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The epidemic of human immunodeficiency virus type 1 (HIV-1) infection in Thailand has allowed an estimate to be made of the probability of female-to-male HIV-1 transmission per sexual contact. In a study of 1115 21-year-old male military conscripts, of whom 77 (6.9%) were HIV-1 seropositive, sex with female prostitutes was identified as the principal mode of HIV-1 transmission. With a mathematical model including data on conscript's age at first sexual contact, frequency of sex with female prostitutes, and province of origin; as well as province-specific HIV-1 seroprevalence of prostitutes, we estimated the probability of HIV-1 transmission per sexual contact to be 0.031 (95% confidence limits [CL] 0.025-0.040). Allowing for random error in the self-reported frequency of contacts, the estimate was 0.056 (95% CL 0.041-0.075). The transmission probability was significantly greater among men with a history of sexually-transmitted diseases. These estimates are substantially higher than analogous estimates made in North America. This high per-act probability of heterosexual transmission helps to explain the rapid spread of HIV-1 in the emerging epidemic in Thailand and perhaps in other countries where HIV-1 transmission is predominantly heterosexual. [ABSTRACT FROM AUTHOR]

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.

During epidemics of cholera in two rural sites (Bakerganj and Mathbaria), a much higher proportion of patients came for treatment with severe dehydration than was seen in previous years. V. cholerae O1 isolated from these patients was found to be El Tor in its phenotype, but its cholera toxin (CT) was determined to be that of classical biotype. Whether the observed higher proportion of severe dehydration produced by the El Tor biotype was due to a shift from El Tor to classical CT or due to other factors is not clear. However, if cholera due to strains with increased severity spread to other areas where treatment facilities are limited, there are likely to be many more cholera deaths.

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.

We derive the nonparametric maximum likelihood estimate (NPMLE) of the cumulative incidence functions for competing risks survival data subject to interval censoring and truncation. Since the cumulative incidence function NPMLEs give rise to an estimate of the survival distribution which can be undefined over a potentially larger set of regions than the NPMLE of the survival function obtained ignoring failure type, we consider an alternative pseudolikelihood estimator. The methods are then applied to data from a cohort of injecting drug users in Thailand susceptible to infection from HIV-1 subtypes B and E.

Multistate models have been increasingly used to model natural history of many diseases as well as to characterize the follow-up of patients under varied clinical protocols. This modeling allows describing disease evolution, estimating the transition rates, and evaluating the therapy effects on progression. In many cases, the staging is defined on the basis of a discretization of the values of continuous markers (CD4 cell count for HIV application) that are subject to great variability due mainly to short time-scale noise (intraindividual variability) and measurement errors. This led us to formulate a Bayesian hierarchical model where, at a first level, a disease process (Markov model on the true states, which are unobserved) is introduced and, at a second level, the measurement process making the link between the true states and the observed marker values is modeled. This hierarchical formulation allows joint estimation of the parameters of both processes. Estimation of the quantities of interest is performed via stochastic algorithms of the family of Markov chain Monte Carlo methods. The flexibility of this approach is illustrated by analyzing the CD4 data on HIV patients of the Concorde clinical trial.

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.

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.

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.

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.

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.

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.

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.

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.

A review of the data on infectivity per contact for transmission of the HIV suggests that the infectivity may be on the order of 0.1-0.3 per anal intercourse in the period of the initial infection, 10(-4) to 10(-3) in the long asymptomatic period, and 10(-3) to 10(-2) in the period leading into AIDS. The pattern of high contagiousness during the primary infection followed by a large drop in infectiousness may explain the pattern of epidemic spread seen in male homosexual cohorts in the early years of the epidemic. Simulations of cohorts of homosexual males, using that range of parameter values, indicate the following: (a) The initial fast rise and then more or less rapid flattening of the incidence curve of seropositives is primarily due to rapid initial spread, yielding a group of infecteds all of whom pass into the low infectivity asymptomatic period at close to the same time. All this occurs only if the basic reproduction number for the primary infection is > 1. (b) The behavioral changes that have been reported all started after the incidence of new infections began to fall, too late to have a major effect on the initial rise. The behavioral changes had a major effect in slowing down the subsequent rise in the number of seropositives. (c) High activity groups play an important role in the early rapid rise of the epidemic. However, it is not likely that the rapid decrease in rate of growth of seropositives is solely due to saturation of these very high activity groups. Although the evidence for this interpretation of the role of the primary infection is not conclusive, its implications for prevention and for vaccine trials are so markedly different from those of other interpretations that we consider it to be an important hypothesis for further testing.

