A Bayesian model-based reduced major axis regression.

Reduced major axis (RMA) regression, widely used in the fields of zoology, botany, ecology, biology, spectroscopy, and among others, outweighs the ordinary least square regression by relaxing the assumption that the covariates are without measurement errors. A Bayesian implementation of the RMA regression is presented in this paper, and the equivalence of the estimates of the parameters under the Bayesian and the frequentist frameworks is proved. This model-based Bayesian RMA method is advantageous since the posterior estimates, the standard deviations, as well as the credible intervals of the estimates can be obtained through Markov chain Monte Carlo methods directly. In addition, it is straightforward to extend to the multivariate RMA case. The performance of the Bayesian RMA approach is evaluated in the simulation study, and, finally, the proposed method is applied to analyze a dataset in the plantation.

Modeling and maximum likelihood based inference of interval-censored data with unknown upper limits and time-dependent covariates.

Due to the nature of study design or other reasons, the upper limits of the interval-censored data with multiple visits are unknown. A naïve approach is to treat the last observed time as the exact event time, which may induce biased estimators of the model parameters. In this paper, we first develop a Cox model with time-dependent covariates for the event time and a proportional hazards model with frailty for the gap time. We then construct the upper limits using the latent gap times to resolve the issue of interval-censored event time data with unknown upper limits. A data-augmentation technique and a Monte Carlo EM (MCEM) algorithm are developed to facilitate computation. Theoretical properties of the computational algorithm are also investigated. Additionally, new model comparison criteria are developed to assess the fit of the gap time data as well as the fit of the event time data conditional on the gap time data. Our proposed method compares favorably with competing methods in both simulation study and real data analysis.

Bayesian criterion-based assessments of recurrent event models with applications to commercial truck driver behavior studies.

Multitype recurrent events are commonly observed in transportation studies, since commercial truck drivers may encounter different types of safety critical events (SCEs) and take different lengths of on-duty breaks in a driving shift. Bayesian nonhomogeneous Poisson process models are a flexible approach to jointly model the intensity functions of the multitype recurrent events. For evaluating and comparing these models, the deviance information criterion (DIC) and the logarithm of the pseudo-marginal likelihood (LPML) are studied and Monte Carlo methods are developed for computing these model assessment measures. We also propose a set of new concordance indices (C-indices) to evaluate various discrimination abilities of a Bayesian multitype recurrent event model. Specifically, the within-event C-index quantifies adequacy of a given model in fitting the recurrent event data for each type, the between-event C-index provides an assessment of the model fit between two types of recurrent events, and the overall C-index measures the model's discrimination ability among multiple types of recurrent events simultaneously. Moreover, we jointly model the incidence of SCEs and on-duty breaks with driving behaviors using a Bayesian Poisson process model with time-varying coefficients and time-dependent covariates. An in-depth analysis of a real dataset from the commercial truck driver naturalistic driving study is carried out to demonstrate the usefulness and applicability of the proposed methodology.

Bayesian Model Assessment for Jointly Modeling Multidimensional Response Data with Application to Computerized Testing.

Computerized assessment provides rich multidimensional data including trial-by-trial accuracy and response time (RT) measures. A key question in modeling this type of data is how to incorporate RT data, for example, in aid of ability estimation in item response theory (IRT) models. To address this, we propose a joint model consisting of a two-parameter IRT model for the dichotomous item response data, a log-normal model for the continuous RT data, and a normal model for corresponding paper-and-pencil scores. Then, we reformulate and reparameterize the model to capture the relationship between the model parameters, to facilitate the prior specification, and to make the Bayesian computation more efficient. Further, we propose several new model assessment criteria based on the decomposition of deviance information criterion (DIC) the logarithm of the pseudo-marginal likelihood (LPML). The proposed criteria can quantify the improvement in the fit of one part of the multidimensional data given the other parts. Finally, we have conducted several simulation studies to examine the empirical performance of the proposed model assessment criteria and have illustrated the application of these criteria using a real dataset from a computerized educational assessment program.

Bayesian network meta-regression hierarchical models using heavy-tailed multivariate random effects with covariate-dependent variances.

