Acquired immunodeficiency syndrome (AIDS)-free time after human immunodeficiency virus type 1 (HIV-1) seroconversion in homosexual men. Multicenter AIDS Cohort Study Group

To estimate the time interval between human immunodeficiency virus type 1 (HIV-1) seroconversion and acquired immunodeficiency syndrome (AIDS) diagnosis in homosexual men, prospective incident cohorts are difficult to obtain and, if assembled, provide few events owing to the long incubation time. Although seroprevalent cohorts are numerous in size and events, the information is limited due to the unknown times since seroconversion. To combine the information provided by 1,628 seroprevalent men (304 AIDS cases) and 233 seroconverters (12 AIDS cases) being followed in a multicenter study since 1984, the postseroconversion changes in hematologic variables occurring in the incident cohort were used to develop a model that allowed for the imputation of the unknown times since seroconversion for the seroprevalent cohort. Nonparametric life table methods incorporating truncation and censoring were applied for the estimation of the probability distribution of the AIDS-free time after seroconversion. The precision of the estimates was evaluated using bootstrap methods. The analysis suggested that AIDS is unlikely (less than 0.5%) in the first year; 78% of seropositive homosexual men remain AIDS-free 60 months after seroconversion; and the AIDS incidence increases for months 12-36 and levels off at 38 per 1,000 person-semesters for months 42-60. The nonparametric estimate of the incidence rate suggests a median AIDS-free time of 11 years, which is longer than previous estimates based on parametric models.     

MODELS FOR THE INCUBATION OF AIDS AND VARIATIONS ACCORDING TO AGE AND PERIOD

The objective of the methods proposed is to provide a parametric model for the incubation of AIDS and to use the chosen parameterization to test for the effect of age at seroconversion, and, after adjusting for markers of immunosuppression, to assess variations in periods corresponding to different levels of use of AIDS therapies at the population level. We compared the fit of Weibull, log-normal and three-parameter logistic models incorporating truncation in prevalent cohort and interval censored data. We showed the advantages by restricting the analysis to follow-up durations of greater than five years to improve estimation of the tail of the distribution for the prediction of long-term survivors. We applied the proposed methods to the combination of 1649 seroprevalent and 476 seroconverters with 1022 and 177 AIDS cases, respectively, who have been followed in the Multicenter AIDS Cohort Study (MACS) up to April 1995. Differences according to age at seroconversion are quantified in terms of relative percentiles and their associated 95 per cent confidence intervals were calculated using methods of multiple imputation. Using the proposed methods, we found that the log-normal model provides a fit as good as the three-parameter logistic; both are close to the non-parametric estimate and are significantly better than the fit of the Weibull model. Using log-normal parameterization, we found that the older the age at seroconversion, the shorter the time to AIDS (relative percentile = 0.72 for age ⩾40 versus age <25), and that the incubation of AIDS in calendar periods where treatment has been widely administered has been significantly longer among individuals with low CD4 cell counts.     

Time from infection with HIV to onset of AIDS in patients with haemophilia in the UK

The two-stage parametric regression model of Brookmeyer and Goedert has been adapted and fitted to data on the development of AIDS in haemophiliacs in the UK who are seropositive for HIV. The risk of developing AIDS by a given time following seroconversion increases with increasing age at seroconversion. It is likely that the risk increases smoothly with age, although the data have been analysed in three age categories, and it is estimated that by seven years after seroconversion 6 per cent of patients aged under 25 at seroconversion, 20 per cent of those aged 25-44 and 34 per cent of those aged 45 or more have developed AIDS. For a given age at seroconversion the annual risk of developing AIDS increases with increasing time after seroconversion, and at seven years the annual risks of developing AIDS during the next year in the three age groups are estimated to be 2 per cent for those aged less than 25 at seroconversion, and 10 and 11 per cent respectively for those aged 25-44 and 45 or more.     

