Lei Nie

Estimating the odds ratio when exposure has a limit of detection

BACKGROUNDnIn epidemiologic research, little emphasis has been placed on methods to account for left-hand censoring of exposures due to a limit of detection (LOD).nnnMETHODSnWe calculate the odds of anti-HIV therapy naiveté in 45 HIV-infected men as a function of measured log(10) plasma HIV RNA viral load using five approaches including ad hoc methods as well as a maximum likelihood estimate (MLE). We also generated simulations of a binary outcome with 10% incidence and a 1.5-fold increased odds per log increase in a log-normally distributed exposure with 25, 50 and 75% of exposure data below LOD. Simulated data were analysed using the same five methods, as well as the full data.nnnRESULTSnIn the example, the estimated odds ratio (OR) varied by 1.22-fold across methods, from 1.45 to 1.77 per log(10) copies of viral load and the standard error for the log OR varied by 1.52-fold across methods, from 0.31 to 0.47. In the simulations, use of full data or the MLE was unbiased with appropriate confidence interval (CI) coverage. However, as the proportion of exposure below LOD increased, substituting LOD, LOD/ radical 2 or LOD/2 was increasingly biased with increasingly inappropriate CI coverage. Finally, exclusion of values below LOD was unbiased but imprecise.nnnCONCLUSIONSnIn this example and the settings explored by simulation, and among methods readily available to investigators (i.e. sans full data), the MLE provided an unbiased and appropriately precise estimate of the exposure-outcome OR.

Meta-analysis of diagnostic accuracy studies accounting for disease prevalence: alternative parameterizations and model selection.

In a meta-analysis of diagnostic accuracy studies, the sensitivities and specificities of a diagnostic test may depend on the disease prevalence since the severity and definition of disease may differ from study to study due to the design and the population considered. In this paper, we extend the bivariate nonlinear random effects model on sensitivities and specificities to jointly model the disease prevalence, sensitivities and specificities using trivariate nonlinear random-effects models. Furthermore, as an alternative parameterization, we also propose jointly modeling the test prevalence and the predictive values, which reflect the clinical utility of a diagnostic test. These models allow investigators to study the complex relationship among the disease prevalence, sensitivities and specificities; or among test prevalence and the predictive values, which can reveal hidden information about test performance. We illustrate the proposed two approaches by reanalyzing the data from a meta-analysis of radiological evaluation of lymph node metastases in patients with cervical cancer and a simulation study. The latter illustrates the importance of carefully choosing an appropriate normality assumption for the disease prevalence, sensitivities and specificities, or the test prevalence and the predictive values. In practice, it is recommended to use model selection techniques to identify a best-fitting model for making statistical inference. In summary, the proposed trivariate random effects models are novel and can be very useful in practice for meta-analysis of diagnostic accuracy studies.

Network Meta-analysis of Randomized Clinical Trials: Reporting the Proper Summaries

Background In the absence of sufficient data directly comparing multiple treatments, indirect comparisons using network meta-analyses (NMAs) can provide useful information. Under current contrast-based (CB) methods for binary outcomes, the patient-centered measures including the treatment-specific event rates and risk differences (RDs) are not provided, which may create some unnecessary obstacles for patients to comprehensively trade-off efficacy and safety measures. Purpose We aim to develop NMA to accurately estimate the treatment-specific event rates. Methods A Bayesian hierarchical model is developed to illustrate how treatment-specific event rates, RDs, and risk ratios (RRs) can be estimated. We first compare our approach to alternative methods using two hypothetical NMAs assuming a fixed RR or RD, and then use two published NMAs to illustrate the improved reporting. Results In the hypothetical NMAs, our approach outperforms current CB NMA methods in terms of bias. In the two published NMAs, noticeable differences are observed in the magnitude of relative treatment effects and several pairwise statistical significance tests from previous report. Limitations First, to facilitate the estimation, each study is assumed to hypothetically compare all treatments, with unstudied arms being missing at random. It is plausible that investigators may have selected treatment arms on purpose based on the results of previous trials, which may lead to ‘nonignorable missingness’ and potentially bias our estimates. Second, we have not considered methods to identify and account for potential inconsistency between direct and indirect comparisons. Conclusions The proposed NMA method can accurately estimate treatment-specific event rates, RDs, and RRs and is recommended.