Network meta-analysis (NMA) is gaining popularity in evidence synthesis and network meta-regression allows us to incorporate potentially important covariates into network meta-analysis. In this article, we propose a Bayesian network meta-regression hierarchical model and assume a general multivariate t distribution for the random treatment effects. The multivariate t distribution is desired for heavy-tailed random effects and converges to the multivariate normal distribution when the degrees of freedom go to infinity. Moreover, in NMA, some treatments are compared only in a single study. To overcome such sparsity, we propose a log-linear regression model for the variances of the random effects and incorporate aggregate covariates into modeling the variance components. We develop a Markov chain Monte Carlo sampling algorithm to sample from the posterior distribution via the collapsed Gibbs technique. We further use the deviance information criterion and the logarithm of the pseudo-marginal likelihood for model comparison. A simulation study is conducted and a detailed analysis from our motivating case study is carried out to further demonstrate the proposed methodology.

A Bayesian multi-risks survival (MRS) model in the presence of double censorings.

Semi-competing risks data include the time to a nonterminating event and the time to a terminating event, while competing risks data include the time to more than one terminating event. Our work is motivated by a prostate cancer study, which has one nonterminating event and two terminating events with both semi-competing risks and competing risks present as well as two censoring times. In this paper, we propose a new multi-risks survival (MRS) model for this type of data. In addition, the proposed MRS model can accommodate noninformative right-censoring times for nonterminating and terminating events. Properties of the proposed MRS model are examined in detail. Theoretical and empirical results show that the estimates of the cumulative incidence function for a nonterminating event may be biased if the information on a terminating event is ignored. A Markov chain Monte Carlo sampling algorithm is also developed. Our methodology is further assessed using simulations and also an analysis of the real data from a prostate cancer study. As a result, a prostate-specific antigen velocity greater than 2.0 ng/mL per year and higher biopsy Gleason scores are positively associated with a shorter time to death due to prostate cancer.

Bayesian multivariate skew meta-regression models for individual patient data.

We examine a class of multivariate meta-regression models in the presence of individual patient data. The methodology is well motivated from several studies of cholesterol-lowering drugs where the goal is to jointly analyze the multivariate outcomes, low density lipoprotein cholesterol, high density lipoprotein cholesterol, and triglycerides. These three continuous outcome measures are correlated and shed much light on a subject's lipid status. One of the main goals in lipid research is the joint analysis of these three outcome measures in a meta-regression setting. Since these outcome measures are not typically multivariate normal, one must consider classes of distributions that allow for skewness in one or more of the outcomes. In this paper, we consider a new general class of multivariate skew distributions for multivariate meta-regression and examine their theoretical properties. Using these distributions, we construct a Bayesian model for the meta-data and develop an efficient Markov chain Monte Carlo computational scheme for carrying out the computations. In addition, we develop a multivariate L measure for model comparison, Bayesian residuals for model assessment, and a Bayesian procedure for detecting outlying trials. The proposed multivariate L measure, Bayesian residuals, and Bayesian outlying trial detection procedure are particularly suitable and computationally attractive in the multivariate meta-regression setting. A detailed case study demonstrating the usefulness of the proposed methodology is carried out in an individual patient data multivariate meta-regression setting using 26 pivotal Merck clinical trials that compare statins (cholesterol-lowering drugs) in combination with ezetimibe and statins alone on treatment-naïve patients and those continuing on statins at baseline.

A Comparison of Monte Carlo Methods for Computing Marginal Likelihoods of Item Response Theory Models.

Nowadays, Bayesian methods are routinely used for estimating parameters of item response theory (IRT) models. However, the marginal likelihoods are still rarely used for comparing IRT models due to their complexity and a relatively high dimension of the model parameters. In this paper, we review Monte Carlo (MC) methods developed in the literature in recent years and provide a detailed development of how these methods are applied to the IRT models. In particular, we focus on the "best possible" implementation of these MC methods for the IRT models. These MC methods are used to compute the marginal likelihoods under the one-parameter IRT model with the logistic link (1PL model) and the two-parameter logistic IRT model (2PL model) for a real English Examination dataset. We further use the widely applicable information criterion (WAIC) and deviance information criterion (DIC) to compare the 1PL model and the 2PL model. The 2PL model is favored by all of these three Bayesian model comparison criteria for the English Examination data.

A New Monte Carlo Method for Estimating Marginal Likelihoods.