AIDS-free time and survival of an injecting drug users HIV seroconvertors cohort

OBJECTIVE: To analyze AIDS free time, survival and the pre-AIDS survival for a injecting drug users cohort (IDU) of HIV seroconvertors. SUBJECT AND METHODS: Interval for seroconversion was available for 276 IDUs from Centers for AIDS Information and Prevention (CIPS) recruited between 1987 and until June of 1996. AIDS diagnosis and vital status dates were obtained by follow up at hospitals, mortality and AIDS registries, and CIPS visits. The end of follow up was December of 1996. Seroconversion date was estimated as the middle point between last HIV- and first HIV+. Kaplan-Meier extension and Cox regression for truncated data were fitted to estimate AIDS-free and survival times and to observe differences by sex, age consumption time and year of seroconversion. Weibull, and Log-normal parametric models were fitted to estimate median and percentiles of AIDS-free and survival times distribution. RESULTS: 34 cases have been identified as AIDS, 24 as deaths, 9 of them being before AIDS. 63.5% of the individuals were AIDS-free 7 years after seroconversion, and the probability of death was 25.50. Pre-AIDS mortality is around 8.7%. There were not significant differences by sex, age, consumption time and year of seroconversion. Log-normal model fitted better estimating an AIDS-free median time of 10.93 years and 13.67 survival years. CONCLUSION: The incubation period of HIV infection in a cohort of seroconvertors in our environment was around 11 years, not different from that observed out of the Mediterranean area as Holland, Scotland or United States     

Estimation of time since exposure for a prevalent cohort.

In natural history studies of human immunodeficiency virus type 1 (HIV-1) infection a substantial proportion of participants are seropositive at time of enrollment in the study. These participants form a prevalent subcohort. Estimation of the unknown times since exposure to HIV-1 in the prevalent subcohort is of primary importance for estimation of the incubation time of AIDS. The subset of the cohort that tested negative for antibody to HIV-1 at study entry and was observed to seroconvert forms the incident subcohort that provides longitudinal data on markers of maturity (that is, duration) of infection. We use parametric life table regression models incorporating truncation to describe the conditional distribution (imputing model) of the times since seroconversion given a vector of the markers of maturity. Using the fitted model and the values of the markers of maturity of infection provided by the seroprevalent subcohort at entry into the study, we can impute the unknown times since seroconversion for the prevalent subcohort. We implement multiple imputation based on a model-robust estimate of the covariance matrix of parameters of the imputing model to provide confidence intervals for the geometric mean of the time since seroconversion in the prevalent subcohort, and to compare maturity of infection of cohorts recruited in different cities. The accuracy of imputation is further validated by comparisons of imputation-based estimates of AIDS incubation distribution in the seroprevalent subcohort with more direct estimates obtained from the seroincident subcohort.     

SIMULTANEOUSLY MODELLING CENSORED SURVIVAL DATA AND REPEATEDLY MEASURED COVARIATES: A GIBBS SAMPLING APPROACH

Recent methodologic developments in the analysis of longitudinal data have typically addressed one of two aspects: (i) the modelling of repeated measurements of a covariate as a function of time or other covariates, or (ii) the modelling of the effect of a covariate on disease risk. In this paper, we address both of these issues in a single analysis by modelling a continuous covariate over time and simultaneously relating the covariate to disease risk. We use the Markov chain Monte Carlo technique of Gibbs sampling to estimate the joint posterior distribution of the unknown parameters of the model. Simulation studies showed that jointly modelling survival and covariate data reduced bias in parameter estimates due to covariate measurement error and informative censoring. We illustrate the methodology by application to a data set that consists of repeated measurements of the immunologic marker CD4 and times of diagnosis of AIDS for a cohort of anti-HIV-1 positive recipients of anti-HIV-1 positive blood transfusions. We assume a linear random effects model with subject-specific intercepts and slopes and normal errors for the true log and square root CD4 counts, and a proportional hazards model for AIDS-free survival time expressed as a function of current true CD4 value. On the square root scale, the joint approach yielded a mean slope for CD4 that was 7 per cent steeper and a log relative risk of AIDS that was 35 per cent larger than those obtained by analysis of the component sub-models separately.     

