Robert H Lyles

Emory University, Atlanta, Georgia, United States

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Publications (119)315.9 Total impact

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    ABSTRACT: Planned interventions and/or natural conditions often effect change on an ordinal categorical outcome (e.g., symptom severity). In such scenarios, it is sometimes desirable to assign a priori scores to observed changes in status, typically giving higher weight to changes of greater magnitude. We define change indices for such data based upon a multinomial model for each row of a c × c table, where the rows represent the baseline status categories. We distinguish an index designed to assess conditional changes within each baseline category from two others designed to capture overall change. One of these overall indices measures expected change across a target population. The other is scaled to capture the proportion of total possible change in the direction indicated by the data, so that it ranges from -1 (when all subjects finish in the least favorable category) to +1 (when all finish in the most favorable category). The conditional assessment of change can be informative regardless of how subjects are sampled into the baseline categories. In contrast, the overall indices become relevant when subjects are randomly sampled at baseline from the target population of interest, or when the investigator is able to make certain assumptions about the baseline status distribution in that population. We use a Dirichlet-multinomial model to obtain Bayesian credible intervals for the conditional change index that exhibit favorable small-sample frequentist properties. Simulation studies illustrate the methods, and we apply them to examples involving changes in ordinal responses for studies of sleep deprivation and activities of daily living. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.
    Statistics in Medicine 07/2015; DOI:10.1002/sim.6559 · 1.83 Impact Factor
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    ABSTRACT: Pooling biospecimens prior to performing lab assays can help reduce lab costs, preserve specimens, and reduce information loss when subject to a limit of detection. Because many biomarkers measured in epidemiological studies are positive and right-skewed, proper analysis of pooled specimens requires special methods. In this paper, we develop and compare parametric regression models for skewed outcome data subject to pooling, including a novel parameterization of the gamma distribution that takes full advantage of the gamma summation property. We also develop a Monte Carlo approximation of Akaike's Information Criterion applied to pooled data in order to guide model selection. Simulation studies and analysis of motivating data from the Collaborative Perinatal Project suggest that using Akaike's Information Criterion to select the best parametric model can help ensure valid inference and promote estimate precision. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.
    Statistics in Medicine 04/2015; 34(17). DOI:10.1002/sim.6496 · 1.83 Impact Factor
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    Toxicology 03/2015; DOI:10.1016/j.tox.2015.03.009 · 3.62 Impact Factor
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    ABSTRACT: Pooling specimens prior to performing laboratory assays has various benefits. Pooling can help to reduce cost, preserve irreplaceable specimens, meet minimal volume requirements for certain lab tests, and even reduce information loss when a limit of detection is present. Regardless of the motivation for pooling, appropriate analytical techniques must be applied in order to obtain valid inference from composite specimens. When biomarkers are treated as the outcome in a regression model, techniques applicable to individually measured specimens may not be valid when measurements are taken from pooled specimens, particularly when the biomarker is positive and right skewed. In this paper, we propose a novel semiparametric estimation method based on an adaptation of the quasi-likelihood approach that can be applied to a right-skewed outcome subject to pooling. We use simulation studies to compare this method with an existing estimation technique that provides valid estimates only when pools are formed from specimens with identical predictor values. Simulation results and analysis of a motivating example demonstrate that, when appropriate estimation techniques are applied to strategically formed pools, valid and efficient estimation of the regression coefficients can be achieved. © The Author 2015. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail:
    American Journal of Epidemiology 03/2015; 181(7). DOI:10.1093/aje/kwu301 · 5.23 Impact Factor
  • Ji Lin · Robert H Lyles
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    ABSTRACT: We explore the 'reassessment' design in a logistic regression setting, where a second wave of sampling is applied to recover a portion of the missing data on a binary exposure and/or outcome variable. We construct a joint likelihood function based on the original model of interest and a model for the missing data mechanism, with emphasis on non-ignorable missingness. The estimation is carried out by numerical maximization of the joint likelihood function with close approximation of the accompanying Hessian matrix, using sharable programs that take advantage of general optimization routines in standard software. We show how likelihood ratio tests can be used for model selection and how they facilitate direct hypothesis testing for whether missingness is at random. Examples and simulations are presented to demonstrate the performance of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.