Evaluating the marginal likelihood in Bayesian analysis is essential for model selection. Estimators based on a single Markov chain Monte Carlo sample from the posterior distribution include the harmonic mean estimator and the inflated density ratio estimator. We propose a new class of Monte Carlo estimators based on this single Markov chain Monte Carlo sample. This class can be thought of as a generalization of the harmonic mean and inflated density ratio estimators using a partition weighted kernel (likelihood times prior). We show that our estimator is consistent and has better theoretical properties than the harmonic mean and inflated density ratio estimators. In addition, we provide guidelines on choosing optimal weights. Simulation studies were conducted to examine the empirical performance of the proposed estimator. We further demonstrate the desirable features of the proposed estimator with two real data sets: one is from a prostate cancer study using an ordinal probit regression model with latent variables; the other is for the power prior construction from two Eastern Cooperative Oncology Group phase III clinical trials using the cure rate survival model with similar objectives.

Low testosterone at first prostate-specific antigen failure and assessment of risk of death in men with unfavorable-risk prostate cancer treated on prospective clinical trials.

BACKGROUND: Low testosterone at the time of diagnosis of prostate cancer has been associated with a worse prognosis. Whether this is true and how to define the best treatment approach at the time of first prostate-specific antigen (PSA) failure to the authors' knowledge has not been elucidated to date and was studied herein. METHODS: Between 1995 and 2001, a total of 58 men with unfavorable-risk PC who were treated on clinical trials with radiotherapy and androgen deprivation therapy (ADT) had available testosterone levels at the time of PSA failure. Cox and Fine and Gray regressions were performed to ascertain whether low versus normal testosterone was associated with the risk of PC-specific mortality, other-cause mortality, and all-cause mortality adjusting for age, salvage ADT, and known PC prognostic factors. RESULTS: After a median follow-up of 6.68 years after PSA failure, 31 men (53.4%) had died; 10 of PC (32.3%), of which 8 of 11 (72.7%) versus 2 of 47 (4.3%) deaths occurred in men with low versus normal testosterone at the time of PSA failure, respectively. A significant increase in the risk of all-cause mortality (adjusted hazard ratio [AHR], 2.54; 95% confidence interval [95% CI], 1.04-6.21 [P = .04]) and PC-specific mortality (AHR, 13.71; 95% CI, 2.4-78.16 [P = .003]), with a reciprocal trend toward a decreased risk of other-cause mortality (AHR, 0.18; 95% CI, 0.02-1.55 [P = .12]) was observed in men with low versus normal testosterone. CONCLUSIONS: Low, but not necessarily castrate, testosterone levels at the time of PSA failure confer a very poor prognosis. These observations provide evidence to support testosterone testing at the time of PSA failure. Given prolonged survival when abiraterone or docetaxel is added to ADT in men with castrate-sensitive metastatic PC and possibly localized high-risk PC provides a rationale supporting their use with ADT in men with low testosterone in the setting of a phase 2 trial. Cancer 2018;124:1383-90. © 2017 American Cancer Society.

Bayesian Model Assessment in Joint Modeling of Longitudinal and Survival Data with Applications to Cancer Clinical Trials.

Joint models for longitudinal and survival data are routinely used in clinical trials or other studies to assess a treatment effect while accounting for longitudinal measures such as patient-reported outcomes (PROs). In the Bayesian framework, the deviance information criterion (DIC) and the logarithm of the pseudo marginal likelihood (LPML) are two well-known Bayesian criteria for comparing joint models. However, these criteria do not provide separate assessments of each component of the joint model. In this paper, we develop a novel decomposition of DIC and LPML to assess the fit of the longitudinal and survival components of the joint model, separately. Based on this decomposition, we then propose new Bayesian model assessment criteria, namely, ΔDIC and ΔLPML, to determine the importance and contribution of the longitudinal (survival) data to the model fit of the survival (longitudinal) data. Moreover, we develop an efficient Monte Carlo method for computing the Conditional Predictive Ordinate (CPO) statistics in the joint modeling setting. A simulation study is conducted to examine the empirical performance of the proposed criteria and the proposed methodology is further applied to a case study in mesothelioma.

Onset of persistent pseudomonas aeruginosa infection in children with cystic fibrosis with interval censored data.

