Jeremy M G Taylor

University of Michigan, Ann Arbor, Michigan, United States

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Publications (248)982.53 Total impact

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    ABSTRACT: Background: As cancer progresses, methylation patterns change to promote the tumorigenic phenotype. However, stability of methylation markers over time and the extent that biopsy samples are representative of larger tumor specimens are unknown. This information is critical for clinical use of such biomarkers. Methods: Ninety-eight patients with tumor specimens from 2 timepoints were measured for DNA methylation in the promoter regions across 4 genes. Results: There were no significant differences in overall methylation of CCNA1 (cyclin A1), NDN (necdin), deleted in colorectal carcinoma (DCC), and cluster of differentiation 1a (CD1A) within paired specimens (p values = .56, .17, .66, and .58, respectively). All genes showed strong correlations between paired specimens across time. Methylation was most consistent for CCNA1 and NDN over time. Conclusion: This report provides the first evidence that methylation markers measured in biopsy samples are representative of gene methylation in later specimens and suggests that biopsy markers could be representative biomarkers for use in defining personalized treatment utilizing epigenetic changes. © 2015 Wiley Periodicals, Head Neck, 2015.
    Head & Neck 11/2015; DOI:10.1002/hed.24223 · 2.64 Impact Factor
  • Laura L. Fernandes · Susan Murray · Jeremy M. G. Taylor ·
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    ABSTRACT: In addition to getting a preliminary assessment of efficacy, phase II trials can also help to determine dose(s) that have an acceptable toxicity profile over repeated cycles as well as identify subgroups with particularly poor toxicity profiles. Correct modeling of the dose-toxicity relationship in patients receiving multiple cycles of the same dose in oncology trials is crucial. A major challenge lies in taking advantage of the conditional nature of data collection, that is each cycle is observed conditional on having no previous toxicities on earlier cycles. We develop a novel and parsimonious model for the probability of toxicity during a kth cycle of therapy, conditional on not seeing toxicity in any of the k-1 previous cycles using a Markov model, hereafter we refer to these probabilities as conditional probabilities of toxicity. Our model allows the conditional probability of toxicity to depend on randomized dose group, cumulative dose from prior cycles, a measure of how consistently a patient responds to the same dose exposure and individual risk factors influencing the ability to tolerate the treatment regimen. Simulations studying finite sample properties of the model are given. Finally, the approach is demonstrated in a phase II trial studying two dose levels of ifosfamide plus doxorubicin and granulocyte colony-stimulating factor in soft tissue sarcoma patients over four cycles. The Markov model provides correct estimates of the probabilities of toxicity in finite sample simulations. It also correctly models the data from the phase II clinical trial, and identifies particularly high cumulative toxicity in females. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    Biometrical Journal 08/2015; DOI:10.1002/bimj.201400047 · 0.95 Impact Factor
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    Niko A Kaciroti · Trivellore E Raghunathan · Jeremy M G Taylor · Stevo Julius ·

  • Laura L Fernandes · Jeremy M G Taylor · Susan Murray ·
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    ABSTRACT: Many phase I trials in oncology involve multiple dose administrations on the same patient over multiple cycles, with a typical cycle lasting three weeks and having about six cycles per patient with a goal to find the maximum tolerated dose (MTD) and study the dose-toxicity relationship. A patient's dose is unchanged over the cycles and the data is reduced to a binary end point, the occurrence of a toxicity and analyzed either by considering the toxicity from the first dose or from any cycle on the study. In this paper an alternative approach allowing an assessment of toxicity from each cycle and dose variations for patient over cycles is presented. A Markov model for the conditional probability of toxicity on any cycle given no toxicity in previous cycles is formulated as a function of the current and previous doses. The extra information from each cycle provides more precise estimation of the dose-toxicity relationship. Simulation results demonstrating gains in using the Markov model as compared to analyses of a single binary outcome are presented. Methods for utilizing the Markov model to conduct a phase I study, including choices for selecting doses for the next cycle for each patient, are developed and presented via simulation.
