Biomedical subjects

N G Becker

Publications and source records attributed to N G Becker.

At least 19 recordsLinked to original sources

PubMed2001

Inference for an epidemic when susceptibility varies.

A stochastic epidemic model featuring fixed-length latent periods, gamma-distributed infectious periods and randomly varying heterogeneity among susceptibles is considered. A Markov chain Monte Carlo algorithm is developed for performing Bayesian inference for the parameters governing the infectious-period length and the hyper-parameters governing the heterogeneity of susceptibility. This method of analysis applies to a wider class of diseases than methods proposed previously. An application to smallpox data confirms results about heterogeneity suggested by an earlier analysis that relied on less realistic assumptions.

Journal Article↗

PubMed2001

Advances in medical statistics arising from the AIDS epidemic.

Many statisticians have contributed to studies of the HIV epidemic and progression to AIDS. They have developed new statistical methodology, where needed, to address HIV-related issues. The transfer of methods from one area to another often involves a substantial delay. This paper points to methods that were developed in the HIV context and have either already found applications in other areas of medical research or have the potential for such applications, with the hope that this will promote a speedier transfer of the research methods. Among the new tools that HIV studies have placed firmly into the pool of statistical methods for medical research are the methods of back-calculation, methods for the analysis of retrospective ascertainment data and methods of analysis for the combined data from clinical trials and associated longitudinal studies. Notions that have been stimulated substantially are use of surrogate endpoints in clinical trials and screening blood products by the use of pooled serum samples. Research activity in many other areas has been boosted substantially through contributions motivated by HIV/AIDS studies. Noteworthy examples are analyses for doubly-censored lifetime data and methods for assessing vaccines for transmissible diseases.

AIDS Vaccines↗

PubMed2000

Estimating HIV incidence using dates of both HIV and AIDS diagnoses.

Knowledge of HIV incidence is important to formulate sensible strategies aimed at controlling the HIV/AIDS epidemic. Back-projection is one of the methods for reconstructing the HIV incidence curve from AIDS incidence data. However, because of the low risk of developing AIDS during the first few years after infection, precise estimates of HIV incidence for the recent past are unlikely if we use AIDS incidence data only. As a result there have been recent attempts to use, not only the date of AIDS diagnosis, but also to use the date of their first positive HIV test. The objective of this paper is to incorporate into back-projection the additional information provided by those individuals who have tested HIV positive but have not yet developed AIDS. This adds information on a very large number of other individuals, and provides the hope that the precision of back-projection is improved considerably. The date of a positive HIV test or an AIDS diagnosis of an individual, whichever comes first, is used in a generalized convolution equation for the purpose of back-projection. The method is illustrated by an application to Australian HIV and AIDS data. Study results show that dramatic improvement in precision is gained for estimates of HIV incidence in recent years when both HIV and AIDS diagnosis dates are used on all individuals.

Acquired Immunodeficiency Syndrome↗

PubMed2000

Estimating the immunity coverage required to prevent epidemics in a community of households.

An estimation of the immunity coverage needed to prevent future outbreaks of an infectious disease is considered for a community of households. Data on outbreak size in a sample of households from one epidemic are used to derive maximum likelihood estimates and confidence bounds for parameters of a stochastic model for disease transmission in a community of households. These parameter estimates induce estimates and confidence bounds for the basic reproduction number and the critical immunity coverage, which are the parameters of main interest when aiming at preventing major outbreaks in the future. The case when individuals are homogeneous, apart from the size of their household, is considered in detail. The generalization to the case with variable infectivity, susceptibility and/or mixing behaviour is discussed more briefly. The methods are illustrated with an application to data on influenza in Tecumseh, Michigan.

Journal Article↗

PubMed1998

The effect of random vaccine response on the vaccination coverage required to prevent epidemics.

