On sample sizes to estimate the protective efficacy of a vaccine

Effectiveness of Vaccines and Monoclonal Antibodies Against Respiratory Syncytial Virus: Generic Protocol for Register-Based Cohort Study

Several immunization products are currently being developed against respiratory syncytial virus (RSV) for children, pregnant females, and older adults, and some products have already received authorization. Therefore, studies to monitor the effectiveness of these products are needed in the following years. To assist researchers to conduct postmarketing studies, we developed a generic protocol for register-based cohort studies to evaluate immunization product effectiveness against RSV-specific and nonspecific outcomes. To conduct a study on the basis of this generic protocol, the researchers can use any relevant databases or healthcare registers that are available at the study site.

Sample sizes required to estimate the protective efficacy of a vaccine when there is an unequal allocation of individuals across the vaccine and placebo groups

The effectiveness of a vaccine is measured by means of protective vaccine efficacy, defined by V E = 1 - A R V A R U , where A R V and A R U are, respectively, the disease attack rates in the vaccinated and the unvaccinated population. For each of the cohoret and case-control designs, methods have been presented in the literature for calculating the required sample size when the desired width of the confidence interval and the probability of coverage are pre-specified, where an equal number of individuals were assumed to be allocated to the vaccine and placebo group. In this article, we present a method for calculating the required sample size with a specified degree of precision when there is an unequal allocation of individuals across the two groups. The sample size required to achieve a desired power for the relevant level α test has also been explored, keeping the unequal allocation proportion in mind. The fraction of individuals allocated to the placebo group (ρ ) can be so chosen that the total sample size or the expected number of people developing the disease or some other criteria of interest is minimized.

BNT162b2 mRNA COVID-19 against symptomatic Omicron infection following a mass vaccination campaign in southern Brazil: A prospective test-negative design study

BACKGROUND

Evidence regarding effectiveness of BNT162b2 mRNA COVID-19 vaccine against Omicron in Latin America is limited. We estimated BNT162b2 effectiveness against symptomatic COVID-19 in Brazil when Omicron was predominant.

METHODS

This prospective test-negative, case-control study was conducted in Toledo, Brazil, following a mass COVID-19 vaccination with BNT162b2. Patients were included if they were aged ≥12 years, sought care for acute respiratory symptoms in the public health system between November 3, 2021 and June 20, 2022, and were tested for SARS-CoV-2 using RT-PCR. In the primary analysis, we determined the effectiveness of two doses of BNT162b2 against symptomatic COVID-19.

RESULTS

A total of 4,574 were enrolled; of these, 1,758 patients (586 cases and 1,172 controls) were included in the primary analysis. Mean age was 27.7 years, 53.8 % were women, and 90.1 % had a Charlson comorbidity index of zero. Omicron accounted for >97 % of all identified SARS-CoV-2 variants, with BA.1 and BA.2 accounting for 84.3 % and 12.6 %, respectively. Overall adjusted estimate of two-dose vaccine effectiveness against symptomatic COVID-19 was 46.7 % (95 %CI, 19.9 %-64.6 %) after a median time between the second dose and the beginning of COVID-19 symptoms of 94 days (IQR, 60-139 days). Effectiveness waned from 77.7 % at 7-29 days after receipt of a second dose to <30 % (non-significant) after ≥120 days.

CONCLUSION

In a relatively young and healthy Brazilian population, two doses of BNT162b2 provided protection against symptomatic Omicron infection. However, this protection waned significantly over time, underscoring the need for boosting with variant-adapted vaccines in this population prior to waves of disease activity.

TRIAL REGISTRATION NUMBER

ClinicalTrials.gov number, NCT05052307 (https://clinicaltrials.gov/ct2/show/NCT05052307).

BNT162b2 against COVID-19 in Brazil using a test-negative design: Study protocol and statistical analysis plan

INTRODUCTION

Real-world data on COVID-19 vaccine effectiveness are needed to validate evidence from randomized clinical trials. Accordingly, this study aims to evaluate, in a real-world setting in Brazil, the effectiveness of Pfizer-BioNTech BNT162b2 against symptomatic COVID-19 and COVID-19-related complications across diverse populations.

