Estimation of the Force of Infection from Current Status Data Using Generalized Linear Mixed Models

Based on sero-prevalence data of rubella, mumps in the UK and varicella in Belgium, we show how the force of infection, the age-specific rate at which susceptible individuals contract infection, can be estimated using generalized linear mixed models (McCulloch & Searle, 2001). Modelling the dependency of the force of infection on age by penalized splines, which involve fixed and random effects, allows us to use generalized linear mixed models techniques to estimate both the cumulative probability of being infected before a given age and the force of infection. Moreover, these models permit an automatic selection of the smoothing parameter. The smoothness of the estimated force of infection can be influenced by the number of knots and the degree of the penalized spline used. To determine these, a different number of knots and different degrees are used and the results are compared to establish this sensitivity. Simulations with a different number of knots and polynomial spline bases of different degrees suggest - for estimating the force of infection from serological data - the use of a quadratic penalized spline based on about 10 knots.     

Bayesian Experimental Design for Long-Term Longitudinal HIV Dynamic Studies

The study of HIV dynamics is one of the most important developments in recent AIDS research for understanding the pathogenesis of HIV-1 infection and antiviral treatment strategies. Currently a large number of AIDS clinical trials on HIV dynamics are in development worldwide. However, many design issues that arise from AIDS clinical trials have not been addressed. In this paper, we use a simulation-based approach to deal with design problems in Bayesian hierarchical nonlinear (mixed-effects) models. The underlying model characterizes the long-term viral dynamics with antiretroviral treatment where we directly incorporate drug susceptibility and exposure into a function of treatment efficacy. The Bayesian design method is investigated under the framework of hierarchical Bayesian (mixed-effects) models. We compare a finite number of feasible candidate designs numerically, which are currently used in AIDS clinical trials from different perspectives, and provide guidance on how a design might be chosen in practice.     

Bayesian Methods for a Growth-Curve Degradation Model with Repeated Measures

The increasingreliability of some manufactured products has led to fewer observedfailures in reliability testing. Thus, useful inference on thedistribution of failure times is often not possible using traditionalsurvival analysis methods. Partly as a result of this difficulty,there has been increasing interest in inference from degradationmeasurements made on products prior to failure. In the degradationliterature inference is commonly based on large-sample theoryand, if the degradation path model is nonlinear, their implementationcan be complicated by the need for approximations. In this paperwe review existing methods and then describe a fully Bayesianapproach which allows approximation-free inference. We focuson predicting the failure time distribution of both future unitsand those that are currently under test. The methods are illustratedusing fatigue crack growth data.     

A competing risks approach for nonparametric estimation of transition probabilities in a non-Markov illness-death model

Competing risks model time to first event and type of first event. An example from hospital epidemiology is the incidence of hospital-acquired infection, which has to account for hospital discharge of non-infected patients as a competing risk. An illness-death model would allow to further study hospital outcomes of infected patients. Such a model typically relies on a Markov assumption. However, it is conceivable that the future course of an infected patient does not only depend on the time since hospital admission and current infection status but also on the time since infection. We demonstrate how a modified competing risks model can be used for nonparametric estimation of transition probabilities when the Markov assumption is violated.     

Backcalculation of flexible linear models of the human immunodeficiency virus infection curve

The authors present a regression approach to the backcalculation of flexible linear models of the HIV infection curve. They note that "because expected AIDS incidence can be expressed as a linear function of unknown parameters, regression methods may be used to obtain parameter and covariance estimates for a variety of interesting quantities, such as the expected number of people infected in previous time intervals and the projected AIDS incidence in future time intervals. We exploit these ideas to show that estimates based on maximum likelihood are, for practical purposes, equivalent to approximate estimates based on quasi-likelihood and on Poisson regression. These algorithms are readily implemented on a personal computer." These concepts are illustrated by projecting AIDS incidence in the United States up to 1993.     

A Partial Likelihood Estimator of Vaccine Efficacy

A partial likelihood method is proposed for estimating vaccine efficacy for a general epidemic model. In contrast to the maximum likelihood estimator (MLE) which requires complete observation of the epidemic, the suggested method only requires information on the sequence in which individuals are infected and not the exact infection times. A simulation study shows that the method performs almost as well as the MLE. The method is applied to data on the infectious disease mumps.     

Joint Modelling of Recurrent Infections and Antibody Response by Bayesian Data Augmentation

Abstract.  A joint dynamic model for the interdependence between infection, immunity and risk of disease is presented. Recurrent latent infections are modelled as realizations from a renewal process and antibody dynamics as a diffusion with a decreasing drift modified by the stimulating effect of the random infections. The augmented submodels are estimated simultaneously in one large Markov chain Monte Carlo algorithm. As an example, we consider the risk of recurrent ear infections when having only partially observed information on bacterial carriage and antibody concentrations.     

