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.

Design and analysis of arm-in-cage experiments: inference for three-state progressive disease models with common periodic observation times.

We develop statistical methods for designing and analyzing arm-in-cage experiments used to test the efficacy of insect repellents and other topical treatments. In these experiments, a controlled amount of the treatment is applied to a volunteer's forearm, which then is exposed to the insects by being placed into a special cage. Arms are not kept in the cages continuously, but rather placed there periodically for a brief period of time, during which it is noted whether an insect lands (but does not bite) or (lands and) bites. Efficacy of a repellent can be described using a progressive three-state model in which the first two states represent varying degrees of protection (no landing and landing without biting) and the third state occurs once protection is completely lost (biting). Because subjects within a treatment group follow the same cage visit schedule, transition times between states are interval censored into one of several fixed intervals. We develop an approach that uses a mixture of nonparametric and parametric techniques for estimating the parameters of interest when sojourn times are dependent. Design considerations for arm-in-cage experiments are addressed and the proposed methods are illustrated on data from a recent arm-in-cage experiment as well as simulated data.

Efficiency comparisons of rank and permutation tests based on summary statistics computed from repeated measures data.

A popular method of using repeated measures data to compare treatment groups in a clinical trial is to summarize each individual's outcomes with a scalar summary statistic, and then to perform a two-group comparison of the resulting statistics using a rank or permutation test. Many different types of summary statistics are used in practice, including discrete and continuous functions of the underlying repeated measures data. When the repeated measures processes of the comparison groups differ by a location shift at each time point, the asymptotic relative efficiency of (continuous) summary statistics that are linear functions of the repeated measures has been determined and used to compare tests in this class. However, little is known about the non-null behaviour of discrete summary statistics, about continuous summary statistics when the groups differ in more complex ways than location shifts or where the summary statistics are not linear functions of the repeated measures. Indeed, even simple distributional structures on the repeated measures variables can lead to complex differences between the distribution of common summary statistics of the comparison groups. The presence of left censoring of the repeated measures, which can arise when these are laboratory markers with lower limits of detection, further complicates the distribution of, and hence the ability to compare, summary statistics. This paper uses recent theoretical results for the non-null behaviour of rank and permutation tests to examine the asymptotic relative efficiencies of several popular summary statistics, both discrete and continuous, under a variety of common settings. We assume a flexible linear growth curve model to describe the repeated measures responses and focus on the types of settings that commonly arise in HIV/AIDS and other diseases.

Estimation of the timing of perinatal transmission of HIV.

Knowledge of the timing of perinatal transmission of HIV would be valuable for the determination and evaluation of preventive treatments and would shed light on the mechanism of transmission. Estimation of the distribution of the time of perinatal transmission is difficult, however, because tests of infection status can only be undertaken after birth. DNA and RNA polymerase chain reaction (PCR) assays and HIV culture have been the most commonly used diagnostic tests for perinatal HIV infection. Such tests have high sensitivity and specificity, except when they are given shortly after infection. In this paper we use the time-dependent sensitivity of these diagnostic tests to make nonparametric and semiparametric inferences about the distribution of the time of perinatal HIV transmission as well as the cumulative probability of perinatal transmission. The methods are illustrated with data from a clinical trial conducted by the AIDS Clinical Trials group.

Evaluation of HIV-1 immunogen, an immunologic modifier, administered to patients infected with HIV having 300 to 549 x 10(6)/L CD4 cell counts: A randomized controlled trial.

