Validating marker-based incidence estimates in repeatedly screened populations

Disease incidence (new cases of disease per person per year) is usually measured by using longitudinal data. However, several recent proposals for measuring the incidence of human immunodeficiency virus (HIV) rely on cross-sectional data only. These methods assume each person is only sampled once; however, in some instances, it is necessary to consider these cross-sectional methods when individuals are represented more than once in the survey sample. We derive an extension of the cross-sectional incidence estimator that is valid for data from repeatedly screened populations and show under what conditions our new estimator reduces to the old estimator. An example involving estimation of HIV incidence among repeat blood donors is presented.     

Semiparametric approaches for joint modeling of longitudinal and survival data with time-varying coefficients

Summary .   We study joint modeling of survival and longitudinal data. There are two regression models of interest. The primary model is for survival outcomes, which are assumed to follow a time-varying coefficient proportional hazards model. The second model is for longitudinal data, which are assumed to follow a random effects model. Based on the trajectory of a subject's longitudinal data, some covariates in the survival model are functions of the unobserved random effects. Estimated random effects are generally different from the unobserved random effects and hence this leads to covariate measurement error. To deal with covariate measurement error, we propose a local corrected score estimator and a local conditional score estimator. Both approaches are semiparametric methods in the sense that there is no distributional assumption needed for the underlying true covariates. The estimators are shown to be consistent and asymptotically normal. However, simulation studies indicate that the conditional score estimator outperforms the corrected score estimator for finite samples, especially in the case of relatively large measurement error. The approaches are demonstrated by an application to data from an HIV clinical trial.     

HIV incidence in rural South Africa: comparison of estimates from longitudinal surveillance and cross-sectional cBED assay testing

Background

The BED IgG-Capture Enzyme Immunoassay (cBED assay), a test of recent HIV infection, has been used to estimate HIV incidence in cross-sectional HIV surveys. However, there has been concern that the assay overestimates HIV incidence to an unknown extent because it falsely classifies some individuals with non-recent HIV infections as recently infected. We used data from a longitudinal HIV surveillance in rural South Africa to measure the fraction of people with non-recent HIV infection who are falsely classified as recently HIV-infected by the cBED assay (the long-term false-positive ratio (FPR)) and compared cBED assay-based HIV incidence estimates to longitudinally measured HIV incidence.

Methodology/Principal Findings

We measured the long-term FPR in individuals with two positive HIV tests (in the HIV surveillance, 2003–2006) more than 306 days apart (sample size n = 1,065). We implemented four different formulae to calculate HIV incidence using cBED assay testing (n = 11,755) and obtained confidence intervals (CIs) by directly calculating the central 95^th percentile of incidence values. We observed 4,869 individuals over 7,685 person-years for longitudinal HIV incidence estimation. The long-term FPR was 0.0169 (95% CI 0.0100–0.0266). Using this FPR, the cross-sectional cBED-based HIV incidence estimates (per 100 people per year) varied between 3.03 (95% CI 2.44–3.63) and 3.19 (95% CI 2.57–3.82), depending on the incidence formula. Using a long-term FPR of 0.0560 based on previous studies, HIV incidence estimates varied between 0.65 (95% CI 0.00–1.32) and 0.71 (95% CI 0.00–1.43). The longitudinally measured HIV incidence was 3.09 per 100 people per year (95% CI 2.69–3.52), after adjustment to the sex-age distribution of the sample used in cBED assay-based estimation.

Conclusions/Significance

In a rural community in South Africa with high HIV prevalence, the long-term FPR of the cBED assay is substantially lower than previous estimates. The cBED assay performs well in HIV incidence estimation if the locally measured long-term FPR is used, but significantly underestimates incidence when a FPR estimate based on previous studies in other settings is used.     

BED estimates of HIV incidence: resolving the differences, making things simpler

Objective

Develop a simple method for optimal estimation of HIV incidence using the BED capture enzyme immunoassay.

Design

Use existing BED data to estimate mean recency duration, false recency rates and HIV incidence with reference to a fixed time period, T.