A new threshold regression model for survival data with a cure fraction

Due to the fact that certain fraction of the population suffering a particular type of disease get cured because of advanced medical treatment and health care system, we develop a general class of models to incorporate a cure fraction by introducing the latent number N of metastatic-competent tumor cells or infected cells caused by bacteria or viral infection and the latent antibody level R of immune system. Various properties of the proposed models are carefully examined and a Markov chain Monte Carlo sampling algorithm is developed for carrying out Bayesian computation for model fitting and comparison. A real data set from a prostate cancer clinical trial is analyzed in detail to demonstrate the proposed methodology.     

A multistate approach for estimating the incidence of human immunodeficiency virus by using data from a prevalent cohort study

Summary.  Cohort studies of individuals infected with the human immunodeficiency virus (HIV) provide useful information on the past pattern of HIV diagnoses, progression of the disease and use of antiretroviral therapy. We propose a new method for using individual data from an open prevalent cohort study to estimate the incidence of HIV, by jointly modelling the HIV diagnosis, the inclusion in the cohort and the progression of the disease in a Markov model framework. The estimation procedure involves the construction of a likelihood function which takes into account the probability of observing the total number of subjects who are enrolled in the cohort and the probabilities of passage through the stages of disease for each observed subject conditionally on being included in the cohort. The estimator of the HIV infection rate is defined as the function which maximizes a penalized likelihood, and the solution of this maximization problem is approximated on a basis of cubic M -splines. The method is illustrated by using cohort data from a hospital-based surveillance system of HIV infection in Aquitaine, a region of south-western France. A simulation study is performed to study the ability of the model to reconstruct the incidence of HIV from prevalent cohort data.     

Estimation of prolongation of hospital stay attributable to nosocomial infections: New approaches based on multistate models

Evaluation of the impact of nosocomial infection on duration of hospital stay usually relies on estimates obtained in prospective cohort studies. However, the statistical methods used to estimate the extra length of stay are usually not adequate. A naive comparison of duration of stay in infected and non-infected patients is not adequate to estimate the extra hospitalisation time due to nosocomial infections. Matching for duration of stay prior to infection can compensate in part for the bias of ad hoc methods. New model-based approaches have been developed to estimate the excess length of stay. It will be demonstrated that statistical models based on multivariate counting processes provide an appropriate framework to analyse the occurrence and impact of nosocomial infections. We will propose and investigate new approaches to estimate the extra time spent in hospitals attributable to nosocomial infections based on functionals of the transition probabilities in multistate models. Additionally, within the class of structural nested failure time models an alternative approach to estimate the extra stay due to nosocomial infections is derived. The methods are illustrated using data from a cohort study on 756 patients admitted to intensive care units at the University Hospital in Freiburg.     

A mixture model for the detection of Neosporosis without a gold standard

Neosporosis is a bovine disease caused by the parasite Neospora caninum. It is not yet sufficiently studied, and it is supposed to cause an important number of abortions. Its clinical symptoms do not yet allow the reliable identification of infected animals. Its study and treatment would improve if a test based on antibody counts were available. Knowing the distribution functions of observed counts of uninfected and infected cows would allow the determination of a cutoff value. These distributions cannot be estimated directly. This paper deals with the indirect estimation of these distributions based on a data set consisting of the antibody counts for some 200 pairs of cows and their calves. The desired distributions are estimated through a mixture model based on simple assumptions that describe the relationship between each cow and its calf. The model then allows the estimation of the cutoff value and of the error probabilities.     

Bayesian compartmental model for an infectious disease with dynamic states of infection

Population-level proportions of individuals that fall at different points in the spectrum [of disease severity], from asymptomatic infection to severe disease, are often difficult to observe, but estimating these quantities can provide information about the nature and severity of the disease in a particular population. Logistic and multinomial regression techniques are often applied to infectious disease modeling of large populations and are suited to identifying variables associated with a particular disease or disease state. However, they are less appropriate for estimating infection state prevalence over time because they do not naturally accommodate known disease dynamics like duration of time an individual is infectious, heterogeneity in the risk of acquiring infection, and patterns of seasonality. We propose a Bayesian compartmental model to estimate latent infection state prevalence over time that easily incorporates known disease dynamics. We demonstrate how and why a stochastic compartmental model is a better approach for determining infection state proportions than multinomial regression is by using a novel method for estimating Bayes factors for models with high-dimensional parameter spaces. We provide an example using visceral leishmaniasis in Brazil and present an empirically-adjusted reproductive number for the infection.     

Little Magazine Interview Index 2002

Abstract

This is the seventeenth issue of our annual index of interviews, compiled from currently received journal titles in the Sukov Collection of Little Magazines, Department of Special Collections, Memorial Library, University of Wisconsin–Madison. The list for 2002 includes 645 interviews with a mix of well-known and new writers and artists. The slight increase in number over past installments reaffirms the importance of a format that allows writers to speak freely about their work. As previously, the index follows a list of journal titles currently received by the library, but not included in the thirty-eighth edition of the International Directory of Little Magazines and Small Presses (Dustbooks). The titles are organized alphabetically by country of publication, with addresses for further reference. Many of the titles now have their own Websites. Given their often ephemeral nature, we do not attempt to provide valid URLs for those sites. Serials Review 2003; 29:127–136.     