    Journal of Biopharmaceutical Statistics 06/2015; DOI:10.1080/10543406.2015.1052492 · 0.59 Impact Factor
  • Philip S. Boonstra · Jeremy M. G. Taylor · Bhramar Mukherjee ·
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    ABSTRACT: We propose an extension of the expectation-maximization (EM) algorithm, called the hyperpenalized EM (HEM) algorithm, that maximizes a penalized log-likelihood, for which some data are missing or unavailable, using a data-adaptive estimate of the penalty parameter. This is potentially useful in applications for which the analyst is unable or unwilling to choose a single value of a penalty parameter but instead can posit a plausible range of values. The HEM algorithm is conceptually straightforward and also very effective, and we demonstrate its utility in the analysis of a genomic data set. Gene expression measurements and clinical covariates were used to predict survival time. However, many survival times are censored, and some observations only contain expression measurements derived from a different assay, which together constitute a difficult missing data problem. It is desired to shrink the genomic contribution in a data-adaptive way. The HEM algorithm successfully handles both the missing data and shrinkage aspects of the problem.
    Statistics in Biosciences 06/2015; 7(2). DOI:10.1007/s12561-015-9132-x
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    Niko A Kaciroti · Trivellore E Raghunathan · Jeremy M G Taylor · Stevo Julius ·

  • Chiu‐Hsieh Hsu · Jeremy M. G. Taylor · Chengcheng Hu ·
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    ABSTRACT: We consider the situation of estimating the marginal survival distribution from censored data subject to dependent censoring using auxiliary variables. We had previously developed a nonparametric multiple imputation approach. The method used two working proportional hazards (PH) models, one for the event times and the other for the censoring times, to define a nearest neighbor imputing risk set. This risk set was then used to impute failure times for censored observations. Here, we adapt the method to the situation where the event and censoring times follow accelerated failure time models and propose to use the Buckley-James estimator as the two working models. Besides studying the performances of the proposed method, we also compare the proposed method with two popular methods for handling dependent censoring through the use of auxiliary variables, inverse probability of censoring weighted and parametric multiple imputation methods, to shed light on the use of them. In a simulation study with time-independent auxiliary variables, we show that all approaches can reduce bias due to dependent censoring. The proposed method is robust to misspecification of either one of the two working models and their link function. This indicates that a working proportional hazards model is preferred because it is more cumbersome to fit an accelerated failure time model. In contrast, the inverse probability of censoring weighted method is not robust to misspecification of the link function of the censoring time model. The parametric imputation methods rely on the specification of the event time model. The approaches are applied to a prostate cancer dataset. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.
    Statistics in Medicine 05/2015; 34(19). DOI:10.1002/sim.6534 · 1.83 Impact Factor
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    ABSTRACT: Dynamic prediction models make use of patient-specific longitudinal data to update individualized survival probability predictions based on current and past information. Colonoscopy (COL) and fecal occult blood test (FOBT) results were collected from two Australian surveillance studies on individuals characterized as high-risk based on a personal or family history of colorectal cancer. Motivated by a Poisson process, this paper proposes a generalized nonlinear model with a complementary log-log link as a dynamic prediction tool that produces individualized probabilities for the risk of developing advanced adenoma or colorectal cancer (AAC). This model allows predicted risk to depend on a patient's baseline characteristics and time-dependent covariates. Information on the dates and results of COLs and FOBTs were incorporated using time-dependent covariates that contributed to patient risk of AAC for a specified period following the test result. These covariates serve to update a person's risk as additional COL, and FOBT test information becomes available. Model selection was conducted systematically through the comparison of Akaike information criterion. Goodness-of-fit was assessed with the use of calibration plots to compare the predicted probability of event occurrence with the proportion of events observed. Abnormal COL results were found to significantly increase risk of AAC for 1 year following the test. Positive FOBTs were found to significantly increase the risk of AAC for 3 months following the result. The covariates that incorporated the updated test results were of greater significance and had a larger effect on risk than the baseline variables. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.