The response people have to vaccination varies because their immune systems differ and vaccine failures occur. Here we consider the effect that a random response, independent for each vaccinee, has on the vaccination coverage required to prevent epidemics in a large community. For a community of uniformly mixing individuals an explicit expression is found for the critical vaccination coverage (CVC) and the effect of the vaccine response is determined entirely by the mean E(AB), where A and B, respectively, reflect the infectivity and susceptibility of a vaccinated individual. This result shows that the usual concept of vaccine efficacy, which focuses on the amount of protection the vaccine provides the vaccinee against infection, is not adequate to describe the requirements for preventing epidemics when vaccination affect infectivity. The estimation of E(AB) poses a problem because A and B refer to the vaccine response of the same individual. Similar results are found when there are different types of individual, but now the mean E(AB) may differ between types. However, for a community made up of households it is shown that the CVC also depends on other characteristics of the vaccine response distribution. In practice this means that estimating a single measure of vaccine effectiveness is generally not enough to determine the CVC. For a specific community of households it is found that the vaccination coverage required to prevent epidemics decreases as the variation in the vaccine response increases.

Disease Outbreaks↗

PubMed1998

The effect of community structure on the immunity coverage required to prevent epidemics.

Estimation of the immunity coverage required to effectively control disease transmission is an important public health problem. Using data on the eventual size of a major epidemic, we compare estimates based on the simplifying assumption that the community consists of uniformly mixing individuals with estimates obtained when the more complex community structure is acknowledged. The alternative community structures considered include households and localities that are quite separate. Several inequalities are established for estimates of the critical immunity coverage. For several settings, the coverage estimated by assuming an oversimplified community structure is found to actually be an underestimate. A serious consequence of this finding is that we may be misled into believing that we have estimated an immunity coverage that can prevent epidemics when it in fact cannot. The conclusion is that the heterogeneity in the community must be taken into account when estimating the critical immunity coverage.

Disease Outbreaks↗

PubMed1998

Estimating the transmission rate for a highly infectious disease.

It is pointed out that estimates of disease transmission parameters based on the final size of an epidemic are unsatisfactory when all susceptibles are infected and that this is an event with a substantial probability for communities of practical interest. We propose a method for estimating the transmission rate for such highly infectious diseases under the assumptions that the removal process of the disease is fully observed and that the mean duration of the infectious period is known. The method uses smoothed differentiation of the removal process. A simulation study shows that the method performs satisfactorily.

Communicable Diseases↗

PubMed1997

Estimating a delay distribution from incomplete data, with application to reporting lags for AIDS cases.

Statistical inference for the probability distribution of a reporting delay is considered when delays are recorded only after a certain point in time tau. A method is proposed which utilizes data on incidences arising prior to tau. By a suitable choice of parameters we find explicit expressions for maximum likelihood estimates and standard errors. An application to reporting delay data on Australian AIDS diagnoses demonstrates that inclusion of data on AIDS diagnoses made prior to tau results in significant gains in the precision of estimates. A simulation study indicates for this data set that there is minimal bias in the estimates and the large sample formulae for the standard errors give good estimates of the standard deviation of the estimators.

Acquired Immunodeficiency Syndrome↗

PubMed1997

Optimal vaccination strategies for a community of households.

The effectiveness of a vaccination program depends on how the vaccinations are spread over the households of the community. Here we formulate the optimal allocation of vaccinations as a linear programming problem, when the objective is to prevent epidemics with the minimum vaccination coverage. A vaccine efficacy of less than 100%, as is usual in practice, is allowed for. Optimal vaccine allocations attempt to leave the same number of susceptibles in every household if the disease has a very high transmission rate within households. This means that proportionately more individuals need to be vaccinated in larger households if the vaccine efficacy is < 100%. The linear programming formulation can accommodate heterogeneity among individuals of the proportionate mixing form and can also minimize the initial reproduction number for a given achievable vaccination coverage.

Communicable Disease Control↗

PubMed1997

Preventing epidemics with age-specific vaccination schedules.