A copula model for bivariate hybrid censored survival data with application to the MACS study

A copula model for bivariate survival data with hybrid censoring is proposed to study the association between survival time of individuals infected with HIV and persistence time of infection with an additional virus. Survival with HIV is right censored and the persistence time of the additional virus is subject to interval censoring case 1. A pseudo-likelihood method is developed to study the association between the two event times under such hybrid censoring. Asymptotic consistency and normality of the pseudo-likelihood estimator are established based on empirical process theory. Simulation studies indicate good performance of the estimator with moderate sample size. The method is applied to a motivating HIV study which investigates the effect of GB virus type C (GBV-C) co-infection on survival time of HIV infected individuals.     

Estimation of the basic reproduction number for infectious diseases from age-stratified serological survey data

The basic reproduction number of an infection, R ₀, is the average number of secondary infections generated by a single typical infective individual in a totally susceptible population. It is directly related to the effort required to eliminate infection. We consider statistical methods for estimating R ₀ from age-stratified serological survey data. The main difficulty is indeterminacy, since the contacts between individuals of different ages are not observed. We show that, given an estimate of the average age-specific hazard of infection, a particular leading left eigenfunction is required to specify R ₀. We review existing methods of estimation in the light of this indeterminacy. We suggest using data from several infections transmitted via the same route, and we propose that the choice of model be guided by a criterion based on similarity of their contact functions. This approach also allows model uncertainty to be taken into account. If one infection induces no lasting immunity, we show that the only additional assumption required to estimate R ₀ is that the contact function is symmetric. When matched data on two or more infections transmitted by the same route are available, the methods may be extended to incorporate the effect of individual heterogeneity. The approach can also be applied in partially vaccinated populations and to populations comprising loosely linked communities. The methods are illustrated with data on hepatitis A, mumps, rubella, parvovirus, Haemophilus influenzae type b and measles infection.     

Marginal maximum a posteriori estimation using Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) methods, while facilitating the solution of many complex problems in Bayesian inference, are not currently well adapted to the problem of marginal maximum a posteriori (MMAP) estimation, especially when the number of parameters is large. We present here a simple and novel MCMC strategy, called State-Augmentation for Marginal Estimation (SAME), which leads to MMAP estimates for Bayesian models. We illustrate the simplicity and utility of the approach for missing data interpolation in autoregressive time series and blind deconvolution of impulsive processes.     

Cofactors and markers of disease progression in human immunodeficiency virus infection

The identification of factors which are related to human immunodeficiency virus (HIV) disease progression, either by a direct interaction with HIV to increase the rate of disease progression or by providing an indication of an infected individual's likely prognosis, can have great value when understanding HIV pathogenesis and in the development of novel therapeutic approaches. This paper describes the roles of the CD4 cell count and the viral load as markers of disease progression and discusses the recent findings on chemokine receptors in HIV infection. Our current knowledge on these factors is summarized and unresolved statistical issues are highlighted.     

ON OPTIMIZING MULTI-LEVEL DESIGNS: POWER UNDER BUDGET CONSTRAINTS

This paper derives a procedure for efficiently allocating the number of units in multi‐level designs given prespecified power levels. The derivation of the procedure is based on a constrained optimization problem that maximizes a general form of a ratio of expected mean squares subject to a budget constraint. The procedure makes use of variance component estimates to optimize designs during the budget formulating stages. The method provides more general closed form solutions than other currently available formulae. As such, the proposed procedure allows for the determination of the optimal numbers of units for studies that involve more complex designs. A method is also described for optimizing designs when variance component estimates are not available. Case studies are provided to demonstrate the method.     

Application of a new discrete distribution

In epidemiology, an infection lasting n weeks may be monitored by taking weekly serum samples. If tests on samples are independent Bernoulli trials with probability q of correctly testing positive, the apparent duration of infection ( from the first positive test to the last positive test inclusive) may be less than n weeks. This distribution of apparent length also arises when plants in a row of n each have a probability q of germinating, for example. This distribution is shown to be related to that of the number of tails obtained when tossing a coin until two heads are obtained, in a maximum of n tosses. The properties of the 'apparent length' distribution are described, and some compounded (mixed) distributions that can be derived from it are also discussed. The distribution was used to estimate the underlying distribution of the duration of infection, in a longitudinal study of infections of children. The methodology was also used to estimate the proportion of infectious episodes that were not detected. It can be similarly used to correct episode durations and rates in longitudinal studies in which episodes of any kind are detected by regular sampling.