Linear regression with an independent variable subject to a detection limit.

Background: Linear regression with a left-censored independent variable X due to limit of detection (LOD) was recently considered by 2 groups of researchers: Richardson and Ciampi (Am J Epidemiol. 2003;157:355-363), and Schisterman et al (Am J Epidemiol. 2006;163:374-383). Methods: Both groups obtained consistent estimators for the regression slopes by replacing left-censored X with a constant, that is, the expectation of X given X below LOD E(X|X<LOD) in the former group and the sample mean of X given X above LOD in the latter. Results: Schisterman et al argued that their approach would be a better choice because the sample mean of X given X above LOD is available, whereas E(X|X<LOD) is unknown. Other substitution methods, such as replacing the left-censored values with LOD, or LOD/2,have been extensively used in the literature. Simulations were conducted to compare the performance under 2 scenarios in which the independent variable is normally and not normally distributed. Conclusion: Recommendations are given based on theoretical and simulation results. These recommendations are illustrated with one case study.

U.S. Food and Drug Administration Approval: Obinutuzumab in Combination with Chlorambucil for the Treatment of Previously Untreated Chronic Lymphocytic Leukemia

On November 1, 2013, the U.S. Food and Drug Administration (FDA) approved obinutuzumab (GAZYVA; Genentech, Inc.), a CD20-directed cytolytic antibody, for use in combination with chlorambucil for the treatment of patients with previously untreated chronic lymphocytic leukemia (CLL). In stage 1 of the trial supporting approval, patients with previously untreated CD20-positive CLL were randomly allocated (2:2:1) to obinutuzumab + chlorambucil (GClb, n = 238), rituximab + chlorambucil (RClb, n = 233), or chlorambucil alone (Clb, n = 118). The primary endpoint was progression-free survival (PFS), and secondary endpoints included overall response rate (ORR). Only the comparison of GClb to Clb was relevant to this approval and is described herein. A clinically meaningful and statistically significant improvement in PFS with medians of 23.0 and 11.1 months was observed in the GClb and Clb arms, respectively (HR, 0.16; 95% CI, 0.11–0.24; P < 0.0001, log-rank test). The ORRs were 75.9% and 32.1% in the GClb and Clb arms, respectively, and the complete response rates were 27.8% and 0.9% in the GClb and Clb arms, respectively. The most common adverse reactions (≥10%) reported in the GClb arm were infusion reactions, neutropenia, thrombocytopenia, anemia, pyrexia, cough, and musculoskeletal disorders. Obinutuzumab was the first Breakthrough Therapy–designated drug to receive FDA approval. Clin Cancer Res; 20(15); 3902–7. ©2014 AACR.

Statistical methods for multivariate meta-analysis of diagnostic tests: An overview and tutorial

In this article, we present an overview and tutorial of statistical methods for meta-analysis of diagnostic tests under two scenarios: (1) when the reference test can be considered a gold standard and (2) when the reference test cannot be considered a gold standard. In the first scenario, we first review the conventional summary receiver operating characteristics approach and a bivariate approach using linear mixed models. Both approaches require direct calculations of study-specific sensitivities and specificities. We next discuss the hierarchical summary receiver operating characteristics curve approach for jointly modeling positivity criteria and accuracy parameters, and the bivariate generalized linear mixed models for jointly modeling sensitivities and specificities. We further discuss the trivariate generalized linear mixed models for jointly modeling prevalence, sensitivities and specificities, which allows us to assess the correlations among the three parameters. These approaches are based on the exact binomial distribution and thus do not require an ad hoc continuity correction. Lastly, we discuss a latent class random effects model for meta-analysis of diagnostic tests when the reference test itself is imperfect for the second scenario. A number of case studies with detailed annotated SAS code in MIXED and NLMIXED procedures are presented to facilitate the implementation of these approaches.

