Statistical considerations when using a composite endpoint for comparing treatment groups.

When comparing two treatment groups in a time-to-event analysis, it is common to use a composite event consisting of two or more distinct outcomes. The goal of this paper is to develop a statistical methodology to derive efficiency guidelines for deciding whether to expand a study primary endpoint from E1 (for example, non-fatal myocardial infarction and cardiovascular death) to the composite of E1 and E2 (for example, non-fatal myocardial infarction, cardiovascular death or revascularisation). We investigate this problem by considering the asymptotic relative efficiency of a log-rank test for comparing treatment groups with respect to a primary relevant endpoint E1 versus the composite primary endpoint, say E, of E1 and E2, where E2 is some additional endpoint.

A likelihood estimation of HIV incidence incorporating information on past prevalence.

SUMMARY: The prevalence and incidence of an epidemic are basic characteristics that are essential for monitoring its impact, determining public health priorities, assessing the effect of interventions, and for planning purposes. A direct approach for estimating incidence is to undertake a longitudinal cohort study where a representative sample of disease free individuals are followed for a specified period of time and new cases of infection are observed and recorded. This approach is expensive, time consuming and prone to bias due to loss-to-follow-up. An alternative approach is to estimate incidence from cross sectional surveys using biomarkers to identify persons recently infected as in (Brookmeyer and Quinn, 1995; Janssen et al., 1998). This paper builds on the work of Janssen et al. (1998) and extends the theoretical framework proposed by Balasubramanian and Lagakos (2010) by incorporating information on past prevalence and deriving maximum likelihood estimators of incidence. The performance of the proposed method is evaluated through a simulation study, and its use is illustrated using data from the Botswana AIDS Impact (BAIS) III survey of 2008.

Testing and interval estimation for two-sample survival comparisons with small sample sizes and unequal censoring.

While the commonly used log-rank test for survival times between 2 groups enjoys many desirable properties, sometimes the log-rank test and its related linear rank tests perform poorly when sample sizes are small. Similar concerns apply to interval estimates for treatment differences in this setting, though their properties are less well known. Standard permutation tests are one option, but these are not in general valid when the underlying censoring distributions in the comparison groups are unequal. We develop 2 methods for testing and interval estimation, for use with small samples and possibly unequal censoring, based on first imputing survival and censoring times and then applying permutation methods. One provides a heuristic justification for the approach proposed recently by Heinze and others (2003, Exact log-rank tests for unequal follow-up. Biometrics 59, 1151-1157). Simulation studies show that the proposed methods have good Type I error and power properties. For accelerated failure time models, compared to the asymptotic methods of Jin and others (2003, Rank-based inference for the accelerated failure time model. Biometrika 90, 341-353), the proposed methods yield confidence intervals with better coverage probabilities in small-sample settings and similar efficiency when sample sizes are large. The proposed methods are illustrated with data from a cancer study and an AIDS clinical trial.

Response to antiretroviral therapy after a single, peripartum dose of nevirapine.

BACKGROUND: A single dose of nevirapine during labor reduces perinatal transmission of human immunodeficiency virus type 1 (HIV-1) but often leads to viral nevirapine resistance mutations in mothers and infants. METHODS: We studied the response to nevirapine-based antiretroviral treatment among women and infants who had previously been randomly assigned to a single, peripartum dose of nevirapine or placebo in a trial in Botswana involving the prevention of the transmission of HIV-1 from mother to child. All women were treated with antenatal zidovudine. The primary end point for mothers and infants was virologic failure by the 6-month visit after initiation of antiretroviral treatment, estimated within groups by the Kaplan-Meier method. RESULTS: Of 218 women who started antiretroviral treatment, 112 had received a single dose of nevirapine and 106 had received placebo. By the 6-month visit after the initiation of antiretroviral treatment, 5.0% of the women who had received placebo had virologic failure, as compared with 18.4% of those who had received a single dose of nevirapine (P=0.002). Among 60 women starting antiretroviral treatment within 6 months after receiving placebo or a single dose of nevirapine, no women in the placebo group and 41.7% in the nevirapine group had virologic failure (P<0.001). In contrast, virologic failure rates did not differ significantly between the placebo group and the nevirapine group among 158 women starting antiretroviral treatment 6 months or more post partum (7.8% and 12.0%, respectively; P=0.39). Thirty infants also began antiretroviral treatment (15 in the placebo group and 15 in the nevirapine group). Virologic failure by the 6-month visit occurred in significantly more infants who had received a single dose of nevirapine than in infants who had received placebo (P<0.001). Maternal and infant findings did not change qualitatively by 12 and 24 months after the initiation of antiretroviral treatment. CONCLUSIONS: Women who received a single dose of nevirapine to prevent perinatal transmission of HIV-1 had higher rates of virologic failure with subsequent nevirapine-based antiretroviral therapy than did women without previous exposure to nevirapine. However, this applied only when nevirapine-based antiretroviral therapy was initiated within 6 months after receipt of a single, peripartum dose of nevirapine. (ClinicalTrials.gov number, NCT00197587 [ClinicalTrials.gov].).

