General regression model for the subdistribution of a competing risk under left-truncation and right-censoring.

Left-truncation poses extra challenges for the analysis of complex time-to-event data. We propose a general semiparametric regression model for left-truncated and right-censored competing risks data that is based on a novel weighted conditional likelihood function. Targeting the subdistribution hazard, our parameter estimates are directly interpretable with regard to the cumulative incidence function. We compare different weights from recent literature and develop a heuristic interpretation from a cure model perspective that is based on pseudo risk sets. Our approach accommodates external time-dependent covariate effects on the subdistribution hazard. We establish consistency and asymptotic normality of the estimators and propose a sandwich estimator of the variance. In comprehensive simulation studies we demonstrate solid performance of the proposed method. Comparing the sandwich estimator with the inverse Fisher information matrix, we observe a bias for the inverse Fisher information matrix and diminished coverage probabilities in settings with a higher percentage of left-truncation. To illustrate the practical utility of the proposed method, we study its application to a large HIV vaccine efficacy trial dataset.

Doubly robust nonparametric inference on the average treatment effect.

Doubly robust estimators are widely used to draw inference about the average effect of a treatment. Such estimators are consistent for the effect of interest if either one of two nuisance parameters is consistently estimated. However, if flexible, data-adaptive estimators of these nuisance parameters are used, double robustness does not readily extend to inference. We present a general theoretical study of the behaviour of doubly robust estimators of an average treatment effect when one of the nuisance parameters is inconsistently estimated. We contrast different methods for constructing such estimators and investigate the extent to which they may be modified to also allow doubly robust inference. We find that while targeted minimum loss-based estimation can be used to solve this problem very naturally, common alternative frameworks appear to be inappropriate for this purpose. We provide a theoretical study and a numerical evaluation of the alternatives considered. Our simulations highlight the need for and usefulness of these approaches in practice, while our theoretical developments have broad implications for the construction of estimators that permit doubly robust inference in other problems.

A study of vaccine-induced immune pressure on breakthrough infections in the Phambili phase 2b HIV-1 vaccine efficacy trial.

INTRODUCTION: The Merck Adenovirus-5 Gag/Pol/Nef HIV-1 subtype-B vaccine evaluated in predominately subtype B epidemic regions (Step Study), while not preventing infection, exerted vaccine-induced immune pressure on HIV-1 breakthrough infections. Here we investigated if the same vaccine exerted immune pressure when tested in the Phambili Phase 2b study in a subtype C epidemic. MATERIALS AND METHODS: A sieve analysis, which compares breakthrough viruses from placebo and vaccine arms, was performed on 277 near full-length genomes generated from 23 vaccine and 20 placebo recipients. Vaccine coverage was estimated by computing the percentage of 9-mers that were exact matches to the vaccine insert. RESULTS: There was significantly greater protein distances from the vaccine immunogen sequence in Gag (p=0.045) and Nef (p=0.021) in viruses infecting vaccine recipients compared to placebo recipients. Twenty-seven putative sites of vaccine-induced pressure were identified (p<0.05) in Gag (n=10), Pol (n=7) and Nef (n=10), although they did not remain significant after adjustment for multiple comparisons. We found the epitope sieve effect in Step was driven by HLA A∗02:01; an allele which was found in low frequency in Phambili participants compared to Step participants. Furthermore, the coverage of the vaccine against subtype C Phambili viruses was 31%, 46% and 14% for Gag, Pol and Nef, respectively, compared to subtype B Step virus coverage of 56%, 61% and 26%, respectively. DISCUSSION: This study presents evidence of sieve effects in Gag and Nef; however could not confirm effects on specific amino acid sites. We propose that this weaker signal of vaccine immune pressure detected in the Phambili study compared to the Step study may have been influenced by differences in host genetics (HLA allele frequency) and reduced impact of vaccine-induced immune responses due to mismatch between the viral subtype in the vaccine and infecting subtypes.

Mark-specific hazard ratio model with multivariate continuous marks: an application to vaccine efficacy.

In randomized placebo-controlled preventive HIV vaccine efficacy trials, an objective is to evaluate the relationship between vaccine efficacy to prevent infection and genetic distances of the exposing HIV strains to the multiple HIV sequences included in the vaccine construct, where the set of genetic distances is considered as the continuous multivariate "mark" observed in infected subjects only. This research develops a multivariate mark-specific hazard ratio model in the competing risks failure time analysis framework for the assessment of mark-specific vaccine efficacy. It allows improved efficiency of estimation by employing the semiparametric method of maximum profile likelihood estimation in the vaccine-to-placebo mark density ratio model. The model also enables the use of a more efficient estimation method for the overall log hazard ratio in the Cox model. In addition, we propose testing procedures to evaluate two relevant hypotheses concerning mark-specific vaccine efficacy. The asymptotic properties and finite-sample performance of the inferential procedures are investigated. Finally, we apply the proposed methods to data collected in the Thai RV144 HIV vaccine efficacy trial.