    Statistics in Medicine 02/2015; 34(11). DOI:10.1002/sim.6456 · 1.83 Impact Factor
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    ABSTRACT: Misclassification is a long-standing statistical problem in epidemiology. In many real studies, either an exposure or a response variable or both may be misclassified. As such, potential threats to the validity of the analytic results (e.g., estimates of odds ratios) that stem from misclassification are widely discussed in the literature. Much of the discussion has been restricted to the nondifferential case, in which misclassification rates for a particular variable are assumed not to depend on other variables. However, complex differential misclassification patterns are common in practice, as we illustrate here using bacterial vaginosis and Trichomoniasis data from the HIV Epidemiology Research Study (HERS). Therefore, clear illustrations of valid and accessible methods that deal with complex misclassification are still in high demand. We formulate a maximum likelihood (ML) framework that allows flexible modeling of misclassification in both the response and a key binary exposure variable, while adjusting for other covariates via logistic regression. The approach emphasizes the use of internal validation data in order to evaluate the underlying misclassification mechanisms. Data-driven simulations show that the proposed ML analysis outperforms less flexible approaches that fail to appropriately account for complex misclassification patterns. The value and validity of the method are further demonstrated through a comprehensive analysis of the HERS example data. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.
    Statistics in Medicine 02/2015; 34(9). DOI:10.1002/sim.6440 · 1.83 Impact Factor
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    ABSTRACT: The potential for research involving biospecimens can be hindered by the prohibitive cost of performing laboratory assays on individual samples. To mitigate this cost, strategies such as randomly selecting a portion of specimens for analysis or randomly pooling specimens prior to performing laboratory assays may be employed. These techniques, while effective in reducing cost, are often accompanied by a considerable loss of statistical efficiency. We propose a novel pooling strategy based on the k-means clustering algorithm to reduce laboratory costs while maintaining a high level of statistical efficiency when predictor variables are measured on all subjects, but the outcome of interest is assessed in pools. We perform simulations motivated by the BioCycle study to compare this k-means pooling strategy with current pooling and selection techniques under simple and multiple linear regression models. While all of the methods considered produce unbiased estimates and confidence intervals with appropriate coverage, pooling under k-means clustering provides the most precise estimates, closely approximating results from the full data and losing minimal precision as the total number of pools decreases. The benefits of k-means clustering evident in the simulation study are then applied to an analysis of the BioCycle dataset. In conclusion, when the number of lab tests is limited by budget, pooling specimens based on k-means clustering prior to performing lab assays can be an effective way to save money with minimal information loss in a regression setting. Copyright © 2014 John Wiley & Sons, Ltd.
    Statistics in Medicine 12/2014; 33(28). DOI:10.1002/sim.6305 · 1.83 Impact Factor
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    ABSTRACT: Chronic kidney disease (CKD) is characterized by overactivation of the sympathetic nervous system (SNS) that contributes to cardiovascular risk. Decreased nitric oxide (NO) bioavailability is a major factor contributing to SNS overactivity in CKD, since reduced neuronal NO leads to increased central SNS activity. Tetrahydrobiopterin (BH4) is an essential cofactor for nitric oxide synthase that increases NO bioavailability in experimental models of CKD. We conducted a randomized, double-blinded, placebo-controlled trial testing the benefits of oral sapropterin (6R-BH4, a synthetic form of BH4) in CKD. 36 patients with CKD and hypertension were randomized to 12 weeks of: 1) 200mg 6R-BH4 twice daily + 1mg folic acid once daily; versus 2) placebo + folic acid. The primary endpoint was change in resting muscle sympathetic nerve activity (MSNA). Secondary endpoints included arterial stiffness using pulse wave velocity (PWV) and augmentation index (AIx), endothelial function using brachial artery flow-mediated dilatation and endothelial progenitor cells, endothelium independent vasodilatation (EID), microalbuminuria, and blood pressure. We observed a significant reduction in MSNA after 12 weeks of 6R-BH4 (-7.5±2.1 bursts/min vs. +3.2±1.3 bursts/min, p=0.003). We also observed a significant improvement in AIx (by -5.8±2.0% vs. +1.8±1.7 in placebo group, p=0.007). EID increased significantly (by +2.0±0.59%, p=0.004) amongst the 6R-BH4 group, but there was no change in endothelial function. There was a trend towards a reduction in diastolic blood pressure by -4±3 mm Hg at 12 weeks with 6R-BH4 (p=0.055). 6R-BH4 treatment may have beneficial effects on SNS activity and central pulse wave reflections in hypertensive patients with CKD. Copyright © 2014, American Journal of Physiology - Regulatory, Integrative and Comparative Physiology.