BACKGROUND: Persistent Pseudomonas aeruginosa (PPA) infection promotes lung function deterioration in children with cystic fibrosis (CF). Although early CF diagnosis through newborn screening (NBS) has been shown to provide nutritional/growth benefit, it is unclear whether NBS lowers the risk of PPA infection and how the effect of NBS vary with age. Modeling the onset age of PPA infection is challenging because 1) the onset age of PPA infection is interval censored in patient registry data; and 2) some risk factors such as NBS may have time-varying effects. METHODS: This problem fits into the framework of a recently developed Bayesian dynamic Cox model for interval censored data, where each regression coefficient is allowed to be time-varying to an extent determined by the data. RESULTS: Application of the methodology to data from the CF Foundation Patient Registry revealed interesting findings. Compared with patients with meconium ileus or diagnosed through signs or symptoms, patients diagnosed through NBS had significantly lower risks of acquiring PPA infection between age 1 and 2 years, and the benefit in survival rate was found to last up to age 4 years. Two cohorts of five years apart were compared. Patients born in cohort 2003-2004 had significantly lower risks of the PPA infections at any age up to 4 years than those born in 1998-1999. CONCLUSIONS: The study supports benefits of NBS on PPA infection in early childhood. In addition, our analyses demonstrate that patients in the more recent cohort had significantly lower risks of acquiring PPA infection up to age 4 years, which suggests improved CF treatment and care over time.

Exercise Performance in Patients with D-Loop Transposition of the Great Arteries After Arterial Switch Operation: Long-Term Outcomes and Longitudinal Assessment.

The first patients to undergo a successful arterial switch operation (ASO) for d-transposition of the great arteries (D-TGA) are now entering their fourth decade of life. Past studies of ASO survivors' exercise function have yielded conflicting results. We therefore undertook this study to describe the current function of ASO survivors, to identify factors related to inferior exercise performance and to determine whether their exercise function tends to deteriorate over time. A retrospective cohort study was designed examining all patients with D-TGA after the ASO who underwent comprehensive cardiopulmonary exercise testing (CPET). Patients with palliative surgery prior to ASO, ventricular hypoplasia or severe valvar dysfunction were excluded from the study. Data from CPETs in which the peak respiratory exchange ratio was <1.09 were also excluded. We identified 113 patients who met entry criteria and had 186 CPX at our institution between 1/2002 and 1/2013; 41 patients had at least 2 qualifying CPX. Mean age at the time of the initial test was 17 ± 1 year. Peak oxygen consumption (VO2) averaged 84 ± 2 % predicted. Peak VO2 was lower among patients with repaired ventricular septal defects (82 ± 4 vs. 86 ± 3 % predicted; p < 0.05) and among patients with ≥ moderate right-sided obstructive lesions (77 ± 5 vs. 87 ± 3 % predicted; p < 0.05). Surgery prior to 1991 was also associated with a lower peak VO2 (81 ± 3 vs. 87 ± 3 % predicted; p < 0.01). The mean % predicted peak heart rate was 92 ± 1 %, with no significant difference between any of the subgroups. Non-diagnostic exercise-induced STT changes developed in 10 patients (12 studies). In the subgroup with at least 2 exercise tests, the annual decline in % predicted peak VO2 was quite slow (-0.3 % points/year; p < 0.01 vs. expected normal age-related decline). The exercise capacity of ASO survivors is well preserved and is only mildly reduced compared to normal subjects. Moreover, there is only a slight deterioration in exercise capacity over time. VSD repair, residual right-sided obstructive lesions, and earlier surgical era are associated with worse exercise performance. Peak heart rate was preserved with no significant change in follow up testing.

Confident difference criterion: a new Bayesian differentially expressed gene selection algorithm with applications.