Methods

Compare BED and cohort estimates of incidence referring to identical time frames. Generalize this approach to suggest a method for estimating HIV incidence from any cross-sectional survey.

Results

Follow-up and BED analyses of the same, initially HIV negative, cases followed over the same set time period T, produce estimates of the same HIV incidence, permitting the estimation of the BED mean recency period for cases who have been HIV positive for less than T. Follow-up of HIV positive cases over T, similarly, provides estimates of the false-recent rate appropriate for T. Knowledge of these two parameters for a given population allows the estimation of HIV incidence during T by applying the BED method to samples from cross-sectional surveys. An algorithm is derived for providing these estimates, adjusted for the false-recent rate. The resulting estimator is identical to one derived independently using a more formal mathematical analysis. Adjustments improve the accuracy of HIV incidence estimates. Negative incidence estimates result from the use of inappropriate estimates of the false-recent rate and/or from sampling error, not from any error in the adjustment procedure.

Conclusions

Referring all estimates of mean recency periods, false-recent rates and incidence estimates to a fixed period T simplifies estimation procedures and allows the development of a consistent method for producing adjusted estimates of HIV incidence of improved accuracy. Unadjusted BED estimates of incidence, based on life-time recency periods, would be both extremely difficult to produce and of doubtful value.     

Semiparametric additive time-varying coefficients model for longitudinal data with censored time origin

Statistical analysis of longitudinal data often involves modeling treatment effects on clinically relevant longitudinal biomarkers since an initial event (the time origin). In some studies including preventive HIV vaccine efficacy trials, some participants have biomarkers measured starting at the time origin, whereas others have biomarkers measured starting later with the time origin unknown. The semiparametric additive time-varying coefficient model is investigated where the effects of some covariates vary nonparametrically with time while the effects of others remain constant. Weighted profile least squares estimators coupled with kernel smoothing are developed. The method uses the expectation maximization approach to deal with the censored time origin. The Kaplan–Meier estimator and other failure time regression models such as the Cox model can be utilized to estimate the distribution and the conditional distribution of left censored event time related to the censored time origin. Asymptotic properties of the parametric and nonparametric estimators and consistent asymptotic variance estimators are derived. A two-stage estimation procedure for choosing weight is proposed to improve estimation efficiency. Numerical simulations are conducted to examine finite sample properties of the proposed estimators. The simulation results show that the theory and methods work well. The efficiency gain of the two-stage estimation procedure depends on the distribution of the longitudinal error processes. The method is applied to analyze data from the Merck 023/HVTN 502 Step HIV vaccine study.     

Augmented cross-sectional studies with abbreviated follow-up for estimating HIV incidence

Cross-sectional HIV incidence estimation based on a sensitive and less-sensitive test offers great advantages over the traditional cohort study. However, its use has been limited due to concerns about the false negative rate of the less-sensitive test, reflecting the phenomenon that some subjects may remain negative permanently on the less-sensitive test. Wang and Lagakos (2010, Biometrics 66, 864-874) propose an augmented cross-sectional design that provides one way to estimate the size of the infected population who remain negative permanently and subsequently incorporate this information in the cross-sectional incidence estimator. In an augmented cross-sectional study, subjects who test negative on the less-sensitive test in the cross-sectional survey are followed forward for transition into the nonrecent state, at which time they would test positive on the less-sensitive test. However, considerable uncertainty exists regarding the appropriate length of follow-up and the size of the infected population who remain nonreactive permanently to the less-sensitive test. In this article, we assess the impact of varying follow-up time on the resulting incidence estimators from an augmented cross-sectional study, evaluate the robustness of cross-sectional estimators to assumptions about the existence and the size of the subpopulation who will remain negative permanently, and propose a new estimator based on abbreviated follow-up time (AF). Compared to the original estimator from an augmented cross-sectional study, the AF estimator allows shorter follow-up time and does not require estimation of the mean window period, defined as the average time between detectability of HIV infection with the sensitive and less-sensitive tests. It is shown to perform well in a wide range of settings. We discuss when the AF estimator would be expected to perform well and offer design considerations for an augmented cross-sectional study with abbreviated follow-up.     