Statistical monitoring of clinical trials with multivariate response and/or multiple arms: a flexible approach.

Randomized clinical trials with a multivariate response and/or multiple treatment arms are increasingly common, in part because of their efficiency and a greater concern about balancing risks with benefits. In some trials, the specific types and magnitudes of treatment group differences that would warrant early termination cannot easily be specified prior to the onset of the trial and/or could change as the trial progresses. This underscores the need for more flexible monitoring methods than traditional approaches. This paper extends the repeated confidence bands approach for interim monitoring to more general settings where there can be a multivariate response and/or multiple treatment arms and where the metrics for comparing treatment groups can change during the conduct of the trial. We illustrate the approach using the results of a recent AIDS clinical trial and examine its efficiency and robustness via simulation.

Augmented cross-sectional prevalence testing for estimating HIV incidence.

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

Estimating HIV incidence based on combined prevalence testing.

Knowledge of incidence rates of HIV and other infectious diseases is important in evaluating the state of an epidemic as well as for designing interventional studies. Estimation of disease incidence from longitudinal studies can be expensive and time consuming. Alternatively, Janssen et al. (1998, Journal of the American Medical Association 280, 42-48) proposed the estimation of HIV incidence at a single point in time based on the combined use of a standard and "detuned" antibody assay. This article frames the problem from a longitudinal perspective, from which the maximum likelihood estimator of incidence is determined and compared with the Janssen estimator. The formulation also allows estimation for general situations, including different batteries of tests among subjects, inclusion of covariates, and a comparative evaluation of different test batteries to help guide study design. The methods are illustrated with data from an HIV interventional trial and a seroprevalence survey recently conducted in Botswana.

Nonparametric inference and uniqueness for periodically observed progressive disease models.

In many studies examining the progression of HIV and other chronic diseases, subjects are periodically monitored to assess their progression through disease states. This gives rise to a specific type of panel data which have been termed "chain-of-events data"; e.g. data that result from periodic observation of a progressive disease process whose states occur in a prescribed order and where state transitions are not observable. Using a discrete time semi-Markov model, we develop an algorithm for nonparametric estimation of the distribution functions of sojourn times in a J state progressive disease model. Issues of uniqueness for chain-of-events data are not well-understood. Thus, a main goal of this paper is to determine the uniqueness of the nonparametric estimators of the distribution functions of sojourn times within states. We develop sufficient conditions for uniqueness of the nonparametric maximum likelihood estimator, including situations where some but not all of its components are unique. We illustrate the methods with three examples.

GENERALIZED LEAST SQUARES ESTIMATION OF THE MEAN FUNCTION OF A COUNTING PROCESS BASED ON PANEL COUNTS.

This paper considers nonparametric estimation of the mean function of a counting process based on periodic observations, i.e., panel counts. We present estimators derived through minimizing a class of generalized sums of squares subject to a monotonicity constraint. We establish consistency of the estimators and provide procedures to implement them with various weight functions. For specific weight functions, they reduce to the estimator given in Sun and Kalbfleisch (1995), and are closely related to the nonparametric maximum likelihood estimator studied in Wellner and Zhang (2000). With other weight functions, the proposed estimators provide alternatives that can have better efficiency in non-Poisson situations than previous approaches. Simulations are used to examine the finite-sample performance of the proposed estimators.

Inference after variable selection using restricted permutation methods.

When confronted with multiple covariates and a response variable, analysts sometimes apply a variable-selection algorithm to the covariate-response data to identify a subset of covariates potentially associated with the response, and then wish to make inferences about parameters in a model for the marginal association between the selected covariates and the response. If an independent data set were available, the parameters of interest could be estimated by using standard inference methods to fit the postulated marginal model to the independent data set. However, when applied to the same data set used by the variable selector, standard ("naive") methods can lead to distorted inferences. The authors develop testing and interval estimation methods for parameters reflecting the marginal association between the selected covariates and response variable, based on the same data set used for variable selection. They provide theoretical justification for the proposed methods, present results to guide their implementation, and use simulations to assess and compare their performance to a sample-splitting approach. The methods are illustrated with data from a recent AIDS study.

Maternal single-dose nevirapine versus placebo as part of an antiretroviral strategy to prevent mother-to-child HIV transmission in Botswana.

