Daniel Sabanés Bové

Hyper-

We develop an extension of the classical Zellners g-prior to generalized linear models. The prior on the hyperparameter g is handled in a flexible way, so that any continuous proper hyperprior f(g) can be used, giving rise to a large class of hyper-g priors. Connections with the literature are described in detail. A fast and accurate integrated Laplace approximation of the marginal likelihood makes inference in large model spaces feasible. For posterior parameter estimation we propose an efficient and tuning-free Metropolis-Hastings sampler. The methodology is illustrated with variable selection and automatic covariate transformation in the Pima Indians diabetes data set.

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Background Meningiomas are associated with the highest postoperative rate of venous thromboembolic events (VTE) among all intracranial tumors. The aim of this study is to compare two entirely different VTE prophylaxis regimens in 724 consecutive patients undergoing meningioma surgery. Methods Two cohorts at a single institution treated with different regimens to prevent VTE were reviewed retrospectively. Cohort A (n = 482; 314 females, mean age 57 years, range: 11–87 years) received our institutional regimen during the years 1999–2006, consisting of low-molecular-weight heparin (LMWH) and compression stockings. For cohort B (n = 242; 163 females, mean age 56.8 years, range: 16–90 years), during the years 2008–2010, the management included intraoperative 10°–20° leg elevation with intermittent pneumatic compression (IPC), heparin and LMWH administration. We compared the incidence of the endpoints pulmonary embolism (PE), deep venous thrombosis (DVT), hemorrhage and death, taking into account several known associated risk factors. Results For all endpoints, we observed a more favorable outcome with the new regimen. The difference in incidence of PEs (cohort A: 38/482, 8%; cohort B: 6/242, 2.5%) reached statistical significance (p = 0.002). In general, patients with skull base meningiomas had a higher risk for PE (OR 2.77). Regarding VTE prophylaxis, an adjusted subgroup analysis suggests that the new regimen is particularly beneficial for patients with skull base meningiomas. Conclusions We recommend perioperative prophylaxis using a management composed of intraoperative leg-elevation, IPC, early heparin administration and LMWH to reduce the risk for PE.

priors for generalized linear models

Bayesian model selection poses two main challenges: the specification of parameter priors for all models, and the computation of the resulting Bayes factors between models. There is now a large literature on automatic and objective parameter priors in the linear model. One important class are g-priors, which were recently extended from linear to generalized linear models (GLMs). We show that the resulting Bayes factors can be approximated by test-based Bayes factors (Johnson [Scand. J. Stat. 35 (2008) 354–368]) using the deviance statistics of the models. To estimate the hyperparameter g, we propose empirical and fully Bayes approaches and link the former to minimum Bayes factors and shrinkage estimates from the literature. Furthermore, we describe how to approximate the corresponding posterior distribution of the regression coefficients based on the standard GLM output. We illustrate the approach with the development of a clinical prediction model for 30-day survival in the GUSTO-I trial using logistic regression.

Reduction of Thromboembolic Events in Meningioma Surgery: A Cohort Study of 724 Consecutive Patients

BackgroundThe development of risk prediction models is of increasing importance in medical research - their use in practice, however, is rare. Among other reasons this might be due to the fact that thorough validation is often lacking. This study focuses on two Bayesian approaches of how to validate a prediction rule for the diagnosis of pneumonia, and compares them with established validation methods.MethodsExpert knowledge was used to derive a risk prediction model for pneumonia. Data on more than 600 patients presenting with cough and fever at a general practitioner’s practice in Switzerland were collected in order to validate the expert model and to examine the predictive performance of it. Additionally, four modifications of the original model including shrinkage of the regression coefficients, and two Bayesian approaches with the expert model used as prior mean and different weights for the prior covariance matrix were fitted. We quantify the predictive performance of the different methods with respect to calibration and discrimination, using cross-validation.ResultsThe predictive performance of the unshrinked regression coefficients was poor when applied to the Swiss cohort. Shrinkage improved the results, but a Bayesian model formulation with unspecified weight of the informative prior lead to large AUC and small Brier score, naïve and after cross-validation. The advantage of this approach is the flexibility in case of a prior-data conflict.ConclusionsPublished risk prediction rules in clinical research need to be validated externally before they can be used in new settings. We propose to use a Bayesian model formulation with the original risk prediction rule as prior. The posterior means of the coefficients, given the validation data showed best predictive performance with respect to cross-validated calibration and discriminative ability.

Approximate Bayesian Model Selection with the Deviance Statistic

There is now a large literature on objective Bayesian model selection in the linear model based on the g-prior. The methodology has been recently extended to generalized linear models using test-based Bayes factors. In this paper, we show that test-based Bayes factors can also be applied to the Cox proportional hazards model. If the goal is to select a single model, then both the maximum a posteriori and the median probability model can be calculated. For clinical prediction of survival, we shrink the model-specific log hazard ratio estimates with subsequent calculation of the Breslow estimate of the cumulative baseline hazard function. A Bayesian model average can also be employed. We illustrate the proposed methodology with the analysis of survival data on primary biliary cirrhosis patients and the development of a clinical prediction model for future cardiovascular events based on data from the Second Manifestations of ARTerial disease (SMART) cohort study. Cross-validation is applied to compare the predictive performance with alternative model selection approaches based on Harrells c-Index, the calibration slope and the integrated Brier score. Finally, a novel application of Bayesian variable selection to optimal conditional prediction via landmarking is described. Copyright

Validating and updating a risk model for pneumonia - a case study.