Estimating the distribution of a renewal process from times at which events from an independent process are detected

The analysis of length-biased data has been mostly limited to the interarrival interval of a renewal process covering a specific time point. Motivated by a surveillance problem, we consider a more general situation where this time point is random and related to a specific event, for example, status change or onset of a disease. We also consider the problem when additional information is available on whether the event intervals (interarrival intervals covering the random event) end within or after a random time period (which we call a window period) following the random event. Under the assumptions that the occurrence rate of the random event is low and the renewal process is independent of the random event, we provide formulae for the estimation of the distribution of interarrival times based on the observed event intervals. Procedures for testing the required assumptions are also furnished. We apply our results to human immunodeficiency virus (HIV) test data from public test sites in Seattle, Washington, where the random event is HIV infection and the window period is from the onset of HIV infection to the time at which a less sensitive HIV test becomes positive. Results show that the estimator of the intertest interval length distribution from event intervals ending within the window period is less biased than the estimator from all event intervals; the latter estimator is affected by right truncation. Finally, we discuss possible applications to estimating HIV incidence and analyzing length-biased samples with right or left truncated data.     

Performance of a Limiting-Antigen Avidity Enzyme Immunoassay for Cross-Sectional Estimation of HIV Incidence in the United States

Background

A limiting antigen avidity enzyme immunoassay (HIV-1 LAg-Avidity assay) was recently developed for cross-sectional HIV incidence estimation. We evaluated the performance of the LAg-Avidity assay alone and in multi-assay algorithms (MAAs) that included other biomarkers.

Methods and Findings

Performance of testing algorithms was evaluated using 2,282 samples from individuals in the United States collected 1 month to >8 years after HIV seroconversion. The capacity of selected testing algorithms to accurately estimate incidence was evaluated in three longitudinal cohorts. When used in a single-assay format, the LAg-Avidity assay classified some individuals infected >5 years as assay positive and failed to provide reliable incidence estimates in cohorts that included individuals with long-term infections. We evaluated >500,000 testing algorithms, that included the LAg-Avidity assay alone and MAAs with other biomarkers (BED capture immunoassay [BED-CEIA], BioRad-Avidity assay, HIV viral load, CD4 cell count), varying the assays and assay cutoffs. We identified an optimized 2-assay MAA that included the LAg-Avidity and BioRad-Avidity assays, and an optimized 4-assay MAA that included those assays, as well as HIV viral load and CD4 cell count. The two optimized MAAs classified all 845 samples from individuals infected >5 years as MAA negative and estimated incidence within a year of sample collection. These two MAAs produced incidence estimates that were consistent with those from longitudinal follow-up of cohorts. A comparison of the laboratory assay costs of the MAAs was also performed, and we found that the costs associated with the optimal two assay MAA were substantially less than with the four assay MAA.

Conclusions

The LAg-Avidity assay did not perform well in a single-assay format, regardless of the assay cutoff. MAAs that include the LAg-Avidity and BioRad-Avidity assays, with or without viral load and CD4 cell count, provide accurate incidence estimates.     

Expected estimating equations for missing data, measurement error, and misclassification, with application to longitudinal nonignorable missing data

Summary .   Missing data, measurement error, and misclassification are three important problems in many research fields, such as epidemiological studies. It is well known that missing data and measurement error in covariates may lead to biased estimation. Misclassification may be considered as a special type of measurement error, for categorical data. Nevertheless, we treat misclassification as a different problem from measurement error because statistical models for them are different. Indeed, in the literature, methods for these three problems were generally proposed separately given that statistical modeling for them are very different. The problem is more challenging in a longitudinal study with nonignorable missing data. In this article, we consider estimation in generalized linear models under these three incomplete data models. We propose a general approach based on expected estimating equations (EEEs) to solve these three incomplete data problems in a unified fashion. This EEE approach can be easily implemented and its asymptotic covariance can be obtained by sandwich estimation. Intensive simulation studies are performed under various incomplete data settings. The proposed method is applied to a longitudinal study of oral bone density in relation to body bone density.     