BACKGROUND: Single-dose nevirapine given to women and infants reduces mother-to-child HIV transmission, but nevirapine resistance develops in a large percentage of women. OBJECTIVE: To determine whether the maternal nevirapine dose could be eliminated in the setting of zidovudine prophylaxis. DESIGN, SETTING, AND PARTICIPANTS: A 2 x 2 factorial, randomized, clinical trial, with a double-blinded peripartum factor designed to assess the equivalence of maternal single-dose nevirapine versus placebo with respect to HIV transmission. A total of 709 HIV-infected pregnant women were randomized from four district hospitals in Botswana, resulting in 694 live first-born infants. HAART was available for women with AIDS. INTERVENTION: All women received a background of zidovudine from 34 weeks' gestation through delivery, and all infants received single-dose nevirapine at birth and zidovudine from birth through 1 month. Women were randomized to receive either single-dose nevirapine or placebo during labor. MAIN OUTCOME MEASURES: The primary endpoint was infant HIV infection by the 1-month visit. RESULTS: Of the 694 infants in this equivalence study, 15 (4.3%) of 345 in the maternal nevirapine arm were HIV infected by 1 month, versus 13 (3.7%) of 349 in the maternal placebo arm (95% confidence interval for difference, -2.4% to 3.8%), meeting pre-determined equivalence criteria. Nevirapine resistance at 1 month postpartum was detected in 45% of a random sample of women who received nevirapine. CONCLUSIONS: In the setting of maternal zidovudine and infant zidovudine plus single-dose nevirapine, infant HIV infection rates were similar whether women received single-dose nevirapine or placebo. This strategy avoids the potential for maternal nevirapine resistance.

Breastfeeding plus infant zidovudine prophylaxis for 6 months vs formula feeding plus infant zidovudine for 1 month to reduce mother-to-child HIV transmission in Botswana: a randomized trial: the Mashi Study.

CONTEXT: Postnatal transmission of human immunodeficiency virus-1 (HIV) via breastfeeding reverses gains achieved by perinatal antiretroviral interventions. OBJECTIVE: To compare the efficacy and safety of 2 infant feeding strategies for the prevention of postnatal mother-to-child HIV transmission. DESIGN, SETTING, AND PATIENTS: A 2 x 2 factorial randomized clinical trial with peripartum (single-dose nevirapine vs placebo) and postpartum infant feeding (formula vs breastfeeding with infant zidovudine prophylaxis) interventions. In Botswana between March 27, 2001, and October 29, 2003, 1200 HIV-positive pregnant women were randomized from 4 district hospitals. Infants were evaluated at birth, monthly until age 7 months, at age 9 months, then every third month through age 18 months. INTERVENTION: All of the mothers received zidovudine 300 mg orally twice daily from 34 weeks' gestation and during labor. Mothers and infants were randomized to receive single-dose nevirapine or placebo. Infants were randomized to 6 months of breastfeeding plus prophylactic infant zidovudine (breastfed plus zidovudine), or formula feeding plus 1 month of infant zidovudine (formula fed). MAIN OUTCOME MEASURES: Primary efficacy (HIV infection by age 7 months and HIV-free survival by age 18 months) and safety (occurrence of infant adverse events by 7 months of age) end points were evaluated in 1179 infants. RESULTS: The 7-month HIV infection rates were 5.6% (32 infants in the formula-fed group) vs 9.0% (51 infants in the breastfed plus zidovudine group) (P = .04; 95% confidence interval for difference, -6.4% to -0.4%). Cumulative mortality or HIV infection rates at 18 months were 80 infants (13.9%, formula fed) vs 86 infants (15.1% breastfed plus zidovudine) (P = .60; 95% confidence interval for difference, -5.3% to 2.9%). Cumulative infant mortality at 7 months was significantly higher for the formula-fed group than for the breastfed plus zidovudine group (9.3% vs 4.9%; P = .003), but this difference diminished beyond month 7 such that the time-to-mortality distributions through age 18 months were not significantly different (P = .21). CONCLUSIONS: Breastfeeding with zidovudine prophylaxis was not as effective as formula feeding in preventing postnatal HIV transmission, but was associated with a lower mortality rate at 7 months. Both strategies had comparable HIV-free survival at 18 months. These results demonstrate the risk of formula feeding to infants in sub-Saharan Africa, and the need for studies of alternative strategies. TRIAL REGISTRATION: clinicaltrials.gov Identifier: NCT00197587.

Evaluating the role of human papillomavirus vaccine in cervical cancer prevention.