MATERIALS AND METHODS

A test-negative case-control study with follow-up of cases is currently being conducted in Toledo, a city in southern Brazil, following a mass COVID-19 vaccination campaign with BNT162b2. The study is being conducted among patients aged 12 years or older seeking care in the public health system with acute respiratory symptoms and tested for SARS-CoV-2 on reverse transcription polymerase chain reaction (RT-PCR). Cases are RT-PCR positive and controls RT-PCR negative. Test-positive cases are prospectively followed through structured telephone interviews performed at 15 days post-enrollment, and at 1, 3, 6, 9 and 12 months. Baseline demographic, clinical, and vaccination data are being collected by means of structured interviews and medical registry records reviews at the time of enrollment. All RT-PCR-positive samples are screened for mutations to identify SARS-CoV-2 variants.

ETHICS AND DISSEMINATION

The study protocol has been approved by the research ethics committee of all participant sites. Study findings will be disseminated through peer-reviewed publications and conference presentations.

TRAIL REGISTRATION

Clinicatrials.gov: NCT05052307.

Vaccine efficacy trials for Crimean-Congo haemorrhagic fever: Insights from modelling different epidemiological settings

BACKGROUND

Crimean-Congo haemorrhagic fever (CCHF) is a priority emerging pathogen for which a licensed vaccine is not yet available. We aim to assess the feasibility of conducting phase III vaccine efficacy trials and the role of varying transmission dynamics.

METHODS

We calibrate models of CCHF virus (CCHFV) transmission among livestock and spillover to humans in endemic areas in Afghanistan, Turkey and South Africa. We propose an individual randomised controlled trial targeted to high-risk population, and use the calibrated models to simulate trial cohorts to estimate the minimum necessary number of cases (trial endpoints) to analyse a vaccine with a minimum efficacy of 60%, under different conditions of sample size and follow-up time in the three selected settings.

RESULTS

A mean follow-up of 160,000 person-month (75,000-550,000) would be necessary to accrue the required 150 trial endpoints for a target vaccine efficacy of 60 % and clinically defined endpoint, in a setting like Herat, Afghanistan. For Turkey, the same would be achieved with a mean follow-up of 175,000 person-month (50,000-350,000). The results suggest that for South Africa the low endemic transmission levels will not permit achieving the necessary conditions for conducting this trial within a realistic follow-up time. In the scenario of CCHFV vaccine trial designed to capture infection as opposed to clinical case as a trial endpoint, the required person-months is reduced by 70 % to 80 % in Afghanistan and Turkey, and in South Africa, a trial becomes feasible for a large number of person-months of follow-up (>600,000). Increased expected vaccine efficacy > 60 % will reduce the required number of trial endpoints and thus the sample size and follow-time in phase III trials.

CONCLUSIONS

Underlying endemic transmission levels will play a central role in defining the feasibility of phase III vaccine efficacy trials. Endemic settings in Afghanistan and Turkey offer conditions under which such studies could feasibly be conducted.

Modelling the Economic Impact of lnfluenza Vaccine Programs with the Cell-Based Quadrivalent Influenza Vaccine and Adjuvanted Trivalent Influenza Vaccine in Canada

In Canada, approximately 12,000 people annually are hospitalized with influenza. While vaccination is the most effective method for reducing the burden of seasonal influenza, the propagation of vaccine virus strains in eggs can result in egg adaption, resulting in reduced antigenic similarity to circulating strains and thus lower vaccine effectiveness (VE). Cell-based propagation methods avoid these alterations and therefore may be more effective than egg-propagation vaccines. We evaluated three different scenarios: (1) egg-based quadrivalent influenza vaccine (QIVe) for individuals <65 years and adjuvanted trivalent influenza vaccine (aTIV) for ≥65 years; (2) QIVe (<65 years) and high-dose QIV (HD −; QIV; ≥65 years); and (3) cell-based derived QIV (QIVc; <65 years) and aTIV (≥65 years) compared with a baseline scenario of QIVe for all age groups. Modelling was performed using a dynamic age-structured SEIR model, which assessed each strain individually using data from the 2012−2019 seasons. Probabilistic sensitivity analysis assessed the robustness of the results with respect to variation in absolute VE, relative VE, number of egg-adapted seasons, and economic parameters. QIVe + aTIV was cost-saving compared with the baseline scenario (QIVe for all), and QIVe + HD − QIV was not cost-effective in the majority of simulations, reflecting the high acquisition cost of HD − QIV. Overall, while the incremental benefits may vary by influenza season, QIVc + aTIV resulted in the greatest reductions in cases, hospitalizations, and mortality, and was cost-effective (ICER < CAD 50,000) in all simulations.