    Statistics in Medicine 04/2015; 34(18). DOI:10.1002/sim.6500 · 1.83 Impact Factor
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    Jared C. Foster · Bin Nan · Lei Shen · Niko Kaciroti · Jeremy M. G. Taylor ·
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    ABSTRACT: We consider the problem of using permutation-based methods to test for treatment-covariate interactions from randomized clinical trial data. Testing for interactions is common in the field of personalized medicine, as subgroups with enhanced treatment effects arise when treatment-by-covariate interactions exist. Asymptotic tests can often be performed for simple models, but in many cases, more complex methods are used to identify subgroups, and non-standard test statistics proposed, and asymptotic results may be difficult to obtain. In such cases, it is natural to consider permutation-based tests, which shuffle selected parts of the data in order to remove one or more associations of interest; however, in the case of interactions, it is generally not possible to remove only the associations of interest by simple permutations of the data. We propose a number of alternative permutation-based methods, designed to remove only the associations of interest, but preserving other associations. These methods estimate the interaction term in a model, then create data that “looks like” the original data except that the interaction term has been permuted. The proposed methods are shown to outperform traditional permutation methods in a simulation study. In addition, the proposed methods are illustrated using data from a randomized clinical trial of patients with hypertension.
    Statistics in Biosciences 03/2015; DOI:10.1007/s12561-015-9125-9
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    ABSTRACT: Phase I trials often include a dose expansion cohort (DEC), in which additional patients are treated at the estimated maximum tolerated dose (MTD) after dose escalation, with the goal of ensuring that data are available from more than six patients at a single dose level. However, protocols do not always detail how, or even if, the additional toxicity data will be used to reanalyze the MTD or whether observed toxicity in the DEC will warrant changing the assigned dose. A DEC strategy has not been statistically justified. We conducted a simulation study of two phase I designs: the "3+3" and the Continual Reassessment Method (CRM). We quantified how many patients are assigned the true MTD using a 10 to 20 patient DEC and how a sensible reanalysis using the DEC changes the probability of selecting the true MTD. We compared these results with those from an equivalently sized larger CRM that does not include a DEC. With either the 3+3 or CRM, reanalysis with the DEC increased the probability of identifying the true MTD. However, a large CRM without a DEC was more likely to identify the true MTD while still treating 10 or 15 patients at this dose level. Where feasible, a CRM design with no explicit DEC is preferred to designs that fix a dose for all patients in a DEC. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail:
    JNCI Journal of the National Cancer Institute 03/2015; 107(3). DOI:10.1093/jnci/dju429 · 12.58 Impact Factor
  • Philip S. Boonstra · Bhramar Mukherjee · Jeremy M. G. Taylor ·

    Statistica Sinica 01/2015; DOI:10.5705/ss.2013.284 · 1.16 Impact Factor
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    ABSTRACT: It has been postulated that gastroesophageal reflux plays a role in the etiology of head and neck squamous cell carcinomas (HNSCC) and contributes to complications after surgery or during radiotherapy. Antacid medications are commonly used in patients with HNSCC for the management of acid reflux; however, their relationship with outcomes has not been well studied. Associations between histamine receptor-2 antagonists (H2RA) and proton pump inhibitors (PPI) use and treatment outcomes were determined in 596 patients with previously untreated HNSCC enrolled in our SPORE epidemiology program from 2003 to 2008 (median follow-up 55 months). Comprehensive clinical information was entered prospectively in our database. Risk strata were created on the basis of possible confounding prognostic variables (age, demographics, socioeconomics, tumor stage, primary site, smoking status, HPV16 status, and treatment modality); correlations within risk strata were analyzed in a multivariable model. Patients taking antacid medications had significantly better overall survival (OS; PPI alone: P < 0.001; H2RA alone, P = 0.0479; both PPI + H2RA, P = 0.0133). Using multivariable Cox models and adjusting for significant prognostic covariates, both PPIs and H2RAs used were significant prognostic factors for OS, but only H2RAs use for recurrence-free survival in HPV16-positive oropharyngeal patients. We found significant associations between the use of H2RAs and PPIs, alone or in combination, and various clinical characteristics. The findings in this large cohort study indicate that routine use of antacid medications may have significant therapeutic benefit in patients with HNSCC. The reasons for this association remain an active area of investigation and could lead to identification of new treatment and prevention approaches with agents that have minimal toxicities. Cancer Prev Res; 7(12); 1258-69. ©2014 AACR. ©2014 American Association for Cancer Research.