The per-sexual-act probability of transmission of the human immunodeficiency virus type 1 (HIV) from an infected person to a susceptible sex partner can be determined from a simple model if the number of contacts each study participant has with infected partners is known. The unusual epidemiologic situation in the emerging HIV epidemic in Thailand allowed this quantity to be estimated from a cross-sectional study of young men conscripted into the Thai military in 1991. Although the simple model does not fit the data, an errors-in-variables approach provides a model with adequate fit. Other sources of lack of fit, including heterogeneity of the transmission probability, are discussed. With adjustment for measurement error, the per-act probability is estimated to be 0.056, an order of magnitude higher than similar estimates in North America. Because data indicate that recently infected persons may be more infectious, and because extensive HIV transmission in Thailand began in 1988, this difference may be due, in part, to a higher proportion of recently infected individuals in the emerging Thai epidemic from 1988 to 1991.

Methods of estimating the probability density function of infection times for a population, using serial cross-sectional measurements of a marker of disease progression, are presented. The infection time distribution may be calculated back to the beginning of the epidemic, if it is possible to sample individuals who were infected at the beginning of the epidemic; otherwise, under a Markov assumption, the infection time distribution may be calculated conditional on infection after sampling has begun. In either case, the proportion of prevalent cases infected in an arbitrary time interval between the onset and termination of sampling may be measured. Data from the San Francisco Men's Health Study are analyzed; the infection time distribution compares well with that estimated by Bacchetti (1990, Journal of the American Statistical Association 85, 1002-1008) using stored sera from several San Francisco cohort studies.

To describe causally predictive relationships, model parameters and the data used to estimate them must correspond to the social context of causal actions. Causes may act directly upon the individual, during a contact between individuals, or upon a group dynamic. Assuming that outcomes in different individuals are independent puts the causal action directly upon individuals. Analyses making this assumption are thus inappropriate for infectious diseases, for which risk factors alter the outcome of contacts between individuals. Transmission during contact generates nonlinear infection dynamics. These dynamics can so attenuate exposure-infection relationships at the individual level that even risk factors causing the vast majority of infections can be missed by individual-level analyses. On the other hand, these dynamics amplify causal associations between exposure and infection at the ecological level. The amplification and attenuation derive from chains of transmission initiated by exposed individuals but involving unexposed individuals. A study of household exposure to the only vector of dengue in Mexico illustrates the phenomenon. An individual-level analysis demonstrated almost no association between exposure and infection. Ecological analysis, in contrast, demonstrated a strong association. Transmission models that are devoid of any sources of the ecological fallacy are used to illustrate how nonlinear dynamics generate such results.

Objectives: Data from the Tecumseh Community Health Study were used to estimate excess morbidity owing to influenza, and results were compared with estimates made previously using different methodology for an Institute of Medicine report., Methods: Study participants from Tecumseh, Michigan, were classified as infected or noninfected based on laboratory results. The excess numbers of respiratory illnesses, respiratory illness days, and bed and restricted activity days experienced by the infected compared with the noninfected were estimated., Results: The number of excess influenza-related respiratory illnesses was lower than that estimated in the Institute of Medicine report, in which all illnesses of certain characteristics occurring during an influenza season were attributed to influenza. It is now estimated that the US population under 20 years of age experiences a yearly average of 13.8 to 16.0 million influenza-related excess respiratory illnesses; for older individuals, the yearly estimate is 4.1 to 4.4 million excess illnesses., Conclusions: For public health purposes, estimates of excess morbidity as well as of total morbidity associated with influenza should be used in setting health priorities.

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.