Persistent genital infection with human papillomavirus (HPV) is a natural candidate as a surrogate marker for cervical cancer because of the strong epidemiologic and molecular evidence that HPV infection is the causative agent for almost all cervical cancers. However, while infection with high-risk types of HPV appears to be necessary for the development of cervical cancer, most infections are controlled by host immune response and do not lead to cancer in the vast majority of infected women. Because diagnostic tests cannot distinguish a persistent infection in the pathogenesis of cervical cancer from a transient infection, it is difficult to describe the disease mechanism as a progressive process based on observations. Therefore, the disease pathogenesis pathway does not fit into the usual surrogate marker framework, raising practical concerns about using HPV infection as a surrogate for a clinical endpoint in vaccine trials. In this paper, we describe the challenges in defining HPV infection as a surrogate endpoint in a HPV vaccine trial that is aimed at reducing cervical cancer rates and examine potential effects of the vaccine. We then outline some issues in the design and analysis of HPV vaccine trials, including the use of operationally defined HPV infection events meant to capture persistent infections. We conclude with a recommendation for a multistate model that uses HPV infection to help explain the mechanisms of vaccine action rather than validate it as an endpoint substitute.

HIV-1 Subtype C Phylodynamics in the Global Epidemic.

The diversity of HIV-1 and its propensity to generate escape mutants present fundamental challenges to control efforts, including HIV vaccine design. Intra-host diversification of HIV is determined by immune responses elicited by an HIV-infected individual over the course of the infection. Complex and dynamic patterns of transmission of HIV lead to an even more complex population viral diversity over time, thus presenting enormous challenges to vaccine development. To address inter-patient viral evolution over time, a set of 653 unique HIV-1 subtype C gag sequences were retrieved from the LANL HIV Database, grouped by sampling year as <2000, 2000, 2001-2002, 2003, and 2004-2006, and analyzed for the site-specific frequency of translated amino acid residues. Phylogenetic analysis revealed that a total of 289 out of 653 (44.3%) analyzed sequences were found within 16 clusters defined by aLRT of more than 0.90. Median (IQR) inter-sample diversity of analyzed gag sequences was 8.7% (7.7%; 9.8%). Despite the heterogeneous origins of analyzed sequences, the gamut and frequency of amino acid residues in wild-type Gag were remarkably stable over the last decade of the HIV-1 subtype C epidemic. The vast majority of amino acid residues demonstrated minor frequency fluctuation over time, consistent with the conservative nature of the HIV-1 Gag protein. Only 4.0% (20 out of 500; HXB2 numbering) amino acid residues across Gag displayed both statistically significant (p<0.05 by both a trend test and heterogeneity test) changes in amino acid frequency over time as well as a range of at least 10% in the frequency of the major amino acid. A total of 59.2% of amino acid residues with changing frequency of 10%+ were found within previously identified CTL epitopes. The time of the most recent common ancestor of the HIV-1 subtype C was dated to around 1950 (95% HPD from 1928 to 1962). This study provides evidence for the overall stability of HIV-1 subtype C Gag among viruses circulating in the epidemic over the last decade. However selected sites across HIV-1C Gag with changing amino acid frequency are likely to be under selection pressure at the population level.

On the use of adjusted cross-sectional estimators of HIV incidence.

OBJECTIVE: To elucidate when and how cross-sectional estimators of HIV incidence rates based on a sensitive and less sensitive diagnostic test should be adjusted. METHODS: Evaluate the statistical properties of unadjusted and adjusted cross-sectional estimators of HIV incidence, including the adjusted estimators considered by McDougal et al, for the 2 settings where (a) all infected subjects eventually become reactive to the less sensitive test, and (b) a subset of infected subjects indefinitely remain nonreactive to the less sensitive test. Derive the maximum likelihood estimator of incidence for the latter setting and use analytical results and simulation studies to compare the performance of the various estimators. RESULTS: When every infected subject would eventually become reactive to the less sensitive test, the McDougal adjusted estimator is uniformly less precise than the unadjusted estimator and more susceptible to bias. When a subset of the infected population would indefinitely remain nonreactive to the less sensitive test, the McDougal adjusted estimator is less precise than the maximum likelihood estimator, which coincides with an estimator developed by McWalter and Welte using a mathematical modeling approach. When the assumed model is incorrect, the unadjusted estimator overestimates incidence, whereas the maximum likelihood estimator can be biased in either direction. CONCLUSIONS: The standard unadjusted cross-sectional estimator of HIV incidence should be used when all infected individuals would eventually become reactive to the less sensitive test. When a subset of individuals would indefinitely remain nonreactive to the less sensitive test, the maximum likelihood estimator for this setting should be used. Characterizing the proportion of individuals who would indefinitely remain nonreactive is crucial for accurate estimation of HIV incidence.