Median time from seroconversion to AIDS in Italian HIV-positive haemophiliacs: Different parametric estimates

The purpose of this study was to estimate the median incubation time between human immunodeficiency virus (HIV) infection and onset of acquired immunodeficiency syndrome (AIDS), using three parametric models and six estimates of seroconversion time. Study subjects were 732 HIV-positive haemophiliacs enrolled in the Italian Registry of patients with congenital coagulation disorders. Seroconversion time was estimated for each subject according to six different criteria, based on three distributions of seroconversion (uniform, uniform on three sub-intervals and truncated Weibull) and two indices synthesizing each distribution (median and median of three random values). The estimated seroconversion times were subsequently used as starting points in the analysis of incubation. This was performed applying Kaplan-Meier non-parametric survival analysis, and fitting to incubation data three probability density functions, representing three different situations with respect to the hazard of developing AIDS following seroconversion (namely Weibull (WE), generalized exponential (GE) and log-logistic (LL)). The cumulative incidence over an 8-year period ranged from 14.9 to 17.8 per cent when applying the Kaplan-Meier method, from 14.1 to 17.2 per cent when using the WE function, from 14.5 to 17.3 per cent when using the GE function and from 14.4 to 17.3 per cent when using the LL function, depending on the estimate of seroconversion time used. Similarly, the median incubation times ranged from 12.6 to 15.0 years with the WE function, from 14.0 to 16.5 years with the GE function, and from 13.4 to 16.1 years with the LL function. The presence of a bound on the increase of the hazard function seems to affect the incubation more strongly than the eventual decrease following the attainment of the maximum risk. This may be due to the decrease in the hazard beginning when most of the seropositive subjects have already developed AIDS.     

Effects of different parametric estimates of seroconversion time on analysis of progression to AIDS among Italian HIV-positive haemophiliacs.

The purpose of this study was to estimate seroconversion time using different parametric methods and to assess their influence on the estimation of the incubation time between HIV infection and onset of AIDS. Study subjects were 712 HIV-positive haemophiliacs enrolled in the Italian National Registry of patients with congenital coagulation disorders. Seroconversion time was estimated using the mid-point of each seroconversion interval (MID), the median of each interval under an estimated uniform distribution with cutpoints at December 1981 and December 1985 (MUU), the median of each interval under an estimated Weibull distribution (MUW), and the median of three random values drawn from each interval under the Weibull distribution (RUW). Kaplan-Meier survival analysis showed that the cumulative incidence of AIDS over a 7-year period was 11.6 per cent (SE 1.3 per cent) when using the MID estimate of seroconversion time, 10.8 per cent (1.2 per cent) with the MUU estimate, and 13.4 per cent (1.3 per cent) and 12.3 per cent (1.3 per cent) when using MUW and RUW estimates, respectively. This study demonstrates that the estimate of seroconversion time does not seem to be a major factor affecting estimates of AIDS incidence since the different techniques for estimating HIV seroconversion time yielded very similar results.     

Risk of AIDS in HIV seroconverters: A comparison between intravenous drug users and homosexual males

A multicentre cohort study was conducted in Italy to estimate the risk of developing AIDS in 261 intravenous drug users and 89 homosexual males for whom the seroconversion period was known.Four years after HIV seroconversion, AIDS incidence, estimated by Kaplan-Meier survival technique, was 13.8% for intravenous drug users and 16.2% for homosexual males; the difference was not statistically significant.These findings suggest that four years after seroconversion the risk of developing AIDS in HIV seropositive intravenous drug users is no higher than that of subjects who acquired HIV infection through sexual contact.Corresponding author.     

Methods for estimating the AIDS incubation time distribution when date of seroconversion is censored

In most cohort studies on HIV infection and AIDS, data on time from seroconversion to AIDS or death are doubly censored, both at the time origin and at the endpoint of interest. In epidemiological research, the most frequently adopted approach is to restrict the analysis to persons with narrow seroconversion intervals and to impute the midpoint of this interval as date of seroconversion. For many cohort studies, the consequence is that a substantial proportion of the data is not used. We consider four methods that are expected to be less biased when all cohort data are used: two imputation methods, conditional mean and multiple imputation, and two likelihood maximization methods. We derive the likelihood structure of the cohort data and clarify its dependence on study design. All methods are applied to data from the Amsterdam cohort study among injection drug users. In a simulation study the data generation process of this cohort study is imitated. The performance of midpoint, conditional mean and multiple imputation are compared. With midpoint imputation, both an analysis using the full data set, as well as one restricted to the cases with small seroconversion intervals, is performed. Conditional mean imputation comes out as the preferred method. It gives best results with respect to mean squared error. Moreover, when confidence intervals are computed through standard methods that ignore the uncertainty in the imputed date of seroconversion, coverage probabilities are almost correct.     