BACKGROUND: Recently, the Bayesian method becomes more popular for analyzing high dimensional gene expression data as it allows us to borrow information across different genes and provides powerful estimators for evaluating gene expression levels. It is crucial to develop a simple but efficient gene selection algorithm for detecting differentially expressed (DE) genes based on the Bayesian estimators. RESULTS: In this paper, by extending the two-criterion idea of Chen et al. (Chen M-H, Ibrahim JG, Chi Y-Y. A new class of mixture models for differential gene expression in DNA microarray data. J Stat Plan Inference. 2008;138:387-404), we propose two new gene selection algorithms for general Bayesian models and name these new methods as the confident difference criterion methods. One is based on the standardized differences between two mean expression values among genes; the other adds the differences between two variances to it. The proposed confident difference criterion methods first evaluate the posterior probability of a gene having different gene expressions between competitive samples and then declare a gene to be DE if the posterior probability is large. The theoretical connection between the proposed first method based on the means and the Bayes factor approach proposed by Yu et al. (Yu F, Chen M-H, Kuo L. Detecting differentially expressed genes using alibrated Bayes factors. Statistica Sinica. 2008;18:783-802) is established under the normal-normal-model with equal variances between two samples. The empirical performance of the proposed methods is examined and compared to those of several existing methods via several simulations. The results from these simulation studies show that the proposed confident difference criterion methods outperform the existing methods when comparing gene expressions across different conditions for both microarray studies and sequence-based high-throughput studies. A real dataset is used to further demonstrate the proposed methodology. In the real data application, the confident difference criterion methods successfully identified more clinically important DE genes than the other methods. CONCLUSION: The confident difference criterion method proposed in this paper provides a new efficient approach for both microarray studies and sequence-based high-throughput studies to identify differentially expressed genes.

Prospective assessment of deep inspiration breath-hold using 3-dimensional surface tracking for irradiation of left-sided breast cancer.

PURPOSE: Deep inspiration breath hold (DIBH) is used to decrease cardiac irradiation during radiation therapy (RT) for breast cancer. The patients most likely to benefit and the impact on treatment time remain largely unknown. We sought to identify predictors for the use of DIBH and to quantify differences in dosimetry and treatment time using a prospective registry. METHODS AND MATERIALS: A total of 150 patients with left breast cancer were enrolled. All patients were simulated with both free breathing (FB) and DIBH. RT was delivered by either modality. Alternate scans were planned with use of deformable registration to include identical RT volumes. DIBH patients were monitored by a real-time surface tracking system, AlignRT (Vision RT, Ltd, London, United Kingdom). Baseline characteristics and treatment times were compared by Fisher exact test and Wilcoxon rank sum test. Dosimetric endpoints were analyzed by Wilcoxon signed rank test, and linear regression identified predictors for change in mean heart dose (∆MHD). RESULTS: We treated 38 patients with FB and 110 with DIBH. FB patients were older, more likely to have heart and lung disease, and less likely to receive chemotherapy or immediate reconstruction (all P < .05). Treatment times were not significantly different, but DIBH patients had greater variability in times (P = .0002). Of 146 evaluable patients, DIBH resulted in >20 cGy improvement in MHD in 107 patients but a >20 cGy increase in MHD in 14. Both MHD and lung V20 were significantly lower in DIBH than in paired FB plans. On multivariate analysis, younger age (4.18 cGy per year; P < .0001), higher body mass index (6.06 cGy/kg/m(2); P = .0018), and greater change in lung volumes (130 cGy/L; P = .003) were associated with greater ∆MHD. CONCLUSIONS: DIBH improves cardiac dosimetry without significantly impacting treatment time in most patients. Greater inspiratory lung volumes augment this benefit. Because the improvement with DIBH was not uniform, patients should be scanned with both FB and DIBH.

The Impact of Economic Recession on the Incidence and Treatment of Cancer.

PURPOSE: The impact of economic recessions on the incidence and treatment of cancer is unknown. We test the hypothesis that cancer incidence and treatment rates decrease during a recession, and that this relationship is more pronounced in cancers that present with mild, more easily ignored symptoms. METHODS AND MATERIALS: Data on incidence and treatment for all cancers, and breast and pancreatic cancers specifically, from 1973-2008, were collected using Surveillance Epidemiology and End RESULTS (SEER). The data was adjusted for race, income, and education. Unemployment rate was used as the measure of economic recession. Data was log-transformed, and multivariate linear mixed regression was used. RESULTS: Adjusting for socioeconomic factors, the data revealed a significant inverse correlation between unemployment and rates of cancer incidence and treatment. Every 1% increase in unemployment was associated with a 2.2% (95% CI: 1.6-2.8%, p<0.001) reduction in cancer incidence, a 2.0% (1.2-2.8%, p=0.0157) decrease in surgery, and a 9.1% (8.2-10.0% p<0.001) decrease in radiation therapy (RT). Breast cancer incidence and treatment had a dramatic inverse relationship - 7.2% (6.3-8.1%), 6.7% (5.7-7.6%), and 19.0% (18.1-19.8%), respectively (p<0.001 for all). The decrease in incidence was only significant for in situ and localized tumors, but not in regional or distant breast cancer. Compared to breast cancer, pancreatic cancer had a weaker relationship between unemployment and incidence: 2.6% (1.8-3.3%, p=0.0005), surgery: 2.4% (2.0-2.7%, p<0.001), and RT: 1.9% (1.5-2.2% p<0.001). CONCLUSIONS: Increasing unemployment rates are associated with a decrease in the incidence and treatment of all cancers. This effect is exaggerated in breast cancer, where symptoms can more easily be ignored and where there are widely used screening tests relative to pancreatic cancer.