Effectiveness of BBV152/Covaxin and AZD1222/Covishield vaccines against severe COVID-19 and B.1.617.2/Delta variant in India, 2021: A multi-centric hospital-based case-control study

BACKGROUND

India introduced BBV152/Covaxin and AZD1222/Covishield vaccines from January 2021. We estimated effectiveness of these vaccines against severe Coronavirus disease 2019 (COVID-19) among individuals aged ≥45 years.

METHODS

We did a multi-centric, hospital-based, case-control study between May and July 2021. Cases were severe COVID-19 patients and controls were COVID-19 negative individuals from 11 hospitals. Vaccine effectiveness (VE) was estimated for full (2 doses ≥14days) and partial (1 dose ≥21 days) vaccination; duration between two vaccine doses and against the Delta variant. We used a random effects logistic regression model to calculate adjusted odds ratios (aOR) with 95% CI after adjusting for relevant known confounders.

RESULTS

We enrolled 1,143 cases and 2,541 controls. The VE of full vaccination was 85% (95% CI: 79%-89%) with AZD1222/Covishield and 71% (95% CI: 57%-81%) with BBV152/Covaxin. The VE was highest for an interval of 6-8 weeks between two doses of AZD1222/Covishield (94%, 95% CI: 86%-97%) and BBV152/Covaxin (93%, 95% CI: 34%-99%). The VE estimates were similar against the Delta strain and sub-lineages.

CONCLUSION

BBV152/Covaxin and AZD1222/Covishield were effective against severe COVID-19 among the Indian population during the period of dominance of highly transmissible Delta variant in second wave of pandemic. An escalation of two-dose coverage with COVID-19 vaccines is critical to reduce severe COVID-19 and further mitigate the pandemic in the country.

Efficacy of neem (Azadirachta indica) aqueous fruit extracts against Sarcoptes scabiei var. suis in grower pigs

The acaricidal activity of Azadirachta indica (neem) aqueous fruit extracts was evaluated against Sarcoptes scabiei var. suis (mange mites) in an on-farm trial using grower pigs. Aqueous neem fruit extracts of three concentrations 5%, 10%, and 25% w/v and a commercial acaricide, 12.5% amitraz-based Triatix spray (positive control), were compared with pigs that received no treatment (negative control). Thirty grower pigs of the Dalland breed were allocated to the five treatments in a completely randomized experiment. Each experimental animal was sprayed on day 0 and again on day 7. Counts of mange mites, scoring of lesion index, and calculation of rubbing index were done weekly. Topical application of 25% aqueous neem fruit extract had a higher efficacy ratio (p < 0.05) than the other fruit extract concentrations, and performed similarly to an amitraz-based acaricide, suggesting a dose-dependent response. Amitraz (positive control) cured clinical mange on grower pigs after 5 weeks and 25% aqueous neem fruit extract 6 weeks post-treatment. The results indicated that aqueous neem fruit extracts have acaricidal effects against mange mites and can provide a cheaper, safer, and more eco-friendly alternative for the control of Sarcoptes mange in pigs.

Using simulation to aid trial design: Ring-vaccination trials

BACKGROUND

The 2014-6 West African Ebola epidemic highlights the need for rigorous, rapid clinical trial methods for vaccines. A challenge for trial design is making sample size calculations based on incidence within the trial, total vaccine effect, and intracluster correlation, when these parameters are uncertain in the presence of indirect effects of vaccination.