Imputation of the date of HIV seroconversion in cohorts of haemophiliacs

OBJECTIVES: To describe the methods used to impute HIV seroconversion date in the haemophiliac cohorts from GEMES project and to validate its use. METHOD: 632 haemophiliacs coming from three hemophilia units identified as HIV+ and 1.092 individuals coming from 5 project GEMES cohorts with a seroconversion window (time among test HIV and HIV+) less than 3 years where mid point (PM) was assumed as seroconversion date. For both groups, seroconversion date was imputed after estimating the probability distribution of seroconversion by means of the EM algorithm. Two imputation methods are used: one obtained from the expected value and the other from the geometric mean of 5 random samples. from the estimated distribution. Imputations have been validated in the non haemophiliacs cohorts comparing with the PM seroconversion date. Also AIDS free time and survival from the different seroconversion imputed dates were compared. RESULTS: Median seroconversion date is located in May of 1993 for the non haemophiliacs and in 1982 for the haemophiliacs. Not big differences are observed among the imputed seroconversion dates and the mid-point seroconversion date in the non-haemophiliac cohorts. Similar results are found for the haemophiliac cohorts. Also no differences are observed in the estimated AIDS-free time for both groups of cohorts. CONCLUSIONS: Geometric mean imputation from several random samples provides a good estimate of the HIV seroconversion date that can be used to estimate AIDS-free time and survival in haemophiliac cohorts where seroconversion date is ignored.     

不同缺失值填充技术在HIV/AIDS血液样品检测数据中的应用

目的 以HIV/AIDS血液样品检测数据为来源,探索最为准确、高效、方便的填充方法.方法 利用SPSS17.0和SAS 9.1分析数据的缺失机制和缺失模式,采用期望最大化法(EM)、回归法和多重填补法(MI)3种方法对缺失数据进行填充,比较不同填充方法填充后数据的分布、精确度和准确度.结果 该研究缺失机制为随机缺失(x2=1141.21,P ＜0.001);缺失模式为任意缺失.MI填补10次的效果最优.缺失率在10％以下时,EM和回归法填充后准确度高于MI填充10次的准确度,除了血红蛋白外,EM法均比回归法填充后的准确度高;缺失率在20％左右时,MI法填充10次后的准确度高于EM法和回归法,对于血小板和血肌酐2个指标,采用EM法填充后的准确度高于回归法.EM法和回归法填充后的精确度优于MI法,EM法填充后精确度更高.EM法、回归法和MI法填充后数据的偏度系数和峰度系数很接近.结论 对于缺失率＜10％的指标,采用EM法或回归法更方便、准确和精确;对于缺失率在20％左右的指标,采用MI填补更合适.     

Risk factor redistribution of the national HIV/AIDS surveillance data: an alternative approach

OBJECTIVE: The purpose of this study was to assess an alternative statistical approach-multiple imputation-to risk factor redistribution in the national human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) surveillance system as a way to adjust for missing risk factor information. METHODS: We used an approximate model incorporating random variation to impute values for missing risk factors for HIV and AIDS cases diagnosed from 2000 to 2004. The process was repeated M times to generate M datasets. We combined results from the datasets to compute an overall multiple imputation estimate and standard error (SE), and then compared results from multiple imputation and from risk factor redistribution. Variables in the imputation models were age at diagnosis, race/ethnicity, type of facility where diagnosis was made, region of residence, national origin, CD-4 T-lymphocyte cell count within six months of diagnosis, and reporting year. RESULTS: In HIV data, male-to-male sexual contact accounted for 67.3% of cases by risk factor redistribution and 70.4% (SE = 0.45) by multiple imputation. Also among males, injection drug use (IDU) accounted for 11.6% and 10.8% (SE = 0.34), and high-risk heterosexual contact for 15.1% and 13.0% (SE = 0.34) by risk factor redistribution and multiple imputation, respectively. Among females, IDU accounted for 18.2% and 17.9% (SE = 0.61), and high-risk heterosexual contact for 80.8% and 80.9% (SE = 0.63) by risk factor redistribution and multiple imputation, respectively. CONCLUSIONS: Because multiple imputation produces less biased subgroup estimates and offers objectivity and a semiautomated approach, we suggest consideration of its use in adjusting for missing risk factor information.     