Bivariate random effects models for meta-analysis of comparative studies with binary outcomes: Methods for the absolute risk difference and relative risk

Multivariate meta-analysis is increasingly utilised in biomedical research to combine data of multiple comparative clinical studies for evaluating drug efficacy and safety profile. When the probability of the event of interest is rare, or when the individual study sample sizes are small, a substantial proportion of studies may not have any event of interest. Conventional meta-analysis methods either exclude such studies or include them through ad hoc continuality correction by adding an arbitrary positive value to each cell of the corresponding 2u2009×u20092 tables, which may result in less accurate conclusions. Furthermore, different continuity corrections may result in inconsistent conclusions. In this article, we discuss a bivariate Beta-binomial model derived from Sarmanov family of bivariate distributions and a bivariate generalised linear mixed effects model for binary clustered data to make valid inferences. These bivariate random effects models use all available data without ad hoc continuity corrections, and accounts for the potential correlation between treatment (or exposure) and control groups within studies naturally. We then utilise the bivariate random effects models to reanalyse two recent meta-analysis data sets.

Rendering the 3 + 3 Design to Rest: More Efficient Approaches to Oncology Dose-Finding Trials in the Era of Targeted Therapy

Selection of the maximum tolerated dose (MTD) as the recommended dose for registration trials based on a dose-escalation trial using variations of an MTD/3 + 3 design often occurs in the development of oncology products. The MTD/3 + 3 approach is not optimal and may result in recommended doses that are unacceptably toxic for many patients and in dose reduction/interruptions that might have an impact on effectiveness. Instead of the MTD/3 + 3 approach, the authors recommend an integrated approach. In this approach, typically an adaptive/Bayesian model provides a general framework to incorporate and make decisions for dose escalation based on nonclinical data, such as animal efficacy and toxicity data; clinical data, including pharmacokinetics/pharmacodynamics data; and dose/exposure–response data for efficacy and safety. To improve dose-ranging trials, model-based estimation, rather than hypothesis testing, should be used to maximize and integrate the information gathered across trials and doses. This approach may improve identification of optimal recommended doses, which can then be confirmed in registration trials. Clin Cancer Res; 22(11); 2623–9. ©2016 AACR. See all articles in this CCR Focus section, “New Approaches for Optimizing Dosing of Anticancer Agents.”

Estimating the relative excess risk due to interaction: a bayesian approach.

The relative excess odds or risk due to interaction (ie, RERIOR and RERI) play an important role in epidemiologic data analysis and interpretation. Previous authors have advocated frequentist approaches based on nonparametric bootstrap, the method of variance estimates recovery, and profile likelihood for estimating confidence intervals. As an alternative, we propose a Bayesian approach that accounts for parameter constraints and estimates the RERIOR in a case-control study from a linear additive odds-ratio model, or the RERI in a cohort study from a linear additive risk-ratio model. We show that Bayesian credible intervals can often be obtained more easily than frequentist confidence intervals. Furthermore, the Bayesian approach can be easily extended to adjust for confounders. Because posterior computation with inequality constraints can be accomplished easily using free software, the proposed Bayesian approaches may be useful in practice.

Relative excess risk due to interaction: resampling-based confidence intervals.

Relative excess risk due to interaction (RERI) has been used to quantify the joint effects of 2 exposures in epidemiology. However, the construction of confidence intervals (CIs) for RERI is complicated by sparse cells. Assuming that the data contain no zero cells, here we propose constructing CIs for RERI using nonparametric and parametric bootstrap methods with a continuity correction, and compare these proposed methods to existing methods using 3 empirical examples and Monte Carlo simulations. Our results show that, when cell counts are not sparse, CIs resulting from the explored bootstrap methods are generally acceptable in terms of CI coverage and length, although computationally more demanding than existing methods. However, when cell counts are sparse, the proposed bootstrap methods using a continuity correction outperform existing methods and continue to provide acceptable CIs. The continuity correction is needed for the explored bootstrap methods to provide acceptable CIs because resampled data sets may contain zero cells even when the observed data do not.