Comparison of models for analyzing two-group, cross-sectional data with a Gaussian outcome subject to a detection limit

A hierarchical Bayesian analysis for bivariate Weibull distribution under left-censoring scheme

This paper presents a novel approach for analyzing bivariate positive data, taking into account a covariate vector and left-censored observations, by introducing a hierarchical Bayesian analysis. The proposed method assumes marginal Weibull distributions and employs either a usual Weibull likelihood or Weibull-Tobit likelihood approaches. A latent variable or frailty is included in the model to capture the possible correlation between the bivariate responses for the same sampling unit. The posterior summaries of interest are obtained through Markov Chain Monte Carlo methods. To demonstrate the effectiveness of the proposed methodology, we apply it to a bivariate data set from stellar astronomy that includes left-censored observations and covariates. Our results indicate that the new bivariate model approach, which incorporates the latent factor to capture the potential dependence between the two responses of interest, produces accurate inference results. We also compare the two models using the different likelihood approaches (Weibull or Weibull-Tobit likelihoods) in the application. Overall, our findings suggest that the proposed hierarchical Bayesian analysis is a promising approach for analyzing bivariate positive data with left-censored observations and covariate information.

A semiparametric modeling approach for analyzing clinical biomarkers restricted to limits of detection

Before biomarkers can be used in clinical trials or patients' management, the laboratory assays that measure their levels have to go through development and analytical validation. One of the most critical performance metrics for validation of any assay is related to the minimum amount of values that can be detected and any value below this limit is referred to as below the limit of detection (LOD). Most of the existing approaches that model such biomarkers, restricted by LOD, are parametric in nature. These parametric models, however, heavily depend on the distributional assumptions, and can result in loss of precision under the model or the distributional misspecifications. Using an example from a prostate cancer clinical trial, we show how a critical relationship between serum androgen biomarker and a prognostic factor of overall survival is completely missed by the widely used parametric Tobit model. Motivated by this example, we implement a semiparametric approach, through a pseudo-value technique, that effectively captures the important relationship between the LOD restricted serum androgen and the prognostic factor. Our simulations show that the pseudo-value based semiparametric model outperforms a commonly used parametric model for modeling below LOD biomarkers by having lower mean square errors of estimation.

Lasso regularization for left-censored Gaussian outcome and high-dimensional predictors

Background

Biological assays for the quantification of markers may suffer from a lack of sensitivity and thus from an analytical detection limit. This is the case of human immunodeficiency virus (HIV) viral load. Below this threshold the exact value is unknown and values are consequently left-censored. Statistical methods have been proposed to deal with left-censoring but few are adapted in the context of high-dimensional data.

Methods

We propose to reverse the Buckley-James least squares algorithm to handle left-censored data enhanced with a Lasso regularization to accommodate high-dimensional predictors. We present a Lasso-regularized Buckley-James least squares method with both non-parametric imputation using Kaplan-Meier and parametric imputation based on the Gaussian distribution, which is typically assumed for HIV viral load data after logarithmic transformation. Cross-validation for parameter-tuning is based on an appropriate loss function that takes into account the different contributions of censored and uncensored observations. We specify how these techniques can be easily implemented using available R packages. The Lasso-regularized Buckley-James least square method was compared to simple imputation strategies to predict the response to antiretroviral therapy measured by HIV viral load according to the HIV genotypic mutations. We used a dataset composed of several clinical trials and cohorts from the Forum for Collaborative HIV Research (HIV Med. 2008;7:27-40). The proposed methods were also assessed on simulated data mimicking the observed data.

Results

Approaches accounting for left-censoring outperformed simple imputation methods in a high-dimensional setting. The Gaussian Buckley-James method with cross-validation based on the appropriate loss function showed the lowest prediction error on simulated data and, using real data, the most valid results according to the current literature on HIV mutations.

Conclusions

The proposed approach deals with high-dimensional predictors and left-censored outcomes and has shown its interest for predicting HIV viral load according to HIV mutations.

Analysis of False-Negative Human Immunodeficiency Virus Rapid Tests Performed on Oral Fluid in 3 International Clinical Research Studies

Background.

The OraQuick Advance Rapid HIV-1/2 Test is a point-of-care test capable of detecting human immunodeficiency virus (HIV)-specific antibodies in blood and oral fluid. To understand test performance and factors contributing to false-negative results in longitudinal studies, we examined results of participants enrolled in the Botswana TDF/FTC Oral HIV Prophylaxis Trial, the Bangkok Tenofovir Study, and the Bangkok MSM Cohort Study, 3 separate clinical studies of high-risk, HIV-negative persons conducted in Botswana and Thailand.

Methods.

In a retrospective observational analysis, we compared oral fluid OraQuick (OFOQ) results among participants becoming HIV infected to results obtained retrospectively using enzyme immunoassay and nucleic acid amplification tests on stored specimens. We categorized negative OFOQ results as true-negative or false-negative relative to nucleic acid amplification test and/or enzyme immunoassay, and determined the delay in OFOQ conversion relative to the estimated time of infection. We used log-binomial regression and generalized estimating equations to examine the association between false-negative results and participant, clinical, and testing-site factors.

Results.

Two-hundred thirty-three false-negative OFOQ results occurred in 80 of 287 seroconverting individuals. Estimated OFOQ conversion delay ranged from 14.5 to 547.5 (median, 98.5) days. Delayed OFOQ conversion was associated with clinical site and test operator (P < .05), preexposure prophylaxis (P = .01), low plasma viral load (P < .02), and time to kit expiration (P < .01). Participant age, sex, and HIV subtype were not associated with false-negative results. Long OFOQ conversion delay time was associated with antiretroviral exposure and low plasma viral load.

Conclusions.

Failure of OFOQ to detect HIV-1 infection was frequent and multifactorial in origin. In longitudinal trials, negative oral fluid results should be confirmed via testing of blood samples.

A Comparison of Methods for Analyzing Viral Load Data in Studies of HIV Patients

HIV RNA viral load (VL) is a pivotal outcome variable in studies of HIV infected persons. We propose and investigate two frameworks for analyzing VL: (1) a single-measure VL (SMVL) per participant and (2) repeated measures of VL (RMVL) per participant. We compared these frameworks using a cohort of 720 HIV patients in care (4,679 post-enrollment VL measurements). The SMVL framework analyzes a single VL per participant, generally captured within a “window” of time. We analyzed three SMVL methods where the VL binary outcome is defined as suppressed or not suppressed. The omit-participant method uses a 8-month “window” (-6/+2 months) around month 24 to select the participant’s VL closest to month 24 and removes participants from the analysis without a VL in the “window”. The set-to-failure method expands on the omit-participant method by including participants without a VL within the “window” and analyzes them as not suppressed. The closest-VL method analyzes each participant’s VL measurement closest to month 24. We investigated two RMVL methods: (1) repeat-binary classifies each VL measurement as suppressed or not suppressed and estimates the proportion of participants suppressed at month 24, and (2) repeat-continuous analyzes VL as a continuous variable to estimate the change in VL across time, and geometric mean (GM) VL and proportion of participants virally suppressed at month 24. Results indicated the RMVL methods have more precision than the SMVL methods, as evidenced by narrower confidence intervals for estimates of proportion suppressed and risk ratios (RR) comparing demographic strata. The repeat-continuous method had the most precision and provides more information than other considered methods. We generally recommend using the RMVL framework when there are repeated VL measurements per participant because it utilizes all available VL data, provides additional information, has more statistical power, and avoids the subjectivity of defining a “window.”

Two-part test of vaccine effect

Vaccine benefit is usually two-folded: (i) prevent a disease or, failing that, (ii) diminish the severity of a disease. To assess vaccine effect, we propose two adaptive tests. The weighted two-part test is a combination of two statistics, one on disease incidence and one on disease severity. More weight is given to the statistic with the larger a priori effect size, and the weights are determined to maximize testing power. The randomized test applies to the scenario where the total number of infections is relatively small. It uses information on disease severity to bolster power while preserving disease incidence as the primary interest. Properties of the proposed tests are explored asymptotically and by numerical studies. Although motivated by vaccine studies, the proposed tests apply to any trials that involve both binary and continuous outcomes for evaluating treatment effect.

An Evaluation of Statistical Methods for Analyzing Follow-Up Gaussian Laboratory Data with a Lower Quantification Limit

Laboratory data with a lower quantification limit (censored data) are sometimes analyzed by replacing non-quantifiable values with a single value equal to or less than the quantification limit, yielding possibly biased point estimates and variance estimates that are too small. Motivated by a three-period, three-treatment crossover study of a candidate vaginal microbicide in human immunodeficiency virus (HIV)-infected women, we consider four analysis methods for censored Gaussian data with a single follow-up measurement: nonparametric methods, mixed models, mixture models, and dichotomous measures of a treatment effect. We apply these methods to the crossover study data and use simulation to evaluate the statistical properties of these methods in analyzing the treatment effect in a two-treatment parallel-arm or crossover study with censored Gaussian data. Our simulated data and our mixed and mixture models consider treated follow-up data with the same variance as the baseline data or with an inflated variance. Mixed models have the correct type I error, the best power, the least biased Gaussian parameter treatment-effect estimates, and appropriate confidence interval coverage for these estimates. A crossover study analysis with a period effect can greatly increase the required study sample size. For both designs and both variance assumptions, published sample-size estimation methods do not yield a good estimate of the sample size to obtain the stated power.