METHODS AND FINDINGS

We present a stochastic, compartmental model for a ring vaccination trial. After identification of an index case, a ring of contacts is recruited and either vaccinated immediately or after 21 days. The primary outcome of the trial is total vaccine effect, counting cases only from a pre-specified window in which the immediate arm is assumed to be fully protected and the delayed arm is not protected. Simulation results are used to calculate necessary sample size and estimated vaccine effect. Under baseline assumptions about vaccine properties, monthly incidence in unvaccinated rings and trial design, a standard sample-size calculation neglecting dynamic effects estimated that 7,100 participants would be needed to achieve 80% power to detect a difference in attack rate between arms, while incorporating dynamic considerations in the model increased the estimate to 8,900. This approach replaces assumptions about parameters at the ring level with assumptions about disease dynamics and vaccine characteristics at the individual level, so within this framework we were able to describe the sensitivity of the trial power and estimated effect to various parameters. We found that both of these quantities are sensitive to properties of the vaccine, to setting-specific parameters over which investigators have little control, and to parameters that are determined by the study design.

CONCLUSIONS

Incorporating simulation into the trial design process can improve robustness of sample size calculations. For this specific trial design, vaccine effectiveness depends on properties of the ring vaccination design and on the measurement window, as well as the epidemiologic setting.

Vaccines: A review of immune-based interventions to prevent and treat disease

The enormous gains made in public health during the 20th century, through the prevention and treatment of infectious disease, have contributed to dramatic improvements in the quality and length of the human lifespan. Continued advances in medicine are dependent on addressing several challenges including the increase in existing and new resistance to antibiotics, the decrease in productivity of the research and development (R&D) ecosystem, uncertain regulatory pathways, and an economic environment that rewards innovation for developing therapeutics that involve long cycle times from idea to a product. In this article, we consider important issues pertaining to the development of vaccines with particular emphasis on preclinical requirements, optimal dose selection, design, execution, and reporting of clinical trials for regulatory submission, planning and implementation of post-approval life-cycle programs, and emerging themes in therapeutic vaccines.

Sample Size and Data Monitoring for Clinical Trials With Extremely Low Incidence Rates

In clinical trials, statistical analyses on incidence rates detect significant differences between the responses from groups. Sample size estimation is always one of the key aspects in clinical trials that have limited budgets. A prestudy power analysis for sample size calculation is often performed to select an appropriate sample size that will achieve a desired power (ie, the probability of correctly detecting the significant difference if such a difference truly exists) at a prespecified level of significance. In practice, it is expected that a greater sample size is needed to detect a smaller difference. A much larger sample size is required to detect a relatively small difference, especially for those clinical studies with extremely low incidence rates. Thus, sample size calculation based on prestudy power analysis may not be feasible in practice. In this case, as an alternative, the authors propose to justify a selected sample size based on a precision analysis and a sensitivity analysis. A recommended step-by-step procedure for sample size determination in clinical trials with extremely low incidence rate is given. A statistical procedure for data safety monitoring based on the probability statement during the conduct of the clinical trial is also proposed.

Understanding long-term protection of human papillomavirus vaccination against cervical carcinoma: Cancer registry-based follow-up

Phase III clinical trials of human papilloma virus (HPV) vaccination have shown ≥95% efficacy against HPV16/18 associated cervical intraepithelial neoplasia (CIN) Grade 2/3. Long-term surveillance is, however, needed to determine the overall vaccine efficacy (VE) against CIN3 and invasive cervical carcinoma (ICC). During population-based recruitment between September 2002 and March 2003, 1,749 16- to 17-year old Finns participated in a multi-national randomized Phase III HPV6/11/16/18 vaccine (FUTURE II) trial for the determination of VE against HPV16/18 positive CIN2/3. The passive follow-up started at the country-wide, population-based Finnish Cancer Registry (FCR) six months after the active follow-up and voluntary cross-vaccination in April 2007. A cluster randomized, population-based reference cohort of 15,744 unvaccinated, originally 18-19 year old Finns was established in two phases in 2003 and 2005 after the FUTURE II recruitment. We linked these cohorts with the FCR in 2007-2011 (HPV vaccine and placebo cohorts) and 2006-2010 and 2008-2012 (unvaccinated reference cohorts 1 and 2) to compare their incidences of CIN3 and ICC. The four years passive follow-up resulted in 3,464, 3,444 and 62,876 person years for the HPV6/11/16/18, original placebo and reference cohorts, after excluding cases discovered during the clinical follow-up and individuals not at risk. The numbers of CIN3 and ICC cases identified were 0 and 0, 3 and 0, 59 and 3 for the HPV6/11/16/18, placebo and the unvaccinated reference cohorts. The corresponding CIN3 incidence rates were 0/100,000 (95% confidence interval 0.0-106.5), 87.1/100,000 (95% CI 17.9-254.5) and 93.8/100,000 (95% CI 71.4-121), respectively. Long-term surveillance up to 8 years (and longer) post vaccination of the HPV6/11/16/18 vaccine and placebo cohorts, and the unvaccinated reference cohort (not exposed to interventions) for the most stringent efficacy end-points by passive cancer registry-based follow-up is feasible.