Controlling HIV Epidemics among Injection Drug Users: Eight Years of Cross-Border HIV Prevention Interventions in Vietnam and China

Introduction

HIV in Vietnam and Southern China is driven by injection drug use. We have implemented HIV prevention interventions for IDUs since 2002–2003 in Lang Son and Ha Giang Provinces, Vietnam and Ning Ming County (Guangxi), China.

Methods

Interventions provide peer education and needle/syringe distribution. Evaluation employed serial cross-sectional surveys of IDUs 26 waves from 2002 to 2011, including interviews and HIV testing. Outcomes were HIV risk behaviors, HIV prevalence and incidence. HIV incidence estimation used two methods: 1) among new injectors from prevalence data; and 2) a capture enzyme immunoassay (BED testing) on all HIV+ samples.

Results

We found significant declines in drug-related risk behaviors and sharp reductions in HIV prevalence among IDUs (Lang Son from 46% to 23% [p<0.001], Ning Ming: from 17% to 11% [p = 0.003], and Ha Giang: from 51% to 18% [p<0.001]), reductions not experienced in other provinces without such interventions. There were significant declines in HIV incidence to low levels among new injectors through 36–48 months, then some rebound, particularly in Ning Ming, but BED-based estimates revealed significant reductions in incidence through 96 months.

Discussion

This is one of the longest studies of HIV prevention among IDUs in Asia. The rebound in incidence among new injectors may reflect sexual transmission. BED-based estimates may overstate incidence (because of false-recent results in patients with long-term infection or on ARV treatment) but adjustment for false-recent results and survey responses on duration of infection generally confirm BED-based incidence trends. Combined trends from the two estimation methods show sharp declines in incidence to low levels. The significant downward trends in all primary outcome measures indicate that the Cross-Border interventions played an important role in bringing HIV epidemics among IDUs under control. The Cross-Border project offers a model of HIV prevention for IDUs that should be considered for large-scale replication.     

Cross‐sectional human immunodeficiency virus incidence estimation accounting for heterogeneity across communities

Accurate estimation of human immunodeficiency virus (HIV) incidence rates is crucial for the monitoring of HIV epidemics, the evaluation of prevention programs, and the design of prevention studies. Traditional cohort approaches to measure HIV incidence require repeatedly testing large cohorts of HIV‐uninfected individuals with an HIV diagnostic test (eg, enzyme‐linked immunosorbent assay) for long periods of time to identify new infections, which can be prohibitively costly, time‐consuming, and subject to loss to follow‐up. Cross‐sectional approaches based on the usual HIV diagnostic test and biomarkers of recent infection offer important advantages over standard cohort approaches, in terms of time, cost, and attrition. Cross‐sectional samples usually consist of individuals from different communities. However, small sample sizes limit the ability to estimate community‐specific incidence and existing methods typically ignore heterogeneity in incidence across communities. We propose a permutation test for the null hypothesis of no heterogeneity in incidence rates across communities, develop a random‐effects model to account for this heterogeneity and to estimate community‐specific incidence, and provide one way to estimate the coefficient of variation. We evaluate the performance of the proposed methods through simulation studies and apply them to the data from the National Institute of Mental Health Project ACCEPT, a phase 3 randomized controlled HIV prevention trial in Sub‐Saharan Africa, to estimate the overall and community‐specific HIV incidence rates.     

Bayesian evidence synthesis for a transmission dynamic model for HIV among men who have sex with men

Understanding infectious disease dynamics and the effect on prevalence and incidence is crucial for public health policies. Disease incidence and prevalence are typically not observed directly and increasingly are estimated through the synthesis of indirect information from multiple data sources. We demonstrate how an evidence synthesis approach to the estimation of human immunodeficiency virus (HIV) prevalence in England and Wales can be extended to infer the underlying HIV incidence. Diverse time series of data can be used to obtain yearly "snapshots" (with associated uncertainty) of the proportion of the population in 4 compartments: not at risk, susceptible, HIV positive but undiagnosed, and diagnosed HIV positive. A multistate model for the infection and diagnosis processes is then formulated by expressing the changes in these proportions by a system of differential equations. By parameterizing incidence in terms of prevalence and contact rates, HIV transmission is further modeled. Use of additional data or prior information on demographics, risk behavior change and contact parameters allows simultaneous estimation of the transition rates, compartment prevalences, contact rates, and transmission probabilities.     