CONTEXT: Despite enormous improvements achieved through the use of antiretroviral therapies (ARTs), the risk for eventual human immunodeficiency virus (HIV) disease progression remains high. Agents that enhance the immunologic mechanism for viral recognition might reduce disease progression. OBJECTIVE: To determine whether the addition of HIV-1 Immunogen would confer added clinical efficacy to that achievable by ARTs. DESIGN AND SETTING: Multicenter, double-blind, placebo-controlled, randomized trial beginning March 1996 and ending May 1999 conducted at 77 centers in the United States providing primary care or referral care for persons infected with HIV. PATIENTS: Adults infected with HIV who have baseline CD4 cell counts between 300 x 10(6)/L and 549 x 10(6)/L without prior acquired immunodeficiency syndrome-defining conditions receiving stable ART (or no therapy) were screened and 2527 were randomized. INTERVENTIONS: Ten units of HIV-1 Immunogen, derived from a Zairian HIV isolate, inactivated and formulated with incomplete Freund adjuvant, was administered intramuscularly every 12 weeks. The placebo was incomplete Freund adjuvant. Changes in ARTs were allowed. MAIN OUTCOME MEASURES: HIV progression-free survival; secondary end points included overall survival, changes in HIV RNA, CD4 cell counts, CD4 percentage, body weight, and immunogenicity. RESULTS: The overall event rate was 1.8 per 100 person-years of follow-up. Fifty-three subjects developed clinical progression in each treatment group (relative risk [RR], 0.97; 95% confidence interval [CI], 0.66-1.42; P =.89). There were 19 and 23 deaths in the placebo and HIV-1 Immunogen groups, respectively (RR, 0.81; 95% CI, 0.44-1. 48; P =.49). There were no statistically significant differences between the groups with respect to changes in HIV RNA (P =.59), CD4 percentage (P =.63), or body weight (P =.89). Subjects in the HIV-1 Immunogen group had an increase in average CD4 cell count of approximately 10 x 10(6)/L greater than the placebo group (P =.02). CONCLUSION: HIV-1 Immunogen with unrestricted ART failed to demonstrate an increase in HIV progression-free survival. JAMA. 2000;284:2193-2202.

Randomized study of saquinavir with ritonavir or nelfinavir together with delavirdine, adefovir, or both in human immunodeficiency virus-infected adults with virologic failure on indinavir: AIDS Clinical Trials Group Study 359.

This study compared antiretroviral activity among 6 "salvage" therapy regimens. The study was a prospective, randomized, 2x3 factorial, multicenter study of the AIDS Clinical Trials Group. The study enrolled 277 human immunodeficiency virus (HIV)-infected patients naive to nonnucleoside analogues who had taken indinavir >6 months. The patients had 2000-200,000 HIV RNA copies/mL. Patients received saquinavir with ritonavir or nelfinavir together with delavirdine and/or adefovir and were followed for safety and antiretroviral response between baseline and week 16. At week 16, 30% (77/254) of patients had

The one-sample problem from eradication studies of chronic viral infections.

In studies of chronic viral infections, the objective is to estimate probabilities of developing viral eradication and resistance. Complications arise as the laboratory methods used to assess eradication status result in unusual types of censored observations. This paper proposes nonparametric methods for the one-sample analysis of viral eradication/resistance data. We show that the unconstrained nonparametric maximum likelihood estimator of the subdistributions of eradication and resistance are obtainable in closed form. In small samples, these estimators may be inadmissible; thus, we also present an algorithm for obtaining the constrained MLEs based on an isotonic regression of the unconstrained MLEs. Estimators of several functionals of the eradication and resistance subdistributions are also developed and discussed. The methods are illustrated with results from recent hepatitis C clinical trials.

Should data and safety monitoring boards share confidential interim data?

Consider the following situation: Two clinical trials are underway, closely related in terms of the interventions being compared and the target populations. In preparing for a planned interim analysis, the statistician for trial 1 finds that the results support a recommendation to stop the trial early. Should the statistician ask the investigators for trial 2 to make interim results of their trial available to the data and safety monitoring board (DSMB) for trial 1? If so, in what form? Would the answers change if the trial 1 results showed a strong but not convincing trend? What is the obligation of the trial 2 investigators to respond to such a request? What role do the two DSMBs have, either in initiating a request or in agreeing to respond to it? In this article, we examine this situation in some detail, having faced it occasionally in our own experience with clinical trials and DSMBs. The chief argument in favor of sharing data is that data from trial 2 are obviously relevant to the question being addressed by trial 1 and therefore ought to be available to those who must interpret the results from that trial. On the other hand, there are several reasons for not sharing interim data. For example, sharing is incompatible with the independence of the trials; the time for synthesizing evidence from both trials is after the two teams of investigators have presented the full analysis and interpretation of their separate trials. For this and other conceptual and practical reasons we conclude that it is better, in most cases, for DSMBs to consider only information that has already been made public in some form.