Allospecific CD154 + T-cytotoxic memory cells as potential surrogate for rejection risk in pediatric intestine transplantation.

Clinical end-points dictate large trial enrollments and exclude children with the rare intestine transplant procedure (ITx), who experience higher drug-related morbidity. We evaluate the novel rejection-risk parameter, allo-(antigen)-specific CD154 + TcMs (i) as surrogates for ACR using Prentice's criteria, (ii) for association with immunosuppression targets to determine Fleming's surrogate end-point designation, and (iii) as time-to-event end-point in a simulated comparison of alemtuzumab (NCT#01208337, n = 14) and rabbit anti-human thymocyte globulin (rATG, n = 16) among 30 children with ITx. CD154 + TcM were measured in MLR before, and at 1-60 and 61-200 days after ITx (NCT#01163578). CD154 + TcM correlate significantly with rejection severity (Spearman r = 0.685, p = 2.03E-5) and associate with biopsy-proven ITx rejection with sensitivity/specificity of 94%/84% [corrected] independent of immunosuppressant. Previously stated sensitivity of 90% is incorrect. [corrected]. The rejection-risk threshold of CD154 + TcM resolves rapidly in 200-day follow-up (46 ± 20 vs. 158 ± 59 days, p = 0.009, K-M) with alemtuzumab, which demonstrates lower 90-day ACR incidence (50% vs. 69%, p=NS, Fisher's exact), and is associated with accelerated prednisone minimization to ≤2.5 mg/day, compared with rATG (120 ± 28 vs. 180 ± 30 days, p = 0.027, K-M). As a surrogate end-point, time-to-rejection-risk resolution measured with CD154 + TcM portends 50% reduction in sample sizes in a simulated trial of alemtuzumab vs. rATG. Rejection-risk assessment with CD154 + TcM may enable informed immunosuppression minimization, and preliminary efficacy comparisons in pediatric ITx.

Joint inferences on vaccine efficacy against infection and disease with application to the first HIV vaccine efficacy trial.

In many clinical trials, subjects are followed for two stages of outcomes, and it is of interest to compare the incidence of each outcome between two randomized groups. The outcome of the first stage may influence the outcome of the second stage. Moreover, the relative risks of the two outcomes may be linked, with the time-dependent profile of relative risk for the second outcome functionally dependent on that of the first. For example, during exposure to HIV, virologic and host factors simultaneously impact the probability of infection and the subsequent viral trajectories, and the efficacy of a tested vaccine to prevent infection and to prevent viral failure may work in concert. We address this problem by modeling the relationship between the stage two hazard function and covariates via Cox's proportional hazards model (Cox, 1972), with the stage one log-hazard ratio theta(*) at the first event time Tl, included as a covariate. With theta(*) estimated using three methods, 1) nonparametric kernel smoothing; 2) locally parametric penalized splines; and 3) fully parametric cubic linear splines, we subsequently develop inference procedures for the regression parameter in the stage two Cox model based on each of the estimator of theta(*). The inferential procedures are studied in simulations and are illustrated with application to data from the world's first preventive HIV vaccine efficacy trial.

Long-term safety analysis of preventive HIV-1 vaccines evaluated in AIDS vaccine evaluation group NIAID-sponsored Phase I and II clinical trials.

This report evaluates long-term safety data from 3189 human immunodeficiency virus type 1 (HIV-1) uninfected, healthy volunteers who were enrolled into 51 National Institute of Allergy and Infectious Diseases (NIAID)-sponsored Phase I and II multicentred, randomized, double-blind trials of recombinant HIV-1 subunit vaccines (23 studies), synthetic peptide vaccines (7 studies), live vaccinia-vector recombinant envelope vaccines (7 studies), canarypox vector recombinant vaccines (13 studies), a DNA vaccine (1 study), and a Salmonella-vector vaccine (1 study). During the 12,340 person-years of follow-up, participants were monitored for adverse events including immune dysfunction/autoimmunity, anaphylaxis, cancer, death, and vaccine allergy. The analysis provides evidence that a preparation of a C4-V3 polypeptide vaccine emulsified in incomplete Freund's caused serious toxicity, but otherwise no safety problems considered serious were identified for any of the vaccines and adjuvants studied. These data serve to solidify the growing safety base of current vaccine technologies utilized in candidate vaccines for HIV-1 infection.