Estimation of vaccine efficacy and the vaccination threshold

This paper considers the effect of imperfect vaccination in a susceptible-infected-removal (SIR) epidemic model. The minimum proportion of the population that needs to be vaccinated to prevent a major epidemic depends on the vaccine efficacy and the basic reproductive rate for the SIR model, allowing for imperfect and variable vaccination. Martingale theory is used to derive estimates and associated standard errors for these parameters. Asymptotic properties of the resulting estimators are investigated. Data for a mumps outbreak are used as an illustrative example.

Vaccine Clinical Trials – A Statistical Primer

We discuss some of the key statistical issues that arise in all stages of vaccine development and, where necessary, contrast drug and vaccine clinical trials.

Implications of genetic traits on vaccine efficacy

Literature on genetic screening in the community suggests that people having specific genotypes may either get or protect from infection, for example, malaria, human papilloma virus, and haemophilic influenza, for which vaccines are either already developed or being targeted. In such a situation, the evaluation of the efficacy of vaccine in the community needs to be examined with caution. In this paper, I present a method for the estimation of vaccine efficacy (VE) in the presence of genetic traits/component (theta) and the sample size required to estimate the 95 per cent CI with a given relative width for the estimated vaccine efficacy. Considering true efficacy ranging from 40 to 80 per cent and the possible values of the genetic component (theta) ranging from 0 to 60 per cent, the VE was estimated. The 95 per cent confidence intervals (CI) for the estimated VE for relative widths (R) 1.0 and 0.1 were computed. The sample sizes required for each of the unvaccinated and vaccinated cohorts were computed for estimating the 95 per cent CI for given incidence rates in the unvaccinated (Iu) cohort. In the presence of genetic traits I found that the VE was consistently overestimated. There existed change in the location as well as the asymmetry of the 95 per cent CIs over the point estimate of VE. The sample size required for estimating 95 per cent CI of VE was substantially reduced, resulting in savings. The more the genetic component (theta) affecting disease in the community, the more the savings in sample size. I examined the above estimators for (i) VE, (ii) 95 per cent CI for VE and (iii) sample size required for estimating 95 per cent CI of VE using the real-life data from the Haemophilus influenzae type b vaccine trial conducted in Finland and the global genetic structure of encapsulated H. influenza. Because of escalated VE and large savings in sample size for estimating the 95 per cent CI for VE, I recommend that the design should consider the genetic component that causes/protects from infection/disease for the evaluation of efficacy of vaccine in the field.

Prospects for phase III-IV HPV vaccination trials in the Nordic countries and in Estonia

BACKGROUND

oncogenic, i.e. high risk human papillomavirus (hrHPV) types are the major cause of invasive cervical cancer (ICC). Putatively licensable vaccines against the hrHPVs have been developed and are approaching clinical phase III trials that use persistent HPV infection as end point. Direct extension of the phase III trials towards long-term end points (ICC and its immediate precursors: carcinoma in situ and severe dysplasia, i.e. cervical intraepithelial neoplasia grade III, CINIII) is important, to avoid early contamination of the target population by opportunistic use of licensed HPV vaccines. Country-wide registration on population and health events in a stable population of 25 million make Estonia and the Nordic countries a unique venue for long-term evaluation of cervical cancer control measures. Mass-screening programmes exist in all Nordic countries, but not in Estonia.

AIM

design of phase III-IV trials for evaluation of protection against ICC and CINIII by preventive HPV vaccines based on cancer registry follow-up.

