Using Bayesian analysis in repeated preclinical in vivo studies for a more effective use of animals

Whilst innovative Bayesian approaches are increasingly used in clinical studies, in the preclinical area Bayesian methods appear to be rarely used in the reporting of pharmacology data. This is particularly surprising in the context of regularly repeated in vivo studies where there is a considerable amount of data from historical control groups, which has potential value. This paper describes our experience with introducing Bayesian analysis for such studies using a Bayesian meta‐analytic predictive approach. This leads naturally either to an informative prior for a control group as part of a full Bayesian analysis of the next study or using a predictive distribution to replace a control group entirely. We use quality control charts to illustrate study‐to‐study variation to the scientists and describe informative priors in terms of their approximate effective numbers of animals. We describe two case studies of animal models: the lipopolysaccharide‐induced cytokine release model used in inflammation and the novel object recognition model used to screen cognitive enhancers, both of which show the advantage of a Bayesian approach over the standard frequentist analysis. We conclude that using Bayesian methods in stable repeated in vivo studies can result in a more effective use of animals, either by reducing the total number of animals used or by increasing the precision of key treatment differences. This will lead to clearer results and supports the “3Rs initiative” to Refine, Reduce and Replace animals in research. Copyright © 2016 John Wiley & Sons, Ltd.     

Simulation-based Bayesian optimal design for multi-factor accelerated life tests

We consider simulation-based methods for the design of multi-stress factor accelerated life tests (ALTs) in a Bayesian decision theoretic framework. Multi-stress factor ALTs are challenging due to the increased number of simulation runs required as a result of stress factor-level combinations. We propose the use of Latin hypercube sampling to reduce the simulation cost without loss of statistical efficiency. Exploration and optimization of expected utility function is carried out by a developed algorithm that utilizes Markov chain Monte Carlo methods and nonparametric smoothing techniques. A comparison of proposed approach to a full grid simulation is provided to illustrate computational cost reduction.     

Bayesian estimation of traffic intensity based on queue length in a multi-server M/M/s queue

In this article, we focus on multi-server queueing systems in which inter-arrival and service times are exponentially distributed (Markovian). We use a Bayesian technique, the sampling/importance resampling method (SIR), to estimate the parameters of these queueing systems, making possible the determination of performance measures that are essential to the evaluation of important practical applications such as computer and telecommunication networks, manufacturing and service systems, health care, and other similar real-life problems. Extensive numerical results are presented to demonstrate the accuracy and efficiency of the technique, as well as some of its limitations.     

Advantages of a wholly Bayesian approach to assessing efficacy in early drug development: a case study

This paper illustrates how the design and statistical analysis of the primary endpoint of a proof‐of‐concept study can be formulated within a Bayesian framework and is motivated by and illustrated with a Pfizer case study in chronic kidney disease. It is shown how decision criteria for success can be formulated, and how the study design can be assessed in relation to these, both using the traditional approach of probability of success conditional on the true treatment difference and also using Bayesian assurance and pre‐posterior probabilities. The case study illustrates how an informative prior on placebo response can have a dramatic effect in reducing sample size, saving time and resource, and we argue that in some cases, it can be considered unethical not to include relevant literature data in this way. Copyright © 2015 John Wiley & Sons, Ltd.     

Semiparametric Estimation of Risk–Return Relationships

This article proposes semiparametric generalized least-squares estimation of parametric restrictions between the conditional mean and the conditional variance of excess returns given a set of parametric factors. A distinctive feature of our estimator is that it does not require a fully parametric model for the conditional mean and variance. We establish consistency and asymptotic normality of the estimates. The theory is nonstandard due to the presence of estimated factors. We provide sufficient conditions for the estimated factors not to have an impact in the asymptotic standard error of estimators. A simulation study investigates the finite sample performance of the estimates. Finally, an application to the CRSP value-weighted excess returns highlights the merits of our approach. