Use of immunological markers and continuous-time Markov models to estimate progression of HIV infection in homosexual men.

OBJECTIVES: We used continuous-time Markov models based on CD4 cell counts and anti-CD3 reactivity (i.e., measure for T-cell quality) to study the progression of HIV infection in a cohort study of homosexual men in Amsterdam. We also compared the effectiveness of anti-CD3 reactivity as a marker for disease progression with that of CD4 cell counts. METHODS: We used data from 467 men (6905 visits) with visits at 3-month intervals between October 1984 and March 1993. To account for measurement error and short time-scale variability, the immunological stage at each visit was determined using a kernel smoother on log-transformed data from each individual. The Markov model had six marker-defined stages and a seventh stage for clinical AIDS. The initial stage-occupation probabilities for seroconverters were used to estimate the incubation time from infection to AIDS. Confidence intervals were calculated using the bootstrap method to account for the effect of smoothing on the variability of our estimates. RESULTS: The CD4 staging scheme estimated the median time from seroconversion to AIDS at 8.3 years [95% confidence interval (CI), 8.1-8.6], and a similar estimate was obtained with the anti-CD3 staging model. The CD4 model predicts that 10.2% (95% CI, 9.9-13.1) will remain AIDS-free 15 years after seroconversion. The mean number of stages visited before AIDS is lower with the CD4 model (7.4; 95% CI, 7.2-7.7) than with the anti-CD3 model (11.3; 95% CI, 10.8-12.0), implying that anti-CD3 predicts progression less well than CD4 cell count. CONCLUSIONS: CD4 lymphocyte counts and anti-CD3 reactivity are each associated with an increased hazard for progression to AIDS. Therefore, men in different CD4-stages (anti-CD3 stages) follow different incubation period distributions to AIDS. However, anti-CD3 predicts progression less well than CD4 cell count. Staged time-continuous Markov models are useful to study immunological markers for HIV disease progression.

The incubation period to AIDS in injecting drug users estimated from prevalent cohort data, accounting for death prior to an AIDS diagnosis.

OBJECTIVE: To estimate the incubation-period distribution (time from seroconversion to AIDS) accounting for death before an AIDS diagnosis (DBAD) in a cohort of injecting drug users (IDU) in Amsterdam, The Netherlands and to compare these estimates with those previously obtained from a contemporaneous study of homosexual and bisexual men in Amsterdam carried out using the same facilities. DESIGN: Participants in a cohort study begun in Amsterdam at the end of 1985 have scheduled follow-up visits every 4 months. All participants of Dutch nationality and who had two or more follow-up visits before January 1996 from which CD4 measurements were available were included in this study. Data concerning AIDS diagnosis and death were verified through review of national and municipal registries. METHODS: Because time of seroconversion was unknown for study participants and because IDU are at substantial risk for DBAD, we used a Markov model with CD4-based stages that allows for DBAD. The parameters in this model were estimated using the method of maximum likelihood and confidence intervals were calculated using bootstrap methods. RESULTS: A total of 173 IDU (134 seroprevalent, 39 seroincident) made 1829 visits. Nearly 10% of the visits were non-consecutive. Forty-five IDU developed AIDS and 25 died without an AIDS diagnosis. We estimated that 24% [95% confidence interval (CI), 17-25%] of IDU die before an AIDS diagnosis. As a result, the median time from seroconversion to AIDS (10.5 years; 95% CI, 9.1-10.7 years) is considerably longer than the median time from seroconversion to death (8.3 years; 95% CI, 7.9-8.5 years). Conditional on survival to an AIDS diagnosis, the median time to AIDS is 8.2 years (95% CI, 7.7-8.7 years). The median survival time after a diagnosis of AIDS is estimated to be 1.0 years. CONCLUSION: The high occurrence of DBAD in IDU has a considerable influence on estimates of the incubation-period distribution. Progression from seroconversion to death was faster in the IDU cohort than in a cohort of homosexual men in Amsterdam (median, 8.3 years and 9.6 years, respectively). However, progression to AIDS conditional on survival to an AIDS diagnosis seems to be similar in both the IDU cohort and in the cohort of homosexual men (median, 8.2 years and 8.3 years, respectively).

Risk factors for HIV infection among abandoned Romanian children.

OBJECTIVE: To determine risk factors for HIV infection among abandoned Romanian infants and children living in a public institution. METHODS: A cross-sectional study was conducted in June 1990 among 101 children between 0 and 4 years of age living in an orphanage. Orphanage and hospital records were reviewed and a blood specimen for hepatitis B and HIV serologic testing obtained from each child. A case-control study was conducted using data from the cross-sectional study. Cases were HIV-positive children; one HIV-negative control, matched by age, was selected for each case. RESULTS: Overall, 20 (20%) children were HIV-positive, 88 (87%) tested positive for antibody to hepatitis B core antigen, and 32 (32%) were hepatitis B surface antigen-positive. In the case-control study, HIV-positive children had received more therapeutic injections [mean, 280; median, 231] than age-matched HIV-negative children [mean; 142, median, 155; P = 0.02]. Cases were more likely than controls to have received over 200 lifetime injections (odds ratio, 5.7; 95% confidence interval, 1.2-32.7). Blood transfusions and mother-to-child transmission were excluded as routes of HIV transmission. By reviewing sterilization records and interviewing local health-care workers, we determined that needles and syringes were often re-used without proper disinfection in the orphanage. CONCLUSIONS: These data provide strong epidemiologic evidence that indiscriminate injections with contaminated needles and syringes were responsible for HIV transmission in this population.

Effect of interventions to control sexually transmitted disease on the incidence of HIV infection in female sex workers.

OBJECTIVE: To compare the seroincidence of HIV infection among female sex workers in Abidjan, Côte d'Ivoire before and during an intervention study to control sexually transmitted diseases (STD) and to study the effect of two STD diagnosis and treatment strategies on the prevalence of STD and on the seroincidence of HIV infection. METHOD: A screening facility for STD and HIV had been available since October 1992 for female sex workers. From June 1994, women who were HIV seronegative or HIV-2 positive during the screening could enroll in the intervention study in which participants reported once a month to a confidential clinic where they received health education, condoms and STD treatment if indicated. Women in the study were randomized either to a basic STD diagnosis and treatment strategy, which included a gynecologic examination when symptomatic, or to an intensive strategy that included a gynecologic examination regardless of symptoms. An outcome assessment every 6 months included a gynecologic examination, HIV serology and laboratory tests for STD. RESULTS: Of 542 women enrolled in the study, 225 (42%) had at least one outcome assessment. The HIV-1 seroincidence rate during the intervention study was significantly lower than before the study (6.5 versus 16.3 per 100 person-years; P = 0.02). During the study, the HIV-1 seroincidence rate was slightly lower in the intensive than in the basic strategy (5.3 versus 7.6 per 100 person-years; P = 0.5). CONCLUSION: National AIDS control programs should consider adopting as policy the type of integrated approach used in this intervention study for HIV prevention in female sex workers.

Time course of viremia and antibody seroconversion following human immunodeficiency virus exposure.

Rational application of diagnostic assays in the management of healthcare workers (HCWs) following occupational exposure is needed to rule out pre-existing human immunodeficiency virus (HIV) infection, detect HIV infection or seroconversion as early as possible in the small proportion individuals who become infected, and to rule out infection in the high proportion of individuals who remain uninfected following occupational exposure to HIV. An understanding of the time course of viremia and seroconversion following HIV exposure is essential in developing recommendations for management of occupational exposure among HCWs. Several data sources that address the timing and dynamics of HIV viremia and seroconversion following primary infection are reviewed. The implications of each data source for management of occupational exposure among HCWs is assessed. Although the majority of infected HCWs seroconvert within 2 months of exposure, the possibility of delayed seroconversion is well established, with approximately 5% of infected HCWs estimated to seroconvert >6 months after exposure. In contrast, the period of viremia (detectable by p24 antigen or RNA assays) preceding antibody seroconversion is consistently brief (1-3 weeks). Animal inoculation studies indicate that a variable period of localized viral replication in lymphoid tissue draining inoculation sites exists prior to systemic viremia and subsequent seroconversion.

Evaluation of a sensitive/less-sensitive testing algorithm using the 3A11-LS assay for detecting recent HIV seroconversion among individuals with HIV-1 subtype B or E infection in Thailand.

The development of a serologic algorithm to determine recent HIV seroconversion, using sensitive/less-sensitive testing strategies, has generated widespread interest in applying this approach to estimate HIV-1 incidence in various populations around the world. To evaluate this approach in non-B subtypes, longitudinal specimens (n = 522) collected from 90 incident infections among injecting drug users in Bangkok (subtype B infection, n = 18; subtype E infection, n = 72) were tested by the 3A11-LS assay. Standardized optical density (SOD) was calculated, using median values, and the window period between seroconversion as determined by sensitive and less sensitive tests was estimated by a maximum-likelihood model described previously. Our results show that the mean window period of the 3A11-LS assay was 155 days (95% CI, 128-189 days) for subtype B but was 270 days (95% CI, 187-349 days) for subtype E specimens from Thailand. About 4% of individuals with incident subtype E infections remained below the threshold (SOD of 0.75), even 2 years after seroconversion. Among the patients with clinical AIDS and declining antibodies, none of the 7 individuals with subtype B, but 10 (8.7%) of 115 with subtype E infections, were misclassified as recent infections. Lowering the cutoff to an SOD of 0.45 for subtype E specimens resulted in a mean window period of 185 days (95% CI, 154-211 days), with all individuals seroconverting, and reduced the number of subtype E-infected patients with AIDS who were misclassified as having recent infection to 2.6%. Our results demonstrate that the 3A11-LS assay has different performance characteristics in detecting recent infections among individuals infected with subtypes B or E. Determining appropriate cutoffs and mean window periods for other HIV-1 subtypes will be necessary before this approach can be reliably implemented in settings where non-B subtypes are common.

Sample size determination for pair-matched case-control studies where the goal is interval estimation of the odds ratio.

Samples sizes are calculated for case-control studies where 1:1 matching has been employed, and where the goal is the interval estimation of the odds ratio. The optimal sample size is defined to be the smallest value for which a 100(1 - alpha)% confidence interval for the log odds ratio will not exceed a specified width 2 delta with specified probability (1 - gamma). This approach is similar in spirit to the power-based approach for sample size determination when significance testing is the goal. Tables of sample sizes are presented for various choices of parameters. We also find considerable disagreement with a published method based on expected numbers of discordant pairs.

Guidelines for designing rapid assessment surveys of HIV seroprevalence among hospitalized patients. Centers for Disease Control and Prevention.

The Centers for Disease Control and Prevention has developed guidelines for determining HIV seroprevalence among patients seeking medical care at acute-care hospitals. The guidelines enable hospital staff members to perform a simple, rapid, and inexpensive survey to determine seroprevalence among the patient population, protecting the anonymity of those who are tested. The guidelines are based on national experience with large-scale anonymous, unlinked HIV serosurveys. The data from a rapid assessment survey are particularly useful for evaluating the need to provide routine, voluntary HIV counseling and testing and treatment for HIV infection. Beyond that, such data can be used in targeting education efforts, in reinforcing the use of appropriate universal precautions, in resource allocation, and in determining the need for further studies of HIV infection among the population in the hospital catchment area.

Steady-state calculation of the risk of HIV infection from transfusion of screened blood from repeat donors.

All blood donations in the United States are screened for human immunodeficiency virus (HIV), the virus that causes AIDS; in spite of this, potentially infectious donations are still made by donors who are infectious but have not yet developed detectable HIV antibodies. A steady-state model for blood donations is used to calculate the expected number of potentially infectious blood donations made by repeat blood donors in a specified time interval. The expected number of potentially infectious donations made by each infectious blood donor who subsequently becomes HIV positive is calculated, and estimators of this quantity are presented. The relative risks due to donations from repeat and first-time donors is discussed. Estimates of the proportion of all blood donations made at 19 American Red Cross regional blood centers that are potentially infectious are presented.

Hold everything! Holding policies for protecting plasma supplies.

In spite of advances in testing technologies for detecting infections such as human immunodeficiency virus (HIV), hepatitis B virus (HBV) and hepatitis C virus (HCV), occasionally blood or plasma is collected that is potentially infectious, but is not detected as such by existing screening tests. We consider the effect of a holding policy for further reducing the number of potentially infectious units that are released for fractionation. The policy dictates a holding period during which all donated units are stored. If a donor tests positive for the infection in question at a subsequent donation, then all of that donor's units currently in storage are discarded. Otherwise, donated units are released at the end of the holding period. In the case of a single disease, we determine optimal holding periods as well as policies that are as effective as the best screening tests currently available.

Simple methods for assessing haplotype-environment interactions in case-only and case-control studies.

For investigating haplotype-environment interactions in case-control studies, one can implement statistical methods based either on a retrospective likelihood (modeling the probability of haplotype and environment conditional on disease status) or a prospective likelihood (modeling the probability of disease status conditional on haplotype and environment). Retrospective approaches are generally more powerful than prospective approaches, but require an explicit model of the joint distribution of haplotype and environmental factors in the sample with the latter being particularly unattractive to specify. To resolve this issue, we propose a number of simple retrospective procedures for haplotype-environment interaction analysis that do not require explicit modeling of environmental covariates in the sample. We first consider a cases-only procedure, followed by a simple likelihood for case-control data that is proportional to the full-retrospective likelihood. Finally, we consider a retrospective procedure for inference on haplotype-environment interaction effects in matched or finely-stratified case-control studies. Our methods are based on the assumptions that haplotypes and environmental covariates are independent in the target population and that disease is rare. We illustrate our approaches using case-control data from the Finland-United States Investigation of Non-Insulin Dependent Diabetes Mellitus (FUSION) genetic study and simulated data.

Estimating the extent of tracking in interval-censored chain-of-events data.

This paper describes a method for determining whether the times between a chain of successive events (which all individuals experience in the same order) are correlated, for data in which the exact event times are not observed. Such data arise when individuals are only observed occasionally to determine which events have occurred. In such data, the (unknown) event times are interval censored. In addition, some individuals may have experienced some of the events before their first observation and may be lost to follow-up before experiencing the last event. Using a frailty model proposed by Aalen (1988, Mathematical Scientist 13, 90-103) but which has never been used to analyze real data, we examine whether individuals who develop early markers of HIV infection can also be expected to develop antibody and other indicators of HIV infection more rapidly.

Conditional regression analysis of the exposure-disease odds ratio using known probability-of-exposure values.

Conditional inference methods are proposed for the odds ratio between binary exposure and disease variables when only the probability of exposure is known for each study subject. We develop a conditional likelihood approach that removes nuisance parameters and permits inferences to be made about important parameters in log odds ratio regression models. We also discuss a heuristic procedure based on estimating the (unknown) number of truly exposed individuals; this procedure provides a simple framework for interpreting our likelihood-based statistics, and leads to a Mantel-Haenszel-type estimator and a goodness-of-fit test. As an example of the use of this methodology, we present an analysis of some genetic data of Swift et al. (1976, Cancer Research 36, 209-215).

Continued fraction representation for expected cell counts of a 2 x 2 table: a rapid and exact method for conditional maximum likelihood estimation.