Nonlinear multiple imputation for continuous covariate within semiparametric Cox model: application to HIV data in Senegal

Multiple imputation is commonly used to impute missing covariate in Cox semiparametric regression setting. It is to fill each missing data with more plausible values, via a Gibbs sampling procedure, specifying an imputation model for each missing variable. This imputation method is implemented in several softwares that offer imputation models steered by the shape of the variable to be imputed, but all these imputation models make an assumption of linearity on covariates effect. However, this assumption is not often verified in practice as the covariates can have a nonlinear effect. Such a linear assumption can lead to a misleading conclusion because imputation model should be constructed to reflect the true distributional relationship between the missing values and the observed values. To estimate nonlinear effects of continuous time invariant covariates in imputation model, we propose a method based on B‐splines function. To assess the performance of this method, we conducted a simulation study, where we compared the multiple imputation method using Bayesian splines imputation model with multiple imputation using Bayesian linear imputation model in survival analysis setting. We evaluated the proposed method on the motivated data set collected in HIV‐infected patients enrolled in an observational cohort study in Senegal, which contains several incomplete variables. We found that our method performs well to estimate hazard ratio compared with the linear imputation methods, when data are missing completely at random, or missing at random. Copyright © 2013 John Wiley & Sons, Ltd.     

A comparison of multiple imputation and fully augmented weighted estimators for Cox regression with missing covariates

Several approaches exist for handling missing covariates in the Cox proportional hazards model. The multiple imputation (MI) is relatively easy to implement with various software available and results in consistent estimates if the imputation model is correct. On the other hand, the fully augmented weighted estimators (FAWEs) recover a substantial proportion of the efficiency and have the doubly robust property. In this paper, we compare the FAWEs and the MI through a comprehensive simulation study. For the MI, we consider the multiple imputation by chained equation and focus on two imputation methods: Bayesian linear regression imputation and predictive mean matching. Simulation results show that the imputation methods can be rather sensitive to model misspecification and may have large bias when the censoring time depends on the missing covariates. In contrast, the FAWEs allow the censoring time to depend on the missing covariates and are remarkably robust as long as getting either the conditional expectations or the selection probability correct due to the doubly robust property. The comparison suggests that the FAWEs show the potential for being a competitive and attractive tool for tackling the analysis of survival data with missing covariates. Copyright © 2010 John Wiley & Sons, Ltd.     

A multiple imputation method for missing covariates in non-linear mixed-effects models with application to HIV dynamics.

We propose a three-step multiple imputation method, implemented by Gibbs sampler, for estimating parameters in non-linear mixed-effects models with missing covariates. Estimates obtained by the proposed multiple imputation method are compared to those obtained by the mean-value imputation method and the complete-case method through simulations. We find that the proposed multiple imputation method offers smaller biases and smaller mean-squared errors for the estimates of covariate coefficients compared to other two methods. We apply the three missing data methods to modelling HIV viral dynamics from an AIDS clinical trial. We believe that the results from the proposed multiple imputation method are more reliable than that from the other two commonly used methods.     

Identification of significant host factors for HIV dynamics modelled by non-linear mixed-effects models

Non-linear mixed-effects models are powerful tools for modelling HIV viral dynamics. In AIDS clinical trials, the viral load measurements for each subject are often sparse. In such cases, linearization procedures are usually used for inferences. Under such linearization procedures, however, standard covariate selection methods based on the approximate likelihood, such as the likelihood ratio test, may not be reliable. In order to identify significant host factors for HIV dynamics, in this paper we consider two alternative approaches for covariate selection: one is based on individual non-linear least square estimates and the other is based on individual empirical Bayes estimates. Our simulation study shows that, if the within-individual data are sparse and the between-individual variation is large, the two alternative covariate selection methods are more reliable than the likelihood ratio test, and the more powerful method based on individual empirical Bayes estimates is especially preferable. We also consider the missing data in covariates. The commonly used missing data methods may lead to misleading results. We recommend a multiple imputation method to handle missing covariates. A real data set from an AIDS clinical trial is analysed based on various covariate selection methods and missing data methods.     