A counterfactual p-value approach for benefit-risk assessment in clinical trials.

Clinical trials generally allow various efficacy and safety outcomes to be collected for health interventions. Benefit-risk assessment is an important issue when evaluating a new drug. Currently, there is a lack of standardized and validated benefit-risk assessment approaches in drug development due to various challenges. To quantify benefits and risks, we propose a counterfactual p-value (CP) approach. Our approach considers a spectrum of weights for weighting benefit-risk values and computes the extreme probabilities of observing the weighted benefit-risk value in one treatment group as if patients were treated in the other treatment group. The proposed approach is applicable to single benefit and single risk outcome as well as multiple benefit and risk outcomes assessment. In addition, the prior information in the weight schemes relevant to the importance of outcomes can be incorporated in the approach. The proposed CPs plot is intuitive with a visualized weight pattern. The average area under CP and preferred probability over time are used for overall treatment comparison and a bootstrap approach is applied for statistical inference. We assess the proposed approach using simulated data with multiple efficacy and safety endpoints and compare its performance with a stochastic multi-criteria acceptability analysis approach.

Cost implications and complications of overtreatment of low-risk prostate cancer in the United States.

BACKGROUND: Evidence-based consensus guidelines recommend only observation for men with low-risk prostate cancer and life expectancy less than 10 years. This report describes the incidence, drivers, cost, and morbidity of overtreatment of low-risk prostate cancer within the United States. METHODS: The SEER-Medicare Program was used to identify 11,744 men aged 66 years or older diagnosed with low-risk prostate cancer in 2004 through 2007. Overtreatment of prostate cancer was defined as definitive treatment of a patient with a life expectancy of less than 10 years. Expected survival was estimated using NCCN methodology. Costs were the amount paid by Medicare in years after minus year before diagnosis. Toxicities were relevant Medicare diagnoses/interventions. P values are 2-sided. RESULTS: Of 3001 men with low-risk prostate cancer and a life expectancy of less than 10 years, 2011 men (67%) were overtreated. On multivariable logistic regression, overtreated men were more likely to be married (odds ratio [OR], 1.29; 95% CI, 1.05-1.59; P=.02), reside in affluent regions (P<.001), and harbor more advanced disease at diagnosis (P<.001). Two-year toxicity was greater in overtreated patients (P<.001). Relative to active surveillance/watchful waiting/observation, the median additional cost per definitive treatment was $18,827 over 5 years; the cumulative annual cost attributable to overtreatment in the United States was $58.7 million. The ability to avoid treating the 80% of men with low-grade disease who will never die of prostate cancer would save $1.32 billion per year nationally. CONCLUSIONS: Overtreatment of low-risk prostate cancer is partially driven by sociodemographic factors and occurs frequently, with marked impact on patient quality of life and health-related costs.

Bayesian probability of success for clinical trials using historical data.

Developing sophisticated statistical methods for go/no-go decisions is crucial for clinical trials, as planning phase III or phase IV trials is costly and time consuming. In this paper, we develop a novel Bayesian methodology for determining the probability of success of a treatment regimen on the basis of the current data of a given trial. We introduce a new criterion for calculating the probability of success that allows for inclusion of covariates as well as allowing for historical data based on the treatment regimen, and patient characteristics. A new class of prior distributions and covariate distributions is developed to achieve this goal. The methodology is quite general and can be used with univariate or multivariate continuous or discrete data, and it generalizes Chuang-Stein's work. This methodology will be invaluable for informing the scientist on the likelihood of success of the compound, while including the information of covariates for patient characteristics in the trial population for planning future pre-market or post-market trials.