RESULTS

in the Nordic countries, population based randomisation of all 15-year-old women to the vaccination (vaccine and placebo) and reference cohorts entering conventional Pap-smear screening after a clinical phase III trial would assure comparability of the cohorts. Enrollment of 10094 vaccinees +10094 placebo vaccinees +30282 other hrHPV negative women without vaccination at the age of 16 would give 80% power for the demonstration of 70% vaccine efficacy (VE) against ICC in 20 years by cancer registry follow-up. On the other hand, vaccination of 8303 Estonian hrHPV negative women among the entire 15-year-old female birth cohort (about 10000 women) with an already licensed HPV vaccine would enable demonstration of 70% VE against ICC by 20 years of registry follow-up of these and comparable 16606 women identified among the 16-19-year-old birth cohorts.

CONCLUSIONS

evaluation of the protective effect of an HPV vaccine against ICC is possible both in countries with or without mass-screening. The effects of vaccination on spread of different HPVs in the population would need to be monitored, especially in Estonia. Ethical aspects, cost-benefit evaluation and comparisons with other new means of cervical cancer control warrant further investigation.

Urn models and vaccine efficacy estimation

We derive the distribution of the number of infections among unvaccinated and vaccinated individuals for model 1 (leaky) and model 2 (all/nothing) vaccines, assuming random mixing of a homogeneous population. For all/nothing vaccines, we show that the distribution of the number of infected vaccinated individuals conditioning on n observed infections follows a hypergeometric distribution, and the vaccine efficacy estimate (VE) can be derived from the usual estimate of the total population size in a capture-recapture sampling program. For leaky vaccines, we show that the number of vaccinated infected follows a distribution that was first derived by Wallenius. We found that the current point estimates of VE for each model perform very well, but the urn model construction presented here provides a strong framework for estimation and hypothesis testing on the parameters, and can be applied when the available data are a sample of the population. Since the method does not require an underlying transmission model, it can be applied to estimate the VE for non-contagious diseases.

Attack rates of human papillomavirus type 16 and cervical neoplasia in primiparous women and field trial designs for HPV16 vaccination

BACKGROUND

Identification of human papillomavirus type 16 (HPV16) as the major risk factor for cervical neoplasia, and mass production of DNA free HPV capsids have paved the way to preventive vaccination trials. Design of such trials requires reliable attack rate data.

OBJECTIVE

Determination of (1) HPV16 and (2) cervical neoplasia attack rates in primiparous women. Estimation of actuarial sample sizes for HPV16 vaccination phase IV trials.

DESIGN

A longitudinal cohort study.

METHODS

Population based Finnish Maternity Cohort (FMC) and Finnish Cancer Registry (FCR) were linked for the identification of two cohorts of primiparous women: (1) a random subsample of the FMC: 1656 women with two pregnancies between 1983-9 or 1990-6 and living in the Helsinki metropolitan area, and (2) all 72,791 primiparous women living in the same area during 1983-94. Attack rate for persistent HPV16 infection (1) was estimated in 1279 seronegative women by proportion of seroconversions between the first and the second pregnancy. Comparable 10 year cumulative incidence rate (CR) of cervical intraepithelial neoplasia grade III and cervical cancer (CIN III+) (2) was estimated based on cases registered at the FCR during 1991-4.

RESULTS

The HPV16 attack rates were 13.8% (< 18 years), 7.0% (18-19 years), 2.3% (21 years), 2.4% (23 years), and 4.5% (< 25 years). Number of vaccinees required for a 5 year efficacy trial with persistent HPV16 infection as the end point ranged between 1000 and 3900, assuming 80% power, 90%-70% vaccine efficacy (VE), and misclassification. The CRs of CIN III+ were 0.33% (< 18 years), 0.44% (18-19 years), 0.21% (20-24 years), and 0.28% (< 25 years). Number of vaccinees required for a 10 year efficacy trial with HPV16 positive CIN III+ as the end point was 15,000 assuming 80% power, 90% VE, and 75% aetiological fraction of CIN III+ for HPV16.

CONCLUSIONS

The attack rates of HPV16 and CIN III+ identify primiparous women under 25 years of age among target populations for postnatal HPV vaccination at phase II/III trials.

