number already affected. That is, the incidence depends on the prevalence, a characteristic of many infectious diseases. Because of this dependence, interventions against infectious diseases can have not only direct protective effects for the person receiving an intervention, but also indirect effects resulting from changes in the intensity of transmission in the population. This paper develops the conceptual framework for four types of study designs that differentiate and account for direct and indirect effects of intervention programs in dependent happenings.

Measures of the effects of vaccination in a randomly mixing population

Vaccine efficacy in the field is often derived from the relative attack rates in the vaccinated and unvaccinated after an outbreak. In this paper, vaccine efficacy is defined in terms of the probability that the infectious agent is transmitted from an infected to a susceptible person, and a method for estimating it from the usual attack rate data is given. We explore two mechanisms of vaccine action defined by Smith et al, but include an underlying dynamic epidemic model of an acute directly transmitted disease. We show analytically that under the model in which the vaccine mechanism reduces the probability of infection given a certain exposure, vaccine efficacy based on the relative attack rates underestimates the protective effect of the vaccine based on the relative transmission probabilities. Under the other model in which the vaccine mechanism offers complete protection to a certain proportion of those vaccinated, and no protection to the other vaccinated proportion, the vaccine efficacy based on the relative attack rates will equal that based on the transmission probabilities. Parameters for the effectiveness of a vaccination programme are defined in terms of the direct and indirect benefit to a single person as well as the total and average benefit to the entire population, and derived from the dynamic model for an outbreak of an acute directly transmitted disease. These effects can also be estimated without an actual separate unvaccinated population, independent of assumptions about the vaccine mechanism. The variation of these measures as functions of the fraction of vaccinated people in the population is explored numerically.

Direct and indirect effects in vaccine efficacy and effectiveness

In 1915, Greenwood and Yule noted that for valid vaccine efficacy studies, exposure to infection in the vaccinated and the unvaccinated must be equal (Proc R Soc Med 1915;8(part 2):113-94). The direct effect of a vaccine, however, needs to be defined by the protection it confers given a specific amount of exposure to infection, not just a comparable exposure. In this paper, two classes of parameters are distinguished along lines differing from the conventional distinction between efficacy and effectiveness. Efficacy parameters attempt to control for exposure to infection and represent direct effects on individuals. Direct effectiveness parameters represent a mixture of direct effects on individuals and indirect effects in the population.

[Direct and indirect effects of vaccines: an annotation on the estimation of the vaccine efficacy from outbreaks caused by acute infection agents such as measles]

A good measure of the efficacy of vaccines should be based on an index that standardizes the exposure to infection of those who have been immunized and those who have not. In addition, the measure should not be influenced by indirect effects. In the case of outbreaks directly transmitted agents that cause acute infections diseases, the household secondary rates of attack are the best indicator of vaccine efficacy provided that the data are collected at the household level. If the data are not collected in this manner, the best indicator will be the estimated probability of transmission, even though this estimator and its meaning less obvious than the secondary attack of rate. Other strategies to estimate the efficacy of an immunization are more appropriate for situations that are more complex than outbreaks caused by acute infectious agents.