Covariate analysis of viral eradication studies.

An important issue arising in therapeutic studies of hepatitis C and HIV is the identification of and adjustment for covariates associated with viral eradication and resistance. Analyses of such data are complicated by the fact that eradication is an occult event that is not directly observable, resulting in unique types of censored observations that do not arise in other competing risks settings. This paper proposes a semiparametric regression model to assess the association between multiple covariates and the eradication/resistance processes. The proposed methods are based on a piecewise proportional hazards model that allows parameters to vary between observation times. We illustrate the methods with data from recent hepatitis C clinical trials.

Efficacy and safety of adefovir dipivoxil with antiretroviral therapy: a randomized controlled trial.

CONTEXT: Adefovir dipivoxil is a nucleotide analog that has demonstrated effective antiretroviral activity against human immunodeficiency virus (HIV) with once-daily administration. OBJECTIVE: To determine if adefovir confers antiretroviral or immunologic benefit when added to stable antiretroviral therapy. DESIGN: Multicenter, 24-week, randomized, double-blind, placebo-controlled study. Enrollment was conducted from June 3, 1996, through May 6, 1997. SETTING: Thirty-three US HIV treatment centers. PARTICIPANTS: Of 1171 patients screened, 442 patients infected with HIV receiving stable antiretroviral therapy for at least 8 weeks with plasma HIV RNA greater than 2500 copies/mL and CD4+ cell count above 0.20 x 10(9)/L were randomized. INTERVENTION: Patients were randomized to receive either a single 120-mg/d dose of adefovir dipivoxil (n = 219) or an indistinguishable placebo (n = 223). All patients received L-carnitine, 500 mg/d. Open-label adefovir was offered after 24 weeks and was continued until the end of the study. MAIN OUTCOME MEASURES: Changes in HIV RNA from baseline, based on area under the curve and CD4+ cell levels, adverse events, and effect of baseline genotypic resistance on response to adefovir. RESULTS: Patients assigned to adefovir demonstrated a 0.4-log10 decline from baseline in HIV RNA compared with no change in the placebo group (P<.001), which continued through 48 weeks. CD4+ cell counts did not change. During the initial 24 weeks, elevated hepatic enzyme levels (P<.001), gastrointestinal tract complaints (P<.001), and weight loss (P<.001) were associated with use of adefovir. Between 24 weeks and 48 weeks elevations in serum creatinine occurred in 60% of patients, usually returning to baseline after discontinuation of adefovir. Patients with lamivudine or lamivudine and zidovudine resistance mutations demonstrated anti-HIV effects with adefovir (P< or =.01 vs placebo group). CONCLUSIONS: This study suggests that once-daily adefovir therapy reduces HIV RNA and is active against isolates resistant to lamivudine or lamivudine and zidovudine. Nephrotoxicity occurred when treatment extended beyond 24 weeks but was reversible.

Group sequential analyses for the mean function of a repeated measure process.

In many clinical trials, treatment efficacy is based upon response to a biological marker that is measured repeatedly during the course of follow-up. However, in some of these trials it is not clear, a priori, how treatment effects on the marker may manifest themselves or what kinds of effects are clinically meaningful and/or acceptable. It is, therefore, desirable to allow flexibility in design and monitoring process by not prespecifying a stopping rule or even the parameter on which inferences will be based. Using the more general results in Hu and Lagakos, this paper extends the idea of the repeated confidence intervals for a parameter (Jennison and Turnbull) to repeated confidence bands for the mean function of a repeated measure process. We illustrate the approach and some considerations in its application with the results of a recent AIDS clinical trial.

Use of the Wei-Lin-Weissfeld method for the analysis of a recurring and a terminating event.