Omnibus tests for comparison of competing risks with adjustment for covariate effects.

This article develops omnibus tests for comparing cause-specific hazard rates and cumulative incidence functions at specified covariate levels. Confidence bands for the difference and the ratio of two conditional cumulative incidence functions are also constructed. The omnibus test is formulated in terms of a test process given by a weighted difference of estimates of cumulative cause-specific hazard rates under Cox proportional hazards models. A simulation procedure is devised for sampling from the null distribution of the test process, leading to graphical and numerical technques for detecting significant differences in the risks. The approach is applied to a cohort study of type-specific HIV infection rates.

Effects of treatment intensification with hydroxyurea in HIV-infected patients with virologic suppression.

BACKGROUND: Virologic rebound can result from suboptimal antiviral potency in combination antiretroviral therapy. DESIGN: Multicenter, partially blinded, prospective, randomized study of 202 HIV-infected subjects to determine whether therapy intensification improves long-term rates of virologic suppression. METHODS: Subjects had plasma HIV RNA < 200 copies/ml, CD4 cell count of > 200 x 10(6) cells/l, and treatment with indinavir (IDV) + zidovudine (ZDV) + lamivudine (3TC) for at least 6 months before randomization to stay on this regimen or to receive IDV + didanosine (ddI) + stavudine (d4T) plus or minus hydroxyurea (HU) (600 mg twice daily). Treatment failure was defined as either confirmed rebound of HIV RNA level to > 200 copies/ml or a drug toxicity necessitating treatment discontinuation. RESULTS: Treatment failure occurred more frequently in subjects randomized to the HU-containing arm (32.4%), than in those taking IDV + ddI + d4T (17.6%) or IDV + ZDV + 3TC (7.6%). The time to treatment failure was shorter for the HU-containing arm compared with the IDV + ZDV + 3TC (P < 0.0001) or IDV + ddI + d4T arms (P = 0.032). Dose-limiting toxicities rather than virologic rebound accounted for the differences between treatment failure among the study arms. Pancreatitis led to treatment discontinuation in 4% of subjects in treatment arms containing ddI + d4T. Three subjects with pancreatitis died, all randomized to the HU-containing arm. CONCLUSIONS: Switching to IDV + ddI + d4T + HU in patients treated with IDV + ZDV + 3TC was associated with a worse outcome, principally because of drug toxicity.

An efficient test for comparing sequence diversity between two populations.

We address the problem of comparing interindividual genomic sequence diversity between two populations. Although the methods are general, for concreteness we focus on comparing two human immunodeficiency virus (HIV) infected populations. From a viral isolate(s) taken from each individual in a sample of persons from each population, suppose one or multiple measurements are made on the genetic sequence of a coding region of HIV. Given a definition of genetic distance between sequences, the goal is to test if the distribution of interindividual distances differs between populations. If distances between all pairs of sequences within each group are used, then data-dependencies arising from the use of multiple sequences from individuals invalidates the use of a standard two-sample test such as the t-test. Where this problem has been recognized, a typical solution has been to apply a standard test to a reduced dataset comprised of one sequence or a consensus sequence from each patient. Disadvantages of this procedure are that the conclusion of the test depends on the choice of utilized sequences, often an arbitrary decision, and exclusion of replicate sequences from the analysis may needlessly sacrifice statistical power. We present a new test free of these drawbacks, which is based on a statistic that linearly combines all possible standard test statistics calculated from independent sequence subsamples. We describe statistical power advantages of the test and illustrate its use by application to nucleotide sequence distances measured from HIV-1 infected populations in southern Africa (GenBank accession numbers AF110959--AF110981) and North America/Europe. The test makes minimal assumptions, is maximally efficient and objective, and is broadly applicable.

Virologic and regimen termination surrogate end points in AIDS clinical trials.

Suppression of plasma human immunodeficiency virus (HIV) RNA levels has been widely accepted as an appropriate surrogate end point for HIV disease progression, and it is currently used as the primary end point to determine efficacy in many antiretroviral trials. However, this end point does not always measure other important effects of treatment, such as inducement of multidrug resistance, which depletes future therapy options, and toxic effects. An alternative that directly factors in these treatment costs is a composite regimen termination end point, defined as a protocol-determined change in regimen due to either virologic failure or treatment-related toxic effects. Pros and cons for using purely virologic vs various composite primary end points are discussed. Conclusions include (1) a trial's clinical objective guides the choice of primary end point, (2) a purely virologic end point is often preferable, (3) it may be important to analyze both end point types in interpreting study results, and (4) long-term clinical outcome studies are needed for identifying the most predictive surrogate end points.