    Cancer Prevention Research 12/2014; 7(12):1258-69. DOI:10.1158/1940-6207.CAPR-14-0002 · 4.44 Impact Factor
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    Jared C Foster · Jeremy M G Taylor · Niko Kaciroti · Bin Nan ·
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    ABSTRACT: We consider the use of randomized clinical trial (RCT) data to identify simple treatment regimes based on some subset of the covariate space, [Formula: see text]. The optimal subset, [Formula: see text], is selected by maximizing the expected outcome under a treat-if-in-[Formula: see text] regime, and is restricted to be a simple, as it is desirable that treatment decisions be made with only a limited amount of patient information required. We consider a two-stage procedure. In stage 1, non-parametric regression is used to estimate treatment effects for each subject, and in stage 2 these treatment effect estimates are used to systematically evaluate many subgroups of a simple, prespecified form to identify [Formula: see text]. The proposed methods were found to perform favorably compared with two existing methods in simulations, and were applied to prehypertension data from an RCT. © Published by Oxford University Press 2014. This work is written by (a) US Government employee(s) and is in the public domain in the US.
    Biostatistics 11/2014; 16(2). DOI:10.1093/biostatistics/kxu049 · 2.65 Impact Factor
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    ABSTRACT: Objective: . Given the long natural history of prostate cancer, we assessed differing graphical formats for imparting knowledge about the longitudinal risks of prostate cancer recurrence with or without 'hormone' or 'androgen deprivation' therapy. Methods: . Male volunteers without a history of prostate cancer were randomized to 1 of 8 risk communication instruments that depicted the likelihood of prostate cancer returning or spreading over 1, 2, and 3 years. The tools differed in format (line, pie, bar, or pictograph) and whether the graph also included no numbers, 1 number (indicating the number of affected individuals), or 2 numbers (indicting both the number affected and the number unaffected). The main outcome variables evaluated were graphical preference and knowledge. Results: . A total of 420 men were recruited; respondents were least familiar and experienced with pictographs (P < 0.0001), and only 10% preferred this particular format. Overall accuracy ranged from 79% to 92%, and when assessed across all graphical subtypes, the addition of numerical information did not improve verbatim knowledge (P = 0.1). Self-reported numeracy was a strong predictor of accuracy of responses (odds ratio [OR] = 2.6, P = 0.008), and the impact of high numeracy varied across graphical type, having a greater impact on line (OR = 5.1; 95% confidence interval [CI] = 1.6-16; P = 0.04) and pie charts (OR = 7.1; 95% CI = 2.6-19; P =0.01), without an impact on pictographs (OR = 0.4; 95% CI = 0.1-1.7; P = 0.17) or bar charts (OR = 0.5; 95% CI = 0.1-1.8; P = 0.24). Conclusion: . For longitudinal presentation of risk, baseline numeracy was strongly prognostic for outcome. However, the addition of numbers to risk graphs improved only the delivery of verbatim knowledge for subjects with lower numeracy. Although subjects reported the least familiarity with pictographs, they were one of the most effective means of transferring information regardless of numeracy.
    Medical Decision Making 10/2014; 35(1). DOI:10.1177/0272989X14551639 · 3.24 Impact Factor
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    Michael R Elliott · Anna S C Conlon · Yun Li · Nico Kaciroti · Jeremy M G Taylor ·
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    ABSTRACT: Because of the time and expense required to obtain clinical outcomes of interest, such as functional limitations or death, clinical trials often focus the effects of treatment on earlier and more easily obtained surrogate markers. Preliminary work to define surrogates focused on the fraction of a treatment effect "explained" by a marker in a regression model, but as notions of causality have been formalized in the statistical setting, formal definitions of high-quality surrogate markers have been developed in the causal inference framework, using either the "causal effect" or "causal association" settings. In the causal effect setting, high-quality surrogate markers have a large fraction of the total treatment effect explained by the effect of the treatment on the marker net of the treatment on the outcome. In the causal association setting, high-quality surrogate markers have large treatment effects on the outcome when there are large treatment effects on the marker, and small effects on the outcome when there are small effects on the marker. A particularly important feature of a surrogate marker is that the direction of a treatment effect be the same for both the marker and the outcome. Settings in which the marker and outcome are positively associated but the marker and outcome have beneficial and harmful or harmful and beneficial treatment effects, respectively, have been referred to as "surrogate paradoxes". If this outcome always occurs, it is not problematic; however, as correlations among the outcome, marker, and their treatment effects weaken, it may occur for some trials and not for others, leading to potentially incorrect conclusions, and real-life examples that shortened thousands of lives are unfortunately available. We propose measures for assessing the risk of the surrogate paradox using the meta-analytic causal association framework, which allows us to focus on the probability that a given treatment will yield treatment effect in different directions between the marker and the outcome, and to determine the size of a beneficial effect of the treatment on the marker required to minimize the risk of a harmful effect of the treatment on the outcome. We provide simulations and consider two applications.