We consider application of the Wei-Lin-Weissfeld (WLW) method for multiple failure time data when analysing a disease process consisting of a recurring outcome, such as clinical progression, and a terminating outcome, such as death. In order to adapt WLW for this situation, 'events' must be specified that define multiple failure times and whether these are censored. Various choices of events are possible, and each corresponds to inferences about a different aspect of the underlying disease process. Definitions which regard the terminating outcome as a censor of the recurring outcome focus on specific cause-specific hazard functions, while event definitions which make no distinction between a recurring and terminating outcome focus on hazard functions of the induced failure times. Some event definitions require strong statistical assumptions to yield valid inferences and are not recommended. The application of WLW for recurring/terminating processes is illustrated with the results of two recently conducted clinical trials in persons with HIV.

HIV treatment strategies utilizing virologic and immunologic markers as criteria for changing treatments.

Currently available antiviral drugs used in the treatment of AIDS patients are effective for a limited time. Therapy consisting of different drugs given in sequence thus has the potential to yield the greatest possible benefit to patients, yet it is not known in what order the drugs should be administered, or for how long. Can patient-specific information, such as viral load or determination of mutation status, be used to make these decisions on a patient by patient basis? We propose a general model for the relationship between treatment, virologic or immunologic markers, and clinical disease progression that can provide answers to these questions. We develop guidelines for optimizing progression under several settings. Optimal survival is derived for full, partial, or no interim information.

Non-parametric inference of a failure time distribution when the failure times are estimated.

We consider the estimation of a failure time distribution F when, instead of N i.i.d. realizations T1, T2, ..., TN from F, the observations consist of estimates of the Ti. If the Ti could be observed, a natural non-parametric estimator of F would be the Kaplan-Meier estimator. Thus, we examine the properties of the Kaplan-Meier estimator based on the estimates of the Ti. We also consider a weighted Kaplan-Meier estimator which gives more emphasis to those estimated times based on more information. We evaluate the small sample bias and precision of F when the estimated failure times arise from additive or multiplicative error structures. Because this problem has particular application in the study of non-compliance of subjects in clinical trials, we also investigate the bias and precision of the estimators of the distribution function based on a complex error structure that would arise in the non-compliance setting. Here Ti denotes the unobserved time to non-compliance for the ith subject, and is estimated using repeated observations from a laboratory marker whose behaviour is affected by non-compliance. The techniques are illustrated with the results of a recent AIDS clinical trial.

A comparison of immediate with deferred zidovudine therapy for asymptomatic HIV-infected adults with CD4 cell counts of 500 or more per cubic millimeter. AIDS Clinical Trials Group.

BACKGROUND: The clinical benefits of zidovudine remain unproved in patients with asymptomatic human immunodeficiency virus (HIV) infection when CD4 cell counts exceed 500 per cubic millimeter. We compared zidovudine therapy given immediately with deferred therapy in such subjects. METHODS: Beginning in 1987, subjects with asymptomatic HIV infection and 500 or more CD4 cells per cubic millimeter were randomly assigned to receive placebo or zidovudine (either 500 or 1500 mg per day, starting immediately). In 1989, the study was modified so that open-label treatment with 500 mg of zidovudine per day (deferred therapy) was offered when CD4 cell counts fell below 500 per cubic millimeter. The study end points included overall survival, survival free of the acquired immunodeficiency syndrome (AIDS), toxic effects, and changes in CD4 cell counts. RESULTS: There were 1637 subjects who could be evaluated: 547 in the deferred-therapy group, 549 in the group receiving 500 mg of zidovudine immediately, and 541 in the 1500-mg group. The subjects were followed for up to 6.5 years (group medians, 4.8, 4.8, and 4.9, respectively). There was no significant difference in AIDS-free survival in the deferred-therapy group as compared with the low-dose or high-dose groups (81 cases of progression to AIDS or death vs. 81 and 74, respectively; P = 0.95 and P = 0.13) or in overall survival (51 deaths vs. 47 and 46; P = 0.25 and P = 0.16). The decline in CD4 cells was slower in both immediate-therapy groups than in the deferred-therapy group (P < 0.001 for both). Adverse effects were uncommon, and before the study modification their incidence was similar among the treatment groups, but severe anemia and granulocytopenia were more frequent in the 1500-mg group than in the deferred-therapy group (P < 0.001). CONCLUSIONS: In asymptomatic, HIV-infected adults with 500 or more CD4 cells per cubic millimeter, treatment with zidovudine slows the decline in the CD4 cell count but does not significantly prolong either AIDS-free or overall survival. These results do not encourage the routine use of zidovudine monotherapy in this population.