Density estimation in live-trapping studies

Unbiased estimation of population density is a major and unsolved problem in animal trapping studies. This paper describes a new and general method for estimating density from closed-population capture–recapture data. Many estimators exist for the size (N) and mean capture probability ( p ) of a closed population. These statistics suffer from an unknown bias due to edge effect that varies with trap layout and home range size. The mean distance between successive captures of an individual (     ) provides information on the scale of individual movements, but is itself a function of trap spacing and grid size. Our aim is to define and estimate parameters that do not depend on the trap layout. In the new method, simulation and inverse prediction are used to estimate jointly the population density (D) and two parameters of individual capture probability, magnitude (g₀) and spatial scale (σ), from the information in     , p and     . The method uses any configuration of traps (e.g. grid, web or line) and any choice of closed-population estimator. It is assumed that home ranges have a stationary distribution in two dimensions, and that capture events may be simulated as the outcome of competing Poisson processes in time. The method is applied to simulated and field data. The estimator appears unusually robust and free from bias.     

Pregnancy does not affect HIV incidence test results obtained using the BED capture enzyme immunoassay or an antibody avidity assay

Background

Accurate incidence estimates are needed for surveillance of the HIV epidemic. HIV surveillance occurs at maternal-child health clinics, but it is not known if pregnancy affects HIV incidence testing.

Methods

We used the BED capture immunoassay (BED) and an antibody avidity assay to test longitudinal samples from 51 HIV-infected Ugandan women infected with subtype A, C, D and intersubtype recombinant HIV who were enrolled in the HIVNET 012 trial (37 baseline samples collected near the time of delivery and 135 follow-up samples collected 3, 4 or 5 years later). Nineteen of 51 women were also pregnant at the time of one or more of the follow-up visits. The BED assay was performed according to the manufacturer''s instructions. The avidity assay was performed using a Genetic Systems HIV-1/HIV-2 + O EIA using 0.1M diethylamine as the chaotropic agent.

Results

During the HIVNET 012 follow-up study, there was no difference in normalized optical density values (OD-n) obtained with the BED assay or in the avidity test results (%) when women were pregnant (n = 20 results) compared to those obtained when women were not pregnant (n = 115; for BED: p = 0.9, generalized estimating equations model; for avidity: p = 0.7, Wilcoxon rank sum). In addition, BED and avidity results were almost exactly the same in longitudinal samples from the 18 women who were pregnant at only one study visit during the follow-up study (p = 0.6, paired t-test).

Conclusions

These results from 51 Ugandan women suggest that any changes in the antibody response to HIV infection that occur during pregnancy are not sufficient to alter results obtained with the BED and avidity assays. Confirmation with larger studies and with other HIV subtypes is needed.     

Weighted regression analysis to correct for informative monitoring times and confounders in longitudinal studies

We address estimation of the marginal effect of a time‐varying binary treatment on a continuous longitudinal outcome in the context of observational studies using electronic health records, when the relationship of interest is confounded, mediated, and further distorted by an informative visit process. We allow the longitudinal outcome to be recorded only sporadically and assume that its monitoring timing is informed by patients' characteristics. We propose two novel estimators based on linear models for the mean outcome that incorporate an adjustment for confounding and informative monitoring process through generalized inverse probability of treatment weights and a proportional intensity model, respectively. We allow for a flexible modeling of the intercept function as a function of time. Our estimators have closed‐form solutions, and their asymptotic distributions can be derived. Extensive simulation studies show that both estimators outperform standard methods such as the ordinary least squares estimator or estimators that only account for informative monitoring or confounders. We illustrate our methods using data from the Add Health study, assessing the effect of depressive mood on weight in adolescents.     