Clinical trials have shown that the prophylactic use of zidovudine and aerosolized pentamidine (or other antibiotics used as prophylaxis against Pneumocystis carinii pneumonia) in acquired immunodeficiency syndrome (AIDS)-free human immunodeficiency virus (HIV)-infected persons delays the development of AIDS, but the effectiveness of such therapy in general use in the population still remains largely undocumented. To help answer this question, the authors estimate the effectiveness of this therapy in a population-based cohort of HIV-infected homosexual and bisexual men in San Francisco. The authors use a continuous-time Markov process to model the decline of CD4+ T-lymphocytes (T4-cells) measured in cells/microliter in HIV-infected persons. The model partitions the HIV (type 1) infection period into six progressive T4-cell count intervals (stages), followed by a seventh stage: AIDS diagnosis. The authors use maximum likelihood methods to fit the model to the observed transitions for 428 HIV-infected men during June 1984 to March 1991, from the San Francisco Men's Health Study. Since zidovudine was not widely used before 1988, the model has a component that controls for calendar time-related biases. The fitted model provides statistical estimates and confidence intervals for measuring therapy effectiveness. The authors estimate that prophylactic therapy reduces the progression rate from stage 4 (T4-cell count, 350-499) to stage 5 (T4-cell count, 200-349) by a factor of 0.26 (95% confidence interval (CI) -0.22 to 0.55); from stage 5 to stage 6 (T4-cell count < 200) by a factor of 0.33 (95% CI 0.04-0.54); and from stage 6 to 7 (AIDS) by a factor of 0.62 (95% CI 0.47-0.73). In addition, therapy started by an HIV-infected person in stage 4 is estimated to reduce the risk of developing AIDS by a factor of 0.83 (95% CI 0.46-0.94) at 6 months and 0.68 (95% CI 0.35-0.89) at 24 months after entering stage 4. Therapy started by HIV-infected persons in more advanced stages is estimated to reduce the risk of developing AIDS by factors ranging from 0.70 (95% CI 0.39-0.90), early in stage 5, to 0.28 (95% CI 0.14-0.45), late in stage 6. Thus, the prophylactic use of zidovudine and pentamidine in routine medical care has a strong, consistent, and significant effect in slowing the clinical course of HIV infection in a population-based cohort.

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 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.

The back-calculation method has been used to estimate the number of HIV infections from AIDS incidence data in a particular population. We present an extension of back calculation that provides estimates of the numbers of HIV infectives in different stages of infection. We model the staging process with a time-dependent Markov process that partitions the HIV infectious period into the following progressive stages and/or substages: stage 1, infected but antibody negative; substages 2-3; antibody positive but asymptomatic; substages 4-6, pre-AIDS symptoms and/or abnormal haematologic indicator, stage 7, clinical AIDS. We also model an eight stage, decreased due to AIDS. The model allows for time-dependent treatment effects that slow the rate of progression in substages 4-7. We use the estimated AIDS incubation period distribution for the Markov model in back calculation from AIDS incidence data to estimate the total number of HIV infections and the parameters of the infection probability distribution. We then use these estimates in the Markov model to estimate the stage-specific numbers of HIV infections over the course of the epidemic in the population under study. Example calculations employ data for epidemic in San Francisco City, Clinic Cohort.

A discrete-time model is devised for the per-time-unit distribution of infectious disease cases in a sample of households. Using the time at which an individual is identified (e.g., when illness symptoms appear) as a marker for being infected, the probabilities of becoming infected from the community or from a single infectious household member are estimated for various risk factor levels. Maximum likelihood procedures for estimating the model parameters are given. An individual may be classified with regard to level of susceptibility and level of infectiousness. The model is fitted to a combination of symptom and viral culture data from a rhinovirus epidemic in Tecumseh, Michigan. In general, it is observed that decreasing risk of infection is associated with increasing age.

A model is formulated for the spread of the human immunodeficiency virus (HIV) and the subsequent development of acquired immunodeficiency syndrome (AIDS) in the population of homosexual men in San Francisco. The dynamic simulation model includes sexually very active and active subpopulations, migration, and a staged progression of HIV-infected persons to AIDS and death. Numerous data sources are used to estimate parameter values in the model. In a companion paper, simulations using the model and parameter estimates are found that are consistent with HIV and AIDS incidence data.

A stochastic infectious disease model was developed by Ball (1986, Advances in Applied Probability 18, 289-310) in which the distribution of the length of the infectious period is allowed to have any distribution that can be described by its Laplace transform. We extend this model such that the infection can be transmitted within the population or from an unspecified source outside the population. Also, discrete heterogeneity in the population can be modeled to incorporate variable susceptibility, variable infectivity, and/or mixing behaviors. The model is fitted to serologic data from two influenza epidemics in Tecumseh, Michigan, using maximum likelihood estimation procedures. The estimates show a clustering pattern by age groups.