    AJP Regulatory Integrative and Comparative Physiology 12/2014; 308(3):ajpregu.00409.2014. DOI:10.1152/ajpregu.00409.2014 · 3.11 Impact Factor
  • Li Tang · Robert H. Lyles · Caroline C. King · Joseph W. Hogan · Yungtai Lo
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    ABSTRACT: In many epidemiological and clinical studies, misclassification may arise in one or several variables, resulting in potentially invalid analytic results (e.g. estimates of odds ratios of interest) when no correction is made. Here we consider the situation in which correlated binary response variables are subject to misclassification. Building on prior work, we provide an approach to adjust for potentially complex differential misclassification via internal validation sampling applied at multiple study time points. We seek to estimate the parameters of a primary generalized linear mixed model that accounts for baseline and/or time-dependent covariates. The misclassification process is modelled via a second generalized linear model that captures variations in sensitivity and specificity parameters according to time and a set of subject-specific covariates that may or may not overlap with those in the primary model. Simulation studies demonstrate the precision and validity of the method proposed. An application is presented based on longitudinal assessments of bacterial vaginosis conducted in the ‘HIV epidemiology research’ study.
    Journal of the Royal Statistical Society Series C Applied Statistics 10/2014; 64(3). DOI:10.1111/rssc.12081 · 1.49 Impact Factor
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    ABSTRACT: Objectives: Robotic sacrocolpopexy has been rapidly incorporated into surgical practice without comprehensive and systematically published outcome data. The aim of this study was to systematically review the currently published peer-reviewed literature on robotic-assisted laparoscopic sacrocolpopexy with more than 6 months of anatomic outcome data. Methods: Studies were selected after applying predetermined inclusion and exclusion criteria to a MEDLINE search. Two independent reviewers blinded to each other's results abstracted demographic data, perioperative information, and postoperative outcomes. The primary outcome assessed was anatomic success rate defined as less than or equal to pelvic organ prolapse quantification system (POP-Q) stage 1. A random effects model was performed for the meta-analysis of selected outcomes. Results: Thirteen studies were selected for the systematic review. Meta-analysis yielded a combined estimated success rate of 98.6% (95% confidence interval, 97.0%-100%). The combined estimated rate of mesh exposure/erosion was 4.1% (95% confidence interval, 1.4%-6.9%), and the rate of reoperation for mesh revision was 1.7%. The rates of reoperation for recurrent apical and nonapical prolapse were 0.8% and 2.5%, respectively. The most common surgical complication (excluding mesh erosion) was cystotomy (2.8%), followed by wound infection (2.4%). Conclusions: The outcomes of this analysis indicate that robotic sacrocolpopexy is an effective surgical treatment of apical prolapse with high anatomic cure rate and low rate of complications.
    09/2014; 20(5):252-260. DOI:10.1097/SPV.0000000000000070
  • Jeanie Park · Robert H Lyles · Susan Bauer-Wu
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    ABSTRACT: Mindfulness meditation (MM) is a stress-reduction technique that may have real biological effects on hemodynamics, but has never previously been tested in chronic kidney disease (CKD). In addition, the mechanisms underlying the potential BP-lowering effects of MM are unknown. We sought to determine if MM acutely lowers BP in CKD patients, and if these hemodynamic changes are mediated by a reduction in sympathetic nerve activity. In 15 hypertensive African-American (AA) males with CKD, we conducted a randomized, crossover study in which participants underwent 14 minutes of MM, or 14 minutes of BP education (control intervention) during 2 separate random-order study visits. Muscle sympathetic nerve activity (MSNA), beat-to-beat arterial BP, heart rate (HR), and respiratory rate (RR) were continuously measured at baseline, and during each intervention. A subset had a third study visit to undergo controlled breathing (CB), to determine if a reduction in RR alone was sufficient in exacting hemodynamic changes. We observed a significantly greater reduction in systolic BP, diastolic BP, mean arterial pressure, HR, as well as MSNA, during MM compared to the control intervention. Participants had a significantly lower RR during MM; however, in contrast to MM, CB alone did not reduce BP, HR, or MSNA. MM acutely lowers BP and HR in AA males with hypertensive CKD, and these hemodynamic effects may be mediated by a reduction in sympathetic nerve activity. RR is significantly lower during MM, but CB alone without concomitant meditation does not acutely alter hemodynamics or sympathetic activity in CKD.