Interpretability and robustness of sieve analysis models for assessing HIV strain variations in vaccine efficacy.

From data on HIV-1 characteristics measured on viruses isolated from vaccinated and unvaccinated persons infected while enrolled in preventive HIV-1 vaccine trials, interpretable inferences into strain variations of vaccine efficacy can be made with recently developed sieve analysis models. Four assumptions are needed for the parameters in these models to have meaningful interpretations in terms of vaccine-induced reductions in strain-specific per-contact transmission probabilities: (A1) vaccination impacts each strain-specific transmission probability homogeneously in vaccinated persons (leaky vaccine effect); (A2) for each strain biological susceptibility to infection given exposure is homogeneous among vaccinated trial participants and among unvaccinated trial participants; (A3) the distribution of exposure is equal in vaccinated and unvaccinated trial participants; (A4) the relative prevalence of circulating HIV-1 strains during the trial follow-up period is constant. Through theoretical considerations and simulations of an ongoing phase III HIV-1 vaccine efficacy trial in Bangkok, we evaluate the importance and necessity of these assumptions. We show that the models still provide estimates of biologically interpretable parameters when A1 is violated, but with bias the extent to which vaccine protection is heterogeneous. We also show that the models are highly robust to departures from A4, with implication that the time-independent models are adequate for applications. In addition, we suggest extensions of the sieve analysis models which incorporate random effects that account for unmeasured heterogeneity in infection risk. With these mixed models, usefully interpretable strain-specific vaccine efficacy parameters can be estimated without requiring A2. The conclusion is that A3, which is justified by randomization and blinding, is the essential assumption for the sieve models to provide reliable interpretable inferences into strain variations in vaccine efficacy.

Comparison of competing risks failure time methods and time-independent methods for assessing strain variations in vaccine protection.

In a preventive vaccine efficacy trial of a vaccine for a genotypically and phenotypically diverse pathogen, it is important to assess if and how vaccine protection against infection or disease varies with characteristics of the exposing pathogen. Gilbert, Self and Ashby developed statistical methods for this problem when the outcome data are counts of the number of vaccinated and unvaccinated trial participants infected by each pathogen strain. However, in many vaccine trials time-to-case information is available, and the extent to which this information improves investigation of differential vaccine protection is unclear. We describe how cause-specific proportional hazards models and other popular competing risks failure time techniques can be applied to this problem. This includes new results on the assumptions required for these methods to give valid inferences about strain-specific vaccine efficacy, and a comparison of theoretical and finite-sample properties between these methods and the time-independent methods. Theoretical considerations, a cholera vaccine trial example, and an extensive simulation study of a human immunodeficiency virus type 1 (HIV-1) vaccine trial show that information about failure times does not appreciably improve estimation or testing unless the pathogen has a high attack rate and the relative prevalence of pathogen strains shifts substantially during the trial follow-up period. An important implication is that practically optimal evaluation of strain-specific vaccine efficacy in HIV-1 vaccine trials will not require knowledge of infection times.

Some statistical issues in the design of HIV-1 vaccine and treatment trials.

This article summarizes material on statistical issues in the design of HIV-1 preventive vaccine trials and antiretroviral HIV-1 treatment trials that was presented at the first school on Modern Statistical Methods in Medical Research, held at the International Centre for Theoretical Physics in Trieste, in September 1999. Design issues for the two trial types are discussed separately and are compared, which highlights the relative complexity of vaccine trials. Vaccine trial designs for assessing various vaccine effects are considered, including classical double-blind individual-randomized designs for evaluating biological vaccine effects on susceptibility to infection, and augmented partners, cluster-randomized, and infant designs for evaluating biological vaccine effects on infectiousness as well as on susceptibility. Within these designs, covered topics include surrogate endpoints for measuring vaccine effects on secondary transmission and on HIV-1 disease progression, and exploratory and confirmatory methods for assessing host immune and viral genotypic or phenotypic correlates of vaccine protection against infection or disease. For antiretroviral trials, covered topics include endpoint selection and structured designs such as fractional factorial and Latin square designs for rapidly screening combination drug regimens and for identifying patterns of HIV-1 genomic evolution that predict loss of drug efficacy.

Comparative analysis of HIV type 1 genotypic resistance across antiretroviral trial treatment regimens.