    Biostatistics 09/2014; 16(2). DOI:10.1093/biostatistics/kxu043 · 2.65 Impact Factor
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    ABSTRACT: BACKGROUND Proinflammatory cytokine levels may be associated with cancer stage, recurrence, and survival. The objective of this study was to determine whether cytokine levels were associated with dietary patterns and fat-soluble micronutrients in patients with previously untreated head and neck squamous cell carcinoma (HNSCC).METHODS This was a cross-sectional study of 160 patients with newly diagnosed HNSCC who completed pretreatment food frequency questionnaires (FFQs) and health surveys. Dietary patterns were derived from FFQs using principal component analysis. Pretreatment serum levels of the proinflammatory cytokines interleukin-6 (IL-6), tumor necrosis factor alpha (TNF-α), and interferon gamma (IFN-γ) were measured using an enzyme-linked immunosorbent assay, and serum carotenoid and tocopherol levels were measured by high-performance liquid chromatography. Multivariable ordinal logistic regression models examined associations between cytokines and quartiles of reported and serum dietary variables.RESULTSThree dietary patterns emerged: whole foods, Western, and convenience foods. In multivariable analyses, higher whole foods pattern scores were significantly associated with lower levels of IL-6, TNF-α, and IFN-γ (P ≤ .001, P = .008, and P = .03, respectively). Significant inverse associations were reported between IL-6, TNF-α, and IFN-γ levels and quartiles of total reported carotenoid intake (P = .006, P = .04, and P = .04, respectively). There was an inverse association between IFN-γ levels and serum α-tocopherol levels (P = .03).CONCLUSIONS Consuming a pretreatment diet rich in vegetables, fruit, fish, poultry, and whole grains may be associated with lower proinflammatory cytokine levels in patients with HNSCC. Cancer 2014. © 2014 American Cancer Society.
    Cancer 09/2014; 120(17). DOI:10.1002/cncr.28778 · 4.89 Impact Factor
  • Jeremy M. G. Taylor · Wenting Cheng · Jared C. Foster ·
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    ABSTRACT: A recent article (Zhang et al., 2012, Biometrics 168, 1010–1018) compares regression based and inverse probability based methods of estimating an optimal treatment regime and shows for a small number of covariates that inverse probability weighted methods are more robust to model misspecification than regression methods. We demonstrate that using models that fit the data better reduces the concern about non-robustness for the regression methods. We extend the simulation study of Zhang et al. (2012, Biometrics 168, 1010–1018), also considering the situation of a larger number of covariates, and show that incorporating random forests into both regression and inverse probability weighted based methods improves their properties.
    Biometrics 09/2014; 71(1). DOI:10.1111/biom.12228 · 1.57 Impact Factor
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    ABSTRACT: Selection of dose for cancer patients treated with radiation therapy (RT) must balance the increased efficacy with the increased toxicity associated with higher dose. Historically, a single dose has been selected for a population of patients (e.g., all stage III non-small cell lung cancer). However, the availability of new biologic markers for toxicity and efficacy allows the possibility of selecting a more personalized dose. We consider the use of statistical models for toxicity and efficacy as a function of RT dose and biomarkers to select an optimal dose for an individual patient, defined as the dose that maximizes the probability of efficacy minus the sum of weighted toxicity probabilities. This function can be shown to be equal to the expected value of the utility derived from a particular family of bivariate outcome utility matrices. We show that if dose is linearly related to the probability of toxicity and efficacy, then any marker that only acts additively with dose cannot improve efficacy, without also increasing toxicity. Using a dataset of lung cancer patients treated with RT, we illustrate this approach and compare it to non-marker-based dose selection. Because typical metrics used in evaluating new markers (e.g., area under the ROC curve) do not directly address the ability of a marker to improve efficacy at a fixed probability of toxicity, we utilize a simulation study to assess the effects of marker-based dose selection on toxicity and efficacy outcomes. Copyright © 2014 John Wiley & Sons, Ltd.