    AJP Regulatory Integrative and Comparative Physiology 05/2014; 307(1). DOI:10.1152/ajpregu.00558.2013 · 3.11 Impact Factor
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    ABSTRACT: Epidemiological studies involving biomarkers are often hindered by prohibitively expensive laboratory tests. Strategically pooling specimens prior to performing these lab assays has been shown to effectively reduce cost with minimal information loss in a logistic regression setting. When the goal is to perform regression with a continuous biomarker as the outcome, regression analysis of pooled specimens may not be straightforward, particularly if the outcome is right-skewed. In such cases, we demonstrate that a slight modification of a standard multiple linear regression model for poolwise data can provide valid and precise coefficient estimates when pools are formed by combining biospecimens from subjects with identical covariate values. When these x-homogeneous pools cannot be formed, we propose a Monte Carlo expectation maximization (MCEM) algorithm to compute maximum likelihood estimates (MLEs). Simulation studies demonstrate that these analytical methods provide essentially unbiased estimates of coefficient parameters as well as their standard errors when appropriate assumptions are met. Furthermore, we show how one can utilize the fully observed covariate data to inform the pooling strategy, yielding a high level of statistical efficiency at a fraction of the total lab cost.
    Biometrics 02/2014; 70(1). DOI:10.1111/biom.12134 · 1.57 Impact Factor
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    ABSTRACT: Population sexual mixing patterns can be quantified using Newman's assortativity coefficient (r). Suggested methods for estimating the SE for r may lead to inappropriate statistical conclusions in situations where intracluster correlation is ignored and/or when cluster size is predictive of the response. We describe a computer-intensive, but highly accessible, within-cluster resampling approach for providing a valid large-sample estimated SE for r and an associated 95% CI. We introduce needed statistical notation and describe the within-cluster resampling approach. Sexual network data and a simulation study were employed to compare within-cluster resampling with standard methods when cluster size is informative. For the analysis of network data when cluster size is informative, the simulation study demonstrates that within-cluster resampling produces valid statistical inferences about Newman's assortativity coefficient, a popular statistic used to quantify the strength of mixing patterns. In contrast, commonly used methods are biased with attendant extremely poor CI coverage. Within-cluster resampling is recommended when cluster size is informative and/or when there is within-cluster response correlation. Within-cluster resampling is recommended for providing valid statistical inferences when applying Newman's assortativity coefficient r to network data.
    Sexually transmitted infections 01/2014; 90(4). DOI:10.1136/sextrans-2013-051282 · 3.40 Impact Factor
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    ABSTRACT: Background: Population-level mixing patterns can be quantified using Newman's assortativity coefficient r. Suggested methods for estimating the standard error for r may lead to inappropriate statistical conclusions in situations where intra-cluster correlation is ignored and/or when cluster size is predictive of the response. Methods: We describe a computer-intensive within-cluster resampling approach for providing a valid large-sample estimated standard error for r and an associated 95% confidence interval. Network data and a simulation model were employed to compare within-cluster resampling to standard methods when cluster size is informative. Results: For the analysis of network data, when cluster size is informative, simulations studies demonstrate that within-cluster resampling produces valid statistical inferences about Newman's assortativity coefficient, a popular statistic used to quantify the strength of mixing patterns. In contrast, commonly used methods are biased with attendant extremely poor confidence interval coverage. Within-cluster resampling is recommended when cluster size is informative and/or when there is within-cluster response correlation. Conclusions: Within-cluster resampling is recommended for providing valid statistical inferences when applying Newman's assortativity coefficient r to network data.
    141st APHA Annual Meeting and Exposition 2013; 11/2013
  • Li Tang · Robert H. Lyles · Ye Ye · Yungtai Lo · Caroline C. King
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    ABSTRACT: The problem of misclassification is common in epidemiological and clinical research. In some cases, misclassification may be incurred when measuring both exposure and outcome variables. It is well known that validity of analytic results (e.g. point and confidence interval estimates for odds ratios of interest) can be forfeited when no correction effort is made. Therefore, valid and accessible methods with which to deal with these issues remain in high demand. Here, we elucidate extensions of well-studied methods in order to facilitate misclassification adjustment when a binary outcome and binary exposure variable are both subject to misclassification. By formulating generalizations of assumptions underlying well-studied “matrix” and “inverse matrix” methods into the framework of maximum likelihood, our approach allows the flexible modeling of a richer set of misclassification mechanisms when adequate internal validation data are available. The value of our extensions and a strong case for the internal validation design are demonstrated by means of simulations and analysis of bacterial vaginosis and trichomoniasis data from the HIV Epidemiology Research Study.