On the inclusion of prevalent cases in HIV/AIDS natural history studies through a marker-based estimate of time since seroconversion

In most cohort studies of HIV infection and AIDS, seroprevalent cases provide a substantial amount of information. Inclusion of these people in natural history studies requires a fairly unbiased method to estimate their seroconversion distribution. When a cohort-based estimate is not feasible, an alternative is to estimate individual seroconversion distributions, based on marker values at entry. In this paper, a non-parametric marker-based estimation method is developed. The method is applied to data from the Amsterdam cohort study on homosexual men. For seroprevalent cases who entered the study between October 1984 and April 1985, individual seroconversion distributions are estimated based on their first measured CD4 count. In subsequent survival analyses, dates of seroconversion are estimated via conditional mean imputation. Inclusion of these seroprevalent cases greatly improves the quality of the data. Age at seroconversion is a significant cofactor for disease progression, a result not found when analysis is restricted to those who seroconvert. To incorporate the uncertainty in the imputed date of seroconversion, a bootstrap procedure is developed for the computation of p-values and confidence intervals. In our analyses, standard procedures, which ignore the uncertainty in the imputed date of seroconversion, perform almost as well.     

Imputation strategies for missing data in a school-based multi-centre study: the Pathways study

Pathways is a multi-centre school-based trial sponsored by the National Heart, Lung, and Blood Institute testing the efficacy of an obesity prevention intervention in American Indian children. During the study's protocol development, we prepared an analysis plan that accounted for missing data. In this paper, we present a case study of the process we used to decide upon the final analysis plan. The primary endpoint of the Pathways study is a comparison of per cent body fat between treatment and usual care groups at the end of a three-year intervention. Other studies on children and Native Americans have had moderate to large amounts of missing data. As a result we were concerned that missing data in Pathways would affect the type I error rate and power of the test of our primary endpoint. We present results from our evaluation of three alternative procedures in this paper. The first is a multiple imputation procedure in which we replace missing values with resampled values from the observed data. The second is based on the Wilcoxon rank sum test; missing data in the intervention group receive the worst ranks. In the third, we use a multiple imputation procedure and replace missing values with predicted values from a regression equation with the coefficients estimated from observed follow-up data and baseline values. We found that the multiple imputation procedure that replaces missing values with predicted values had the best properties of the procedures we considered. The results from our simulation study showed that, for missing data patterns that are relevant to the Pathways study, this procedure has high power and maintains the type I error rate. Published in 2001 by John Wiley & Sons, Ltd.     

Statistical analysis with missing exposure data measured by proxy respondents: a misclassification problem within a missing‐data problem

In studies of older adults, researchers often recruit proxy respondents, such as relatives or caregivers, when study participants cannot provide self‐reports (e.g., because of illness). Proxies are usually only sought to report on behalf of participants with missing self‐reports; thus, either a participant self‐report or proxy report, but not both, is available for each participant. Furthermore, the missing‐data mechanism for participant self‐reports is not identifiable and may be nonignorable. When exposures are binary and participant self‐reports are conceptualized as the gold standard, substituting error‐prone proxy reports for missing participant self‐reports may produce biased estimates of outcome means. Researchers can handle this data structure by treating the problem as one of misclassification within the stratum of participants with missing self‐reports. Most methods for addressing exposure misclassification require validation data, replicate data, or an assumption of nondifferential misclassification; other methods may result in an exposure misclassification model that is incompatible with the analysis model. We propose a model that makes none of the aforementioned requirements and still preserves model compatibility. Two user‐specified tuning parameters encode the exposure misclassification model. Two proposed approaches estimate outcome means standardized for (potentially) high‐dimensional covariates using multiple imputation followed by propensity score methods. The first method is parametric and uses maximum likelihood to estimate the exposure misclassification model (i.e., the imputation model) and the propensity score model (i.e., the analysis model); the second method is nonparametric and uses boosted classification and regression trees to estimate both models. We apply both methods to a study of elderly hip fracture patients. Copyright © 2014 John Wiley & Sons, Ltd.