Assessing drug compliance using longitudinal marker data, with application to AIDS.

The assessment of non-compliance to a study medication is an important issue in the evaluation of clinical trials of self-administered drugs. Traditional methods for evaluating the compliance of subjects include self-reported questionnaires and pharmacologic assays of drug levels in randomly-drawn blood samples, but each of these has important limitations. This paper adapts and extends changepoint methods to assess compliance from longitudinal data on laboratory markers that are affected by the drug. The maximum likelihood estimators for two models are developed and examined. The effect of the drug on the marker process, as well as the spacing of the observations of the marker process relative to the time of non-compliance determine which model parameters are estimable. For the situations examined, the method of maximum likelihood is found to perform well in most cases. However, when non-compliance begins shortly before the last observation of the marker process, these (as well as any other) estimators cannot reliably distinguish non-compliance from compliance. The methods are illustrated with an example from a recent clinical trial of persons infected with HIV.

The duration of zidovudine benefit in persons with asymptomatic HIV infection. Prolonged evaluation of protocol 019 of the AIDS Clinical Trials Group.

OBJECTIVE: To determine the durability of zidovudine-induced delay in clinical progression of asymptomatic human immunodeficiency virus (HIV) disease and to assess the relationship between this effect and the entry CD4+ cell count. DESIGN AND INTERVENTIONS: Extended follow-up data from subjects participating in protocol 019 of the AIDS [acquired immunodeficiency syndrome] Clinical Trials Group were examined. Subjects were offered a total daily dose of 500 mg of open-label zidovudine after the unblinding of the original randomized trial in 1989. Original treatment groups included placebo, 500 mg of zidovudine, or 1500 mg of zidovudine daily in divided doses. Three distinct analyses were conducted to assess the duration of zidovudine's effect on progression to AIDS or death: (1) analysis of all follow-up information from all subjects, (2) analysis of all subjects but with follow-up of original placebo-assigned subjects censored at the time open-label zidovudine was initiated, and (3) analysis of the effect of initiating zidovudine in subjects initially assigned to receive placebo. SETTING: University-based and university-affiliated AIDS research clinics participating in AIDS Clinical Trials Group protocol 019. PATIENTS: A total of 1565 asymptomatic HIV-infected subjects with entry CD4+ cell counts less than 0.50 x 10(9)/L (500/microL). MAIN OUTCOME MEASURE: Time to progression to AIDS or death. RESULTS: During follow-up of up to 4.5 years (mean, 2.6 years), 232 subjects progressed to AIDS or died. In each of the three analyses described herein, zidovudine was associated with a significant (P = .008, .004, .007) decrease in the risk of such progression. However, each of these analyses also indicated a decreasing placebo:zidovudine relative risk with duration of use (P = .002, .08, .04), suggesting a nonpermanent effect. The duration of benefit appeared to be related to entry CD4+ cell count, with greater benefit in those with higher counts at entry. No significant differences in survival were found between those originally randomized to zidovudine or placebo. CONCLUSIONS: Zidovudine at 500 mg/d caused a significant delay in progression to AIDS or death, but its earlier use in asymptomatic disease was not associated with an additional prolongation of survival compared with delayed initiation. The delay in progression diminished over time especially in subjects with entry CD4+ cell counts less than 0.30 x 10(9)/L (300/microL). Treatment strategies that alter drug regimens before the loss of zidovudine benefit should be explored.

Estimation of the infection time and latency distribution of AIDS with doubly censored data.

We consider the nonparametric estimation of the time to infection with HIV and the latency period between infection and the onset of AIDS in data where both the events of infection and AIDS are not directly observed. The methods use self-consistency equations that are more easily and quickly solvable than the nonparametric estimators proposed by De Gruttola and Lagakos (1989, Biometrics 45, 1-11). The techniques are illustrated with data on hemophiliacs who became infected through contamination of the blood factor they were given to control their hemophilia.