    09/2013; Volume 2(Issue 1):49–66. DOI:10.1515/em-2013-0008
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    ABSTRACT: Amyotrophic lateral sclerosis is a disease with highly variable clinical features and prognosis. We analyzed the prognostic indicators of age, sex, bulbar or spinal onset, body mass index (BMI), and forced vital capacity (FVC) for 728 deceased patients from the Emory ALS Clinic. The median overall survival was 29.8 months from symptom onset, 15.8 months from diagnosis, and 14.3 months from the initial clinic visit. While univariate analyses revealed that each of the identified clinical features was strongly associated with patient survival, in multivariable analyses only age, BMI, and FVC measured at the first clinic visit were independent prognostic indicators; bulbar onset and sex were not significantly associated with survival prognosis after adjustment for the other clinical features.
    Neurology: Clinical Practice (Print) 08/2013; 3(4):313-320. DOI:10.1212/CPJ.0b013e3182a1b8ab
  • Robert H Lyles · Lawrence L Kupper
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    ABSTRACT: A common goal in environmental epidemiologic studies is to undertake logistic regression modeling to associate a continuous measure of exposure with binary disease status, adjusting for covariates. A frequent complication is that exposure may only be measurable indirectly, through a collection of subject-specific variables assumed associated with it. Motivated by a specific study to investigate the association between lung function and exposure to metal working fluids, we focus on a multiplicative-lognormal structural measurement error scenario and approaches to address it when external validation data are available. Conceptually, we emphasize the case in which true untransformed exposure is of interest in modeling disease status, but measurement error is additive on the log scale and thus multiplicative on the raw scale. Methodologically, we favor a pseudo-likelihood (PL) approach that exhibits fewer computational problems than direct full maximum likelihood (ML) yet maintains consistency under the assumed models without necessitating small exposure effects and/or small measurement error assumptions. Such assumptions are required by computationally convenient alternative methods like regression calibration (RC) and ML based on probit approximations. We summarize simulations demonstrating considerable potential for bias in the latter two approaches, while supporting the use of PL across a variety of scenarios. We also provide accessible strategies for obtaining adjusted standard errors to accompany RC and PL estimates.
    Journal of Agricultural Biological and Environmental Statistics 03/2013; 18(1):22-38. DOI:10.1007/s13253-012-0115-9 · 0.91 Impact Factor
  • Robert H Lyles · Ying Guo · Sander Greenland
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    ABSTRACT: Ratio estimators of effect are ordinarily obtained by exponentiating maximum-likelihood estimators (MLEs) of log-linear or logistic regression coefficients. These estimators can display marked positive finite-sample bias, however. We propose a simple correction that removes a substantial portion of the bias due to exponentiation. By combining this correction with bias correction on the log scale, we demonstrate that one achieves complete removal of second-order bias in odds ratio estimators in important special cases. We show how this approach extends to address bias in odds or risk ratio estimators in many common regression settings. We also propose a class of estimators that provide reduced mean bias and squared error, while allowing the investigator to control the risk of underestimating the true ratio parameter. We present simulation studies in which the proposed estimators are shown to exhibit considerable reduction in bias, variance, and mean squared error compared to MLEs. Bootstrapping provides further improvement, including narrower confidence intervals without sacrificing coverage.