    Statistics in Medicine 08/2014; 33(30). DOI:10.1002/sim.6285 · 1.83 Impact Factor
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    ABSTRACT: With challenges in data harmonization and environmental heterogeneity across various data sources, meta-analysis of gene–environment interaction studies can often involve subtle statistical issues. In this paper, we study the effect of environmental covariate heterogeneity (within and between cohorts) on two approaches for fixed-effect meta-analysis: the standard inverse-variance weighted meta-analysis and a meta-regression approach. Akin to the results in Simmonds and Higgins (), we obtain analytic efficiency results for both methods under certain assumptions. The relative efficiency of the two methods depends on the ratio of within versus between cohort variability of the environmental covariate. We propose to use an adaptively weighted estimator (AWE), between meta-analysis and meta-regression, for the interaction parameter. The AWE retains full efficiency of the joint analysis using individual level data under certain natural assumptions. Lin and Zeng (, b) showed that a multivariate inverse-variance weighted estimator retains full efficiency as joint analysis using individual level data, if the estimates with full covariance matrices for all the common parameters are pooled across all studies. We show consistency of our work with Lin and Zeng (, b). Without sacrificing much efficiency, the AWE uses only univariate summary statistics from each study, and bypasses issues with sharing individual level data or full covariance matrices across studies. We compare the performance of the methods both analytically and numerically. The methods are illustrated through meta-analysis of interaction between Single Nucleotide Polymorphisms in FTO gene and body mass index on high-density lipoprotein cholesterol data from a set of eight studies of type 2 diabetes.
    Genetic Epidemiology 07/2014; 38(5). DOI:10.1002/gepi.21810 · 2.60 Impact Factor
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    Lili Zhao · Dai Feng · Emily L Bellile · Jeremy M G Taylor ·
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    ABSTRACT: In this paper, we develop a Bayesian approach to estimate a Cox proportional hazards model that allows a threshold in the regression coefficient, when some fraction of subjects are not susceptible to the event of interest. A data augmentation scheme with latent binary cure indicators is adopted to simplify the Markov chain Monte Carlo implementation. Given the binary cure indicators, the Cox cure model reduces to a standard Cox model and a logistic regression model. Furthermore, the threshold detection problem reverts to a threshold problem in a regular Cox model. The baseline cumulative hazard for the Cox model is formulated non-parametrically using counting processes with a gamma process prior. Simulation studies demonstrate that the method provides accurate point and interval estimates. Application to a data set of oropharynx cancer patients suggests a significant threshold in age at diagnosis such that the effect of gender on disease-specific survival changes after the threshold. Copyright © 2013 John Wiley & Sons, Ltd.
    Statistics in Medicine 02/2014; 33(4). DOI:10.1002/sim.5964 · 1.83 Impact Factor

Publication Stats

12k Citations
982.53 Total Impact Points


  • 2000-2015
    • University of Michigan
      • Department of Biostatistics
      Ann Arbor, Michigan, United States
  • 2000-2011
    • Concordia University–Ann Arbor
      Ann Arbor, Michigan, United States
  • 2010
    • Université Victor Segalen Bordeaux 2
      Burdeos, Aquitaine, France
  • 2009
    • The University of Arizona
      Tucson, Arizona, United States
  • 2008
    • William Penn University
      Worcester, Massachusetts, United States
  • 2007
    • University of Bordeaux
      Burdeos, Aquitaine, France
  • 1987-2007
    • University of California, Los Angeles
      • • Department of Biostatistics
      • • Department of Radiation Oncology
      • • Jonsson Comprehensive Cancer Center
      Los Angeles, California, United States
  • 2006
    • Johnson & Johnson
      New Brunswick, New Jersey, United States
  • 1999
    • Case Western Reserve University
      Cleveland, Ohio, United States
  • 1989-1999
    • Harbor-UCLA Medical Center
      Torrance, California, United States
  • 1998
    • Comprehensive Cancer Centers of Nevada
      Las Vegas, Nevada, United States
  • 1996
    • Los Angeles Biomedical Research Institute at Harbor-UCLA Medical Center
      Torrance, California, United States
  • 1995
    • Massachusetts General Hospital
      Boston, Massachusetts, United States
  • 1992
    • University of California, Davis
      Davis, California, United States
  • 1991
    • University of Texas MD Anderson Cancer Center
      • Department of Biomathematics
      Houston, Texas, United States
  • 1986
    • CSU Mentor
      Long Beach, California, United States