From data on HIV-1 genotypes collected from antiretroviral trial participants who fail virologically, we describe methods for comparing distributions of acquired HIV-1 mutations across different treatment regimens. Given a definition of a "mutational distance" that summarizes the genetic change of a subject's virus in a way that captures the resistance cost of exposure to an antiretroviral regimen, these comparative analyses inform about the relative treatability of emergent virus by next-line therapy directed to the same viral target. The utility of the methods is illustrated by application to data from AIDS Clinical Trials Group (ACTG) Study 241. We find that patients failing zidovudine/didanosine/nevirapine accumulated a 2.41-fold greater nonnucleoside reverse transcriptase inhibitor (RTI) mutational distance than patients failing zidovudine/didanosine [95% confidence interval (1.55, 5.26), p < 0.000001], quantitating expectations that adding a nonnucleoside RTI to a double nucleoside regimen may attenuate future effectiveness of nonnucleoside RTI therapy for nucleoside-experienced patients if viremia is not suppressed. We also find that persons with extensive prior experience with suboptimal nucleoside therapy who were virologically failing zidovudine/didanosine/nevirapine or zidovudine/didanosine accumulated a similar nucleoside RTI mutational distance, implying that the addition of the nonnucleoside RTI did not preserve future nucleoside options.

Considerations in choosing a primary endpoint that measures durability of virological suppression in an antiretroviral trial.

OBJECTIVES: At present, many clinical trials of anti-HIV-1 therapies compare treatments by a primary endpoint that measures the durability of suppression of HIV-1 replication. Several durability endpoints are compared. DESIGN: Endpoints are compared by their implicit assumptions regarding surrogacy for clinical outcomes, sample size requirements, and accommodations for inter-patient differences in baseline plasma HIV-1-RNA levels and in initial treatment response. METHODS: Virological failure is defined by the non-suppression of virus levels at a prespecified follow-up time T(early virological failure), or by relapse. A binary virological failure endpoint is compared with three time-to-virological failure endpoints: time from (i) randomization that assigns early failures a failure time of T weeks; (ii) randomization that extends the early failure time T for slowly responding subjects; and (iii) virological response that assigns non-responders a failure time of 0 weeks. Endpoint differences are illustrated with Agouron's trial 511. RESULTS: In comparing high with low-dose nelfinavir (NFV) regimens in Agouron 511, the difference in Kaplan-Meier estimates of the proportion not failing by 24 weeks is 16.7% (P = 0.048), 6.5% (P = 0.29) and 22.9% (P = 0.0030) for endpoints (i), (ii) and (iii), respectively. The results differ because NFV suppresses virus more quickly at the higher dose, and the endpoints weigh this treatment difference differently. This illustrates that careful consideration needs to be given to choosing a primary endpoint that will detect treatment differences of interest. CONCLUSION: A time from randomization endpoint is usually recommended because of its advantages in flexibility and sample size, especially at interim analyses, and for its interpretation for patient management.

Statistical methods for assessing differential vaccine protection against human immunodeficiency virus types.

The human immunodeficiency virus type 1 (HIV-1) is extremely diverse. In assessing the utility of an HIV-1 vaccine, an important issue is the possibility of differential protection. We discuss statistical methods of inferring how the vaccine efficacy may vary with viral type from data that would be collected from a randomized, double-blind, placebo-controlled preventive vaccine efficacy trial. Detailed characterization of virus isolated from individuals infected during the trial will be available. We focus on the highly simplified case in which the viral characteristics are summarized by a single feature, which may be nominal, or a scalar quantity that represents distance between the isolate and the prototype virus or viruses used in the vaccine preparation. We consider discrete categorical and continuous response models for this quantity and identify models whose parameters can be interpreted as log ratios of strain-specific relative risks of infection in a prospective model for HIV-1 exposure and transmission. Methods of inference are described for the multinomial logistic regression (MLR) model for discrete categorical response, and a new semiparametric model which can be viewed as a continuous analog of the MLR model is introduced. The methods are illustrated by application to HIV-1 and hepatitis B vaccine trial data.

Semiparametric efficient estimation in the generalized odds-rate class of regression models for right-censored time-to-event data.

The generalized odds-rate class of regression models for time to event data is indexed by a non-negative constant rho and assumes that [formula: see text] where g: rho(s) = log(rho-1(s-rho - 1)) for rho > 0, g0(s) = log(-logs), S(t[symbol: see text]Z) is the survival function of the time to event for an individual with q x 1 covariate vector Z, beta is a q x 1 vector of unknown regression parameters, and alpha(t) is some arbitrary increasing function of t. When rho = 0, this model is equivalent to the proportional hazards model and when rho = 1, this model reduces to the proportional odds model. In the presence of right censoring, we construct estimators for beta and exp(alpha(t)) and show that they are consistent and asymptotically normal. In addition, we show that the estimator for beta is semiparametric efficient in the sense that it attains the semiparametric variance bound.