The expected cell count for a 2 x 2 contingency table, governed by the noncentral (extended) hypergeometric distribution, is expressed as a terminating continued fraction. The coefficients in the continued fraction are better behaved than the multinomial coefficients required for the usual moment calculation. The expected cell count must be calculated repeatedly in a conditional maximum likelihood analysis of K2 x 2 contingency tables. Since the continued fraction can be easily evaluated, a rapid and numerically stable computational algorithm results. Once this first moment is known, higher moments can be obtained as shown by Harkness (1965, Annals of Mathematical Statistics 36, 938-945). A BASIC program to implement the continued fraction algorithm is given in an appendix.

Sample size requirements for interval estimation of the odds ratio.

Sample sizes are calculated for unmatched case-control (or cohort) studies where the goal is interval estimation of the odds ratio. The procedure used gives the smallest sample size for which a 100(1-alpha)% confidence interval for the log odds ratio will not exceed a specified width with specified probability (1-gamma). Tables of sample sizes for various choices of parameter values are presented. Considerable disagreement is found with a published method which has as its basis expected cell counts.

Repeat screening for HIV: when to test and why.

This paper presents models for repeat HIV screening under conditions of constant low HIV incidence. The models reveal a direct link between the prevalence of undetected HIV infection and the screening interval between repeat HIV tests. We show how to select screening intervals that either achieve a given HIV prevalence level, or optimally balance the cost of repeat HIV testing against the cost of HIV infection. Alternatively, given an existing repeat screening program, the model implies that cost of infection for which the given screening interval is optimal. The method also suggests how to select an HIV testing technology. The models are applied to existing repeat testing programs in the U.S. Army and among legal commercial sex workers in the state of Nevada in the Far West of the United States.

Conditional and unconditional categorical regression models with missing covariates.

We consider methods for analyzing categorical regression models when some covariates (Z) are completely observed but other covariates (X) are missing for some subjects. When data on X are missing at random (i.e., when the probability that X is observed does not depend on the value of X itself), we present a likelihood approach for the observed data that allows the same nuisance parameters to be eliminated in a conditional analysis as when data are complete. An example of a matched case-control study is used to demonstrate our approach.

Fitting semi-Markov models to interval-censored data with unknown initiation times.

In a semi-Markov model, the hazard of making a transition between stages depends on the time spent in the current stage but is independent of time spent in other stages. If the initiation time (time of entry into the network) is not known for some persons and if transition time data are interval censored (i.e., if transition times are not known exactly but are known only to have occurred in some interval), then the length of time these persons spent in any stage is not known. We show how a semi-Markov model can still be fit to interval-censored data with missing initiation times. For the special case of models in which all persons enter the network at the same initial stage and proceed through the same succession of stages to a unique absorbing stage, we present discrete-time nonparametric maximum likelihood estimators of the waiting-time distributions for this type of data.

Discrete-time nonparametric estimation for semi-Markov models of chain-of-events data subject to interval censoring and truncation.

Chain-of-events data are longitudinal observations on a succession of events that can only occur in a prescribed order. One goal in an analysis of this type of data is to determine the distribution of times between the successive events. This is difficult when individuals are observed periodically rather than continuously because the event times are then interval censored. Chain-of-events data may also be subject to truncation when individuals can only be observed if a certain event in the chain (e.g., the final event) has occurred. We provide a nonparametric approach to estimate the distributions of times between successive events in discrete time for data such as these under the semi-Markov assumption that the times between events are independent. This method uses a self-consistency algorithm that extends Turnbull's algorithm (1976, Journal of the Royal Statistical Society, Series B 38, 290-295). The quantities required to carry out the algorithm can be calculated recursively for improved computational efficiency. Two examples using data from studies involving HIV disease are used to illustrate our methods.

Modelling the female-to-male per-act HIV transmission probability in an emerging epidemic in Asia.

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