Commonly used measures of effect, such as risk ratios and odds ratios, may be quite biased when used to assess the effect of factors that alter transmission risks given exposure to infected individuals. This is demonstrated in a simulation model involving a higher-risk behavior and a lower-risk behavior affecting the sexual transmission of human immunodeficiency virus. The bias arises because population contact patterns between higher-risk and lower-risk persons change their relative probabilities of exposure to an infected individual as an epidemic progresses. The assessment of contact patterns is thus central to risk assessment for contagious diseases. A new formulation of selective mixing presented here, together with a structured mixing specification of the social settings of contact, provides a theoretic framework for the investigation of contact pattern determinants.

A national serosurvey was conducted in Mexico from March to October 1986 to identify predictors of dengue transmission and target areas at high risk of severe annual epidemics. A total of 3,408 households in 70 localities with populations less than 50,000 were randomly sampled, and serology was obtained from one subject under age 25 years in each household. When comparing exposure and infection frequencies across the 70 communities, the authors found that median temperature during the rainy season was the strongest predictor of dengue infection, with an adjusted fourfold risk in the comparison of 30 degrees C with 17 degrees C. High temperatures increase vector efficiency by reducing the period of viral replication in mosquitoes. The proportion of houses in a community with larva on the premises was significantly associated with the community proportion infected (odds ratio (OR)adj = 1.9; 95% confidence interval (CI) 1.4-2.5), as was the proportion of households with uncovered water containers present (ORadj = 1.9; 95% CI 1.4-2.7). Because these factors have effects beyond the individual household and subjects infected from them create a risk for other subjects, both analyses of effects and organization of control efforts must be at the community level. A predictive model was constructed using the community level risk factors to classify communities as being at high, medium, or low risk of experiencing an epidemic; 57% of these communities were correctly classified using this model.

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.

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.

We modeled the decline of CD4+ T-lymphocytes (T4 cells) in HIV-infected individuals with a continuous-time Markov process. The model partitions the HIV infection period into six progressive T4-cell count intervals (states), followed by a seventh state: a definitive HIV-infection end point, i.e., AIDS diagnosis or Walter Reed stage 6 (opportunistic infections). The Markov model was used to estimate the state-specific progression rates from data as functions of important progression cofactors. We applied the model to data on 1,796 HIV-positive individuals in the U.S. Army. The estimated mean waiting time from seroconversion to when the T4-cell count persistently drops below 500/mm3, but is greater than 349/mm3, is 4.1 years, and the waiting time to a T4-cell count of less than 200/mm3 is estimated at 8.0 years. The estimated rate of T4-cell decline was higher for HIV-infected individuals with initially high numbers of T4 cells, but the estimated rate of decline remains relatively uniform when the T4-cell count dropped persistently below 500/mm3. The opportunistic infection incubation period, i.e., the time from seroconversion to opportunistic infection diagnosis, is estimated at 9.6 years. Age is found to be an important cofactor. The estimated mean opportunistic infection incubation periods are 11.1, 10.0, and 8.9 years for the youngest (less than or equal to 25 years old), the middle (26-30 years old), and the oldest (greater than 30 years old) age groups, respectively.(ABSTRACT TRUNCATED AT 250 WORDS)

Analysis and interpretation of observational studies of screening effectiveness is difficult because several biases threaten validity, including the structural healthy screenee bias, length bias, and effects of lead time. Although methods for the analysis of observational studies of screening effectiveness have been proposed, most have limitations such as incomplete control of length bias, or a heavy reliance on distributional assumptions. In this report we present a method for the analysis of observational cohort studies of screening effectiveness. Although developed independently and formulated specifically for estimating benefits of screening, our approach is implied by a more general approach developed previously by Robins. Our approach, in contrast to other available methods, avoids the healthy screenee bias, and length and lead time bias, and allows an empirical approach to analysis that need not depend highly on distributional assumptions. We illustrate application of the approach with analysis of published data from a study of breast cancer screening.

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.

Biological interference among viral agents might have significant implications for disease prevention and therapy. Field data for influenza yield conflicting evidence concerning the independence of infection rates, or disease severity, for two co-circulating viruses. To examine the effects of several assumed modes of interference for influenza, simulations of a Monte Carlo micropopulation model of influenza epidemics have been performed. Model parameters were selected so that the simulated attack rates for each of two different viral strains matched actual field data. Rates of infection were compared for single agents and for two viruses with only behavioural interference. Other simulations included temporary immunity to the other virus for the duration of the infection, and/or reduced shedding of viral particles for dual infections. Simulated viral competition had little impact on epidemic severity, duration, or size distribution. Under the conditions studied, viral interference in natural populations would be difficult to infer from field observations of attack rates. Other simulations extended a partial immunity and/or reduced viral shedding during an infection with a second virus. These indicated that interference might be suggested by field data, but it could not be demonstrated conclusively. Still other simulations showed that for epidemics with much higher attack rates for both viruses, it would be relatively easy to demonstrate interference. However, in order to observe interference between influenza strains, it would be necessary to monitor on an almost daily basis, using a method of viral detection which would have to be both highly specific and also very sensitive.