A method is proposed for computing the coverage required to prevent epidemics by age-specific vaccination schedules. The method applies in a very general setting and provides explicit expressions in many cases. It can accommodate vaccination doses administered at different ages, heterogeneity among individuals of different ages, a community structured into households, and waning of vaccine-induced immunity. A comparison of results for two specific community settings, with analogous parameter values, indicates that the immunity coverage required to prevent epidemics in a community of households is less than that required for a community of uniformly mixing individuals.

Age Factors↗

PubMed1997

Uses of the EM algorithm in the analysis of data on HIV/AIDS and other infectious diseases.

The analysis of data on infectious diseases is a natural setting for applications of the EM algorithm, because the infection process is only partially observable. Difficulties in determining the expectation at the E step have been side-stepped by adopting pragmatic models which reflect only part of the mechanism that generates the data. In the HIV/AIDS context the EM algorithm has helped in the reconstruction of the unobserved HIV infection curve, the so-called backprojection problem, as well as in the estimation of the distribution for the incubation period until AIDS, in estimating the infectivity of HIV in partnerships and in estimating parameters describing the decline in the immune system. There is a need for smooth estimates of functions in these applications, suggesting the use of the EMS algorithm or use of the EM algorithm to maximize a penalized likelihood. For data on other infectious diseases the application of the EM algorithm has so far been restricted to analyses of data on the size of outbreaks in a sample of households.

Acquired Immunodeficiency Syndrome↗

PubMed1996

Comparison of trends in HIV infection for two risk categories.

Sensible plans for health-care needs and determination of priorities for expenditure require regular assessment of trends in HIV incidences. In particular, trends in the relative HIV incidences of different risk categories are useful when assessing whether current control strategies are working equally well for all risk categories. Here five tests for such trends are proposed for the analysis of AIDS incidence data and their performances are compared by a simulation study, assuming a log-linear trend in the HIV incidences for two risk categories. A convenient test based on a log-linear model for AIDS incidences is found both effective and robust to the nature of the underlying trend. The maximum likelihood estimate of the trend parameter is found stable even though estimates of other HIV incidence parameters are unstable. Smoothing of estimates of the other HIV incidence parameters is recommended because this dramatically reduces the rate of convergence of the iterative methods used to obtain the estimates.

Acquired Immunodeficiency Syndrome↗

PubMed1996

Simultaneous control of measles and rubella by multidose vaccination schedules.

There is currently a preference for using measles-mumps-rubella vaccine to simultaneously control these three diseases. Here an age-specific transmission model is used to investigate the consequences, on cases of measles and congenital rubella syndrome, of switching from a one-dose vaccination with this vaccine to a two-dose vaccination schedule. The model allows for a period of maternally acquired immunity and assumes that infection leads to permanent immunity, while vaccine-induced immunity is allowed to wane. The vaccination coverage at the second dose is expressed in terms of availability for vaccination, which depends on whether the individual received the first dose and the age of the individual. It is found that the optimal age for the first vaccination is not very sensitive to variations in the force of infection and is close to age 1 year for both measles and rubella. However, the optimal age for a second vaccination, offered indiscriminately, depends significantly on the age-specific forces of infection. This emphasizes that decisions about immunization schedules require reliable information about age-specific forces of infection in the community. In some circumstances control may be significantly more effective when the ages for the second dose differ for measles and rubella. It is found that the addition of a catch-up vaccination, offered to previously unvaccinated children at school entry, makes it more feasible to find a common age for the second dose that controls both measles and rubella effectively.

Adolescent↗

PubMed1996

Immunization levels for preventing epidemics in a community of households made up of individuals of various types.

A method is proposed for computing an epidemic threshold parameter for the spread of a communicable disease in a community of households in which individuals are of p different types. The threshold parameter is the largest eigenvalue of a p x p matrix whose elements depend on the rates of disease transmission between types and the distribution of the household size. More explicit expressions are given for diseases that are highly infectious within households, to the point that the infection of any member of a household results in the infection of all susceptible members of that household. For a variety of vaccination strategies it is described how this approach can be used to determine the level of immunity required to prevent epidemics. A numerical example illustrates the results.