    Journal of Statistical Planning and Inference 12/2012; 142(12):3235-3241. DOI:10.1016/j.jspi.2012.05.005 · 0.68 Impact Factor
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    ABSTRACT: Mixture risk assessment is often hampered by the lack of dose response information on the mixture being assessed, forcing reliance on component formulas such as dose addition. We present a four step approach for evaluating chemical mixture data for consistency with dose addition for use in supporting a component based mixture risk assessment. Following the concepts in the U.S. EPA mixture risk guidance (EPA 2000), toxicological interaction for a defined mixture (all components known) is departure from a clearly articulated definition of component additivity. For the common approach of dose additivity, the EPA guidance identifies three desirable characteristics, foremost of which is that the component chemicals are toxicologically similar. The other two characteristics are empirical: the mixture components have toxic potencies that are fixed proportions of each other (throughout the dose range of interest), and the mixture dose term in the dose additive prediction formula, which we call the combined prediction model (CPM), can be represented by a linear combination of the component doses. A consequent property of the proportional toxic potencies is that the component chemicals must share a common dose response model, where only the dose coefficients depend on the chemical components. A further consequence is that the mixture data must be described by the same mathematical function ("mixture model") as the components, but with a distinct coefficient for the total mixture dose. The mixture response is predicted from the component dose response curves by using the dose additive CPM and the prediction is then compared with the observed mixture results. The four steps are to evaluate: 1) toxic proportionality by determining how well the CPM matches the single chemical models regarding mean and variance; 2) fit of the mixture model to the mixture data; 3) agreement between the mixture data and the CPM prediction; and 4) consistency between the CPM and the mixture model. Because there are four evaluations instead of one, some involving many parameters or dose groups, there are more opportunities to reject statistical hypotheses about dose addition, thus statistical adjustment for multiple comparisons is necessary. These four steps contribute different pieces of information about the consistency of the component and mixture data with the two empirical characteristics of dose additivity. We examine this four step approach in how it can show empirical support for dose addition as a predictor for an untested mixture in a screening level risk assessment. The decision whether to apply dose addition should be based on all four of those evidentiary pieces as well as toxicological understanding of these chemicals and should include interpretations of the numerical and toxicological issues that arise during the evaluation. This approach is demonstrated with neurotoxicity data on carbamate mixtures.
    Toxicology 11/2012; 313(2-3). DOI:10.1016/j.tox.2012.10.016 · 3.62 Impact Factor
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    ABSTRACT: Pooling-based strategies that combine samples from multiple participants for laboratory assays have been proposed for epidemiologic investigations of biomarkers to address issues including cost, efficiency, detection, and when minimal sample volume is available. A modification of the standard logistic regression model has been previously described to allow use with pooled data; however, this model makes assumptions regarding exposure distribution and logit-linearity of risk (i.e., constant odds ratio) that can be violated in practice. We were motivated by a nested case-control study of miscarriage and inflammatory factors with highly skewed distributions to develop a more flexible model for analysis of pooled data. Using characteristics of the gamma distribution and the relation between models of binary outcome conditional on exposure and of exposure conditional on outcome, we use a modified logistic regression to accommodate nonlinearity because of unequal shape parameters in gamma distributed exposure for cases and controls. Using simulations, we compare our approach with existing methods for logistic regression for pooled data considering: (1) constant and dose-dependent effects; (2) gamma and log-normal distributed exposure; (3) effect size; and (4) the proportions of biospecimens pooled. We show that our approach allows estimation of odds ratios that vary with exposure level, yet has minimal loss of efficiency compared with existing approaches when exposure effects are dose-invariant. Our model performed similarly to a maximum likelihood estimation approach in terms of bias and efficiency, and provides an easily implemented approach for estimation with pooled biomarker data when effects may not be constant across exposure. Copyright © 2012 John Wiley & Sons, Ltd.
    Statistics in Medicine 09/2012; 31(22):2461-72. DOI:10.1002/sim.5351 · 1.83 Impact Factor

Publication Stats

3k Citations
315.90 Total Impact Points


  • 1999–2015
    • Emory University
      • • Department of Biostatistics and Bioinformatics
      • • Department of Pathology and Laboratory Medicine
      • • Division of Cardiology
      • • School of Medicine
      Atlanta, Georgia, United States
    • Johns Hopkins Bloomberg School of Public Health
      • Department of Epidemiology
      Baltimore, Maryland, United States
    • University of Pittsburgh
      Pittsburgh, Pennsylvania, United States
  • 2010
    • Cedars-Sinai Medical Center
      • Cedars Sinai Medical Center
      Los Angeles, CA, United States
  • 2006
    • Georgia Department of Public Health
      Marietta, Georgia, United States
  • 1997–2000
    • Johns Hopkins University
      • • Department of Molecular Microbiology and Immunology
      • • Department of Neurology
      • • Department of Epidemiology
      Baltimore, Maryland, United States
  • 1995–1996
    • University of North Carolina at Chapel Hill
      • Department of Biostatistics
      Chapel Hill, NC, United States