A maximum likelihood procedure is given for estimating household and community transmission parameters from observed influenza infection data. The estimator for the household transmission probability is an improvement over the classical secondary attack rate calculations because it factors out community-acquired infections from true secondary infections. The mathematical model used does not require the specification of infection onset times and, therefore, can be used with serologic data which detect asymptomatic infections. Infection data were derived by serology and virus isolation from the Tecumseh Respiratory Illness Study and the Seattle Flu Study for the years 1975-1979. Included were seasons of influenza B and influenza A subtypes H1N1 and H3N2. The transmission characteristics of influenza B and influenza A(H3N2) and A(H1N1) outbreaks during this period are compared. Influenza A(H1N1), A(H3N2) and influenza B are found to be in descending order both in terms of ease of spread in the household and intensity of the epidemic in the community. Children are found to be the main introducers of influenza into households. the degree of estimation error from the misclassification of infected and susceptible individuals is illustrated with a stochastic simulation model. This model simulates the expected number of detected infections at different levels of sensitivity and specificity for the serologic tests used. Other sources of estimation error, such as deviation from the model assumption of uniform community exposure and the possible presence of superspreaders, are also discussed.

A model is devised for the distribution of the total number of cases in households from a homogeneous community. In the model, community-acquired infection serves as a source of initial infection within households as well as of possible further cases. In addition, infected household members can infect others in the household. Maximum likelihood procedures for the model parameters are given. The model is fitted to symptom data on influenza and the common cold. Influenza seems to spread more easily in the community than within the household, while the opposite may be the case for the common cold. The model, which does not require specification of the time of onset of infection for individuals, can be fitted to serological data; this would provide a more accurate measure of household infection than the symptom data used.

To estimate the duration and frequency of the period of HIV infection without detectable antibody, modelling techniques were applied to results of detection of HIV DNA by means of the polymerase chain reaction (PCR) and to data from cases in published reports. PCR was carried out with gag and env region primers on samples from 27 homosexual and 12 haemophilic men for whom stored samples were available from before and after seroconversion; serum was also tested for p24 antigen by antigen-capture enzyme immunoassay. HIV DNA was detectable before seroconversion in 4 men; in all 4 PCR was positive only in the seronegative sample taken closest to the time of seroconversion. In 3 men antigen was detected before seroconversion; in each case HIV DNA was also detected. By a Markov model, the time from infection with HIV (as assessed by detection of HIV DNA) to first detection of HIV antibody was estimated to be 2.4 (SE 2.1) months for the median individual. Modelling of cases of HIV infection with known exposure in published reports gave a median estimate of 2.1 (0.1) months from exposure to antibody detection, and 95% of cases would be expected to seroconvert within 5.8 (0.6) months. HIV infection for longer than 6 months without detectable antibody seems uncommon.

Environmental and genetic sources of variation in blood pressure have been assessed for an 82% sample of the Tecumseh, Michigan, population during the period 1962-1965. Correlations of systolic blood pressure and diastolic blood pressure were calculated for sets of related and unrelated individuals living together and related individuals living apart. These correlations were analyzed using a biologic model which partitions the total phenotypic variance into components associated with shared genes and components associated with shared household environments both within and across generations. Heritabilities were estimated to be 0.42 and 0.30 for systolic blood pressure and diastolic blood pressure, respectively. The model confirms the hypothesis that the determinants of blood pressure consist of both significant genetic (p less than 0.005) and environmental (p less than 0.005) components. However, only the shared household environments within generations were found to be significant for systolic blood pressure (p less than 0.005) and diastolic blood pressure (p less than 0.05). Although not significant, the across generation shared environment between mothers and offspring tended to have some importance, while that between fathers and offspring was negligible. The implication that there may be some maternal influence in addition to the genetic influence on the determination of blood pressure in offspring warrants further investigation.