Vaccination against Lyme disease with recombinant Borrelia burgdorferi outer-surface lipoprotein A with adjuvant. Lyme Disease Vaccine Study Group

BACKGROUND

The risk of acquiring Lyme disease is high in areas in which the disease is endemic, and the development of a safe and effective vaccine is therefore important.

METHODS

We conducted a multicenter, double-blind, randomized trial involving 10,936 subjects who lived in areas of the United States in which Lyme disease is endemic. Participants received an injection of either recombinant Borrelia burgdorferi outer-surface lipoprotein A (OspA) with adjuvant or placebo at enrollment and 1 and 12 months later. In cases of suspected Lyme disease, culture of skin lesions, polymerase-chain-reaction testing, or serologic testing was done. Serologic testing was performed 12 and 20 months after study entry to detect asymptomatic infections.

RESULTS

In the first year, after two injections, 22 subjects in the vaccine group and 43 in the placebo group contracted definite Lyme disease (P=0.009); vaccine efficacy was 49 percent (95 percent confidence interval, 15 to 69 percent). In the second year, after the third injection, 16 vaccine recipients and 66 placebo recipients contracted definite Lyme disease (P<0.001); vaccine efficacy was 76 percent (95 percent confidence interval, 58 to 86 percent). The efficacy of the vaccine in preventing asymptomatic infection was 83 percent in the first year and 100 percent in the second year. Injection of the vaccine was associated with mild-to-moderate local or systemic reactions lasting a median of three days.

CONCLUSIONS

Three injections of vaccine prevented most definite cases of Lyme disease or asymptomatic B. burgdorferi infection.

A review of the design of vaccine efficacy trials and a proposal for the design of the VA Cooperative Study of Active Immunotherapy of HIV Infection

We review the design of vaccine trials based on a search of the medical literature over the past four years, and present the proposed design of a therapeutic HIV vaccine efficacy study by the Department of Veterans Affairs Cooperative Studies Program. We explore the reasons for the atypical design of many vaccine trials, particularly the analysis of efficacy and how it differs from the more usual intent-to-treat analysis used in nonvaccine trials.

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.

Sample size and power for prospective analysis of relative risk

In a placebo-controlled vaccine efficacy trial or a trial of equivalence of vaccines, one may wish to show that relative risk of disease is less than a specified value R0, not equal to one. This paper compares three methods for estimating relative risk in the binomial setting, based on a logarithmic transformation, likelihood scores, and a Poisson approximation. Exact power and size of test are calculated by enumeration of possible binomial outcomes, and power is approximated from asymptotic formulations. Although the score method is generally preferable, for most studies of practical interest the log and score methods are comparable, and the Poisson method is also appropriate for small risks, up to about 0.05. When true and null relative risks are less than one, unequal allocation of study individuals can increase power, and the asymptotic formula for the log method may substantially underestimate power; in such a study the power approximation for the score method is more reliable, even if the log method is used in analysis. Exact power calculations are helpful in planning studies. The log and Poisson methods, but not the score method, apply readily in the case of unequal follow-up.

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.

A bibliography and comments on the use of statistical models in epidemiology in the 1980s

This paper reviews developments in statistical modelling in epidemiology in the 1980's, with emphasis on cohort and case-control studies. The central roles of the logistic and proportional hazard models are highlighted, and it is shown how these models lead to a deeper understanding of classical designs and methods of analysis as well as to efficient new designs and analytical procedures. The important area of model misspecification is discussed, including the problems of omitted latent structure, mis-modelling of available measurements, missing data and errors in measurements. Various designs motivated by the logistic model are illustrated numerically, and designs based on the proportional hazards model are discussed, as are papers on sample size determination. There are brief introductions to the literature on other topics, including attributable risk, disease clustering, family studies and genetics, analysis of disease incidence data, infectious disease, longitudinal data, screening and miscellaneous related topics in statistics. An extensive bibliography is indexed according to the outline of the paper.

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.

Sample sizes for repeated measurements in dichotomous data

When the measurement of outcome varies within studied subjects and the cost of additional subjects is high, taking more than one measurement for each subject constitutes a useful alternative to increase the power or to reduce the total cost of the study. In this paper, I present sample size formulae for repeated measurements in dichotomous data under different situations. I also discuss optimal sample allocation for repeated measurements.