We propose an objective Bayesian approach to the selection of covariates and their penalized splines transformations in generalized additive models. The methodology is based on a combination of continuous mixtures of g-priors for model parameters and a multiplicity-correction prior for the models themselves. We introduce our approach in the normal model and extend it to nonnormal exponential families. A simulation study and an application with binary outcome is provided. An efficient implementation is available in the R package hypergsplines. Supplementary materials for this article are available online.

Objective Bayesian model selection for Cox regression.

The choice of generalized linear mixed models is difficult, because it involves the selection of both fixed and random effects. Classical criteria like Akaikes information criterion (AIC) are often not suitable for the latter task, and others which are useful in linear mixed models are difficult to extend to the generalized case, especially for overdispersed data. A predictive leave-one-out crossvalidation approach is suggested that can be applied for choosing both fixed and random effects, even in models with overdispersion, and is based on proper scoring rules. An attractive feature of this approach is the fact that the model has to be fitted just once to the data set, which makes computations fast and convenient. As the calculation of the leave-one-out predictive distribution is not possible analytically, it is shown how an iteratively weighted least squares algorithm combined with some analytic approximations can be used for this task. A simulation study and two applications of the methodology to binary and count data are provided, as well as comparisons with two other methods.

Objective Bayesian Model Selection in Generalized Additive Models With Penalized Splines

Introduction: Since 2010, Roche-sponsored early development trials in oncology have successfully implemented innovative dose escalation (D/E) strategies including modified continual reassessment methods (CRM) and other Bayesian adaptive designs. Compared to standard 3+3 designs, these methods allow for flexibility to address a variety of clinical questions and to estimate more accurately a molecule’s maximum tolerated dose (MTD). However, CRM designs are sometimes considered as complex and difficult to implement and are not easily understood by clinicians (Le Tourneau et al., 2009, Iasonos et al. 2014). Here, we share our experiences and learnings from the initial exploration, introduction, and wide-spread implementation of CRM in early oncology clinical trials. Methods: We conducted a thorough internal review of the current statistical methods and clinical strategies used in CRM designs. In addition, we systematically collected feedback on the internal experience through surveys and interviews of participating biostatisticians, pharmacologists, clinicians and operations managers. Results: CRMs using two parameter logistic regression models and escalation with overdose control (Neuenschwander et al., 2008) are the most commonly used CRM designs in Roche-sponsored oncology D/E trials. Compared to trials in which 3+3 designs are used, we experienced significant advantages with CRM designs including: flexibility in cohort sizes; formal integration of relevant prior pre-clinical/clinical knowledge of the dose-toxicity relationship; and contribution of all dose limiting toxicities (DLTs) to an MTD determination. On the other hand, we learned about some limitations. The CRM designs modeled binary DLT events where the grade of an event was not considered. Thus, in a cohort where severe DLT event(s) were observed, clinical judgment typically superseded the CRM recommendation towards a lower dose; this decision rule was a priori defined in the protocol. In certain situations, inconsistent prior-information in the dose-toxicity relationship was observed. Therefore, prior assumptions had to be carefully assessed through simulations using multiple dose-toxicity scenarios. Conclusions: Overall, utilization of CRM designs was considered beneficial to Roche early development trials. Based on our experience, CRM designs are flexible and can be tailored to address a variety of clinical research questions. Trial simulation analyses were critical for us to understand the performance of CRM designs, including the accuracy of estimated MTD, trial duration/sample size, and sensitivity to prior assumptions. Furthermore, the introduction and implementation of CRM designs required and promoted strong multidisciplinary collaborations, especially during the design and study protocol set-up phases and the D/E recommendation phase. Citation Format: Jiawen Zhu, Ulrich Beyer, Somnath Sarkar, Gwen Nichols, William Pao, Daniel Sabanes Bove. Experiences and lessons from innovative dose escalation designs in early-phase oncology [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2017; 2017 Apr 1-5; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2017;77(13 Suppl):Abstract nr 3597. doi:10.1158/1538-7445.AM2017-3597

Choice of generalized linear mixed models using predictive crossvalidation

This chapter discusses fundamental concepts of frequentist inference, such as unbiasedness and consistency, standard errors and confidence intervals, significance tests and P-values. There is also a section on the bootstrap method. Exercises are given at the end.

Abstract 3597: Experiences and lessons from innovative dose escalation designs in early-phase oncology

This chapter describes numerical methods for Bayesian inference in non-conjugate settings. Standard numerical techniques and the Laplace approximation provide ways to numerically compute posterior characteristics of interest. Monte Carlo methods, including Monte Carlo integration, rejection and importance sampling as well as Markov chain Monte Carlo are described. Finally, numerical computation of the marginal likelihood, necessary for Bayesian model selection, is discussed. Exercises are given at the end.