Median regression models for longitudinal data with dropouts

Summary .  Recently, median regression models have received increasing attention. When continuous responses follow a distribution that is quite different from a normal distribution, usual mean regression models may fail to produce efficient estimators whereas median regression models may perform satisfactorily. In this article, we discuss using median regression models to deal with longitudinal data with dropouts. Weighted estimating equations are proposed to estimate the median regression parameters for incomplete longitudinal data, where the weights are determined by modeling the dropout process. Consistency and the asymptotic distribution of the resultant estimators are established. The proposed method is used to analyze a longitudinal data set arising from a controlled trial of HIV disease ( Volberding et al., 1990 , The New England Journal of Medicine 322, 941–949). Simulation studies are conducted to assess the performance of the proposed method under various situations. An extension to estimation of the association parameters is outlined.     

Augmented Cross‐Sectional Prevalence Testing for Estimating HIV Incidence

Summary Estimation of an HIV incidence rate based on a cross‐sectional sample of individuals evaluated with both a sensitive and less‐sensitive diagnostic test offers important advantages to incidence estimation based on a longitudinal cohort study. However, the reliability of the cross‐sectional approach has been called into question because of two major concerns. One is the difficulty in obtaining a reliable external approximation for the mean “window period” between detectability of HIV infection with the sensitive and less‐sensitive test, which is used in the cross‐sectional estimation procedure. The other is how to handle false negative results with the less‐sensitive diagnostic test; that is, subjects who may test negative—implying a recent infection—long after they are infected. We propose and investigate an augmented design for cross‐sectional incidence estimation studies in which subjects found in the recent infection state are followed for transition to the nonrecent infection state. Inference is based on likelihood methods that account for the length‐biased nature of the window periods of subjects found in the recent infection state, and relate the distribution of their forward recurrence times to the population distribution of the window period. The approach performs well in simulation studies and eliminates the need for external approximations of the mean window period and, where applicable, the false negative rate.     

Proportional hazards regression for cancer studies

Summary.   There has been some recent work in the statistical literature for modeling the relationship between the size of cancers and probability of detecting metastasis, i.e., aggressive disease. Methods for assessing covariate effects in these studies are limited. In this article, we formulate the problem as assessing covariate effects on a right-censored variable subject to two types of sampling bias. The first is the length-biased sampling that is inherent in screening studies; the second is the two-phase design in which a fraction of tumors are measured. We construct estimation procedures for the proportional hazards model that account for these two sampling issues. In addition, a Nelson–Aalen type estimator is proposed as a summary statistic. Asymptotic results for the regression methodology are provided. The methods are illustrated by application to data from an observational cancer study as well as to simulated data.     

A pseudo-likelihood method for estimating misclassification probabilities in competing-risks settings when true-event data are partially observed

Outcome misclassification occurs frequently in binary-outcome studies and can result in biased estimation of quantities such as the incidence, prevalence, cause-specific hazards, cumulative incidence functions, and so forth. A number of remedies have been proposed to address the potential misclassification of the outcomes in such data. The majority of these remedies lie in the estimation of misclassification probabilities, which are in turn used to adjust analyses for outcome misclassification. A number of authors advocate using a gold-standard procedure on a sample internal to the study to learn about the extent of the misclassification. With this type of internal validation, the problem of quantifying the misclassification also becomes a missing data problem as, by design, the true outcomes are only ascertained on a subset of the entire study sample. Although, the process of estimating misclassification probabilities appears simple conceptually, the estimation methods proposed so far have several methodological and practical shortcomings. Most methods rely on missing outcome data to be missing completely at random (MCAR), a rather stringent assumption which is unlikely to hold in practice. Some of the existing methods also tend to be computationally-intensive. To address these issues, we propose a computationally-efficient, easy-to-implement, pseudo-likelihood estimator of the misclassification probabilities under a missing at random (MAR) assumption, in studies with an available internal-validation sample. We present the estimator through the lens of studies with competing-risks outcomes, though the estimator extends beyond this setting. We describe the consistency and asymptotic distributional properties of the resulting estimator, and derive a closed-form estimator of its variance. The finite-sample performance of this estimator is evaluated via simulations. Using data from a real-world study with competing-risks outcomes, we illustrate how the proposed method can be used to estimate misclassification probabilities. We also show how the estimated misclassification probabilities can be used in an external study to adjust for possible misclassification bias when modeling cumulative incidence functions.