Communicable Disease Control↗

PubMed1996

Preventing epidemics in a community of households.

The occurrence of epidemics of vaccine-preventable diseases, and the immunization coverage required to prevent them, is affected by the presence of households and heterogeneity in the community. We consider a community where individuals live in households and are of different types, according to infectivity and/or susceptibility to infection. We describe a method for computing the critical immunization coverage to prevent epidemics in such communities and discuss the effectiveness of immunization strategies. In a heterogeneous community where individuals live in households several immunization strategies are possible and we examine strategies targeting households, randomly selected individuals, or groups with highly intense transmission, such as school children. We compare estimates of the critical immunization coverage if we assume that disease is spread solely by random mixing with estimates which result if we assume the effects of the household structure. Estimates made under these two sets of assumptions differ. The results provide insights into the community effects of vaccination, and the household structure of the community should be taken into account when designing immunization policies.

Child↗

PubMed1995

Assessment of two-dose vaccination schedules: availability for vaccination and catch-up strategies.

An age-specific transmission model is used to discuss aspects of two-dose vaccination schedules. Motivated by measles, the model allows for a period of maternally acquired immunity and assumes that infection leads to permanent immunity. The model expresses the coverage at the second dose in terms of the availability of individuals for vaccination, where availability depends on whether the individual received the first vaccination and the time between the first and second doses. It is emphasized by illustration that medium-term performance is a more appropriate assessment of vaccination schedules than eventual outcome, particularly since elimination of measles does not seem possible at this time. Failure to take account of individuals' availability for vaccination when designing vaccination schedules can lead to a poor control strategy and to unjustified optimism. When disease transmission is in equilibrium, an instantaneous change to a vaccination schedule with high coverage often results in a period of low incidence followed by a series of substantial epidemics occurring over a long period of time. A gradual increase to the same level of vaccination can dampen these epidemic waves significantly and gives similar numbers of cases in the medium and long terms. It is found that a strategy based on doses offered at ages 1 and 11 years is far from optimal, but the inclusion of a catch-up vaccination at school entry, offered only to previously unvaccinated individuals, can improve this two-dose strategy dramatically.

Age Factors↗

PubMed1995

The effect of household distribution on transmission and control of highly infectious diseases.

Two epidemic threshold parameters are derived for the spread of a highly infectious disease in a community of households, where a household is any group whose members have frequent contacts with each other. It is assumed that the infection of any member of a household results in the infection of all susceptible members of that household. The threshold parameters have simple expressions in terms of the mean household size and the mean and variance of the number of susceptibles per household. They provide a basic reproduction number R0 for the spread of infection from individual to individual and a basic reproduction number RH0 for the spread of infection from household to household. The threshold parameters are used to derive the levels of immunity required for the prevention of major epidemics in the community. They are also used to evaluate various vaccination strategies having the same vaccination coverage. For a community with households of equal size, it is found that random vaccination of individuals is better than immunizing all members of a corresponding fraction of households. In contrast, when households have varying sizes, immunizing all members of large households can be better than a corresponding vaccination coverage of randomly selected individuals. It is illustrated that these threshold parameters can also be used for a community of households with schools or day care centers. In particular, the effectiveness of immunizing all members of a school is quantified.

Child↗

PubMed1995

Threshold parameters for epidemics in different community settings.

Threshold parameters of epidemic models play a central role in the assessment of proposed control strategies for infectious diseases. They have been determined for numerous standard epidemic models. This paper points out, with several examples, that threshold parameters depend on the social setting of the community and the variations in the behavior of the members of the community. Specifically, communities are considered in which individuals have fixed patterns of behavior or random patterns of behavior as well as communities of households with fixed or random patterns of behavior. A threshold parameter is computed for each of the different settings. Some comparisons are made to provide insights into the effects that social settings and behavior changes have on the threshold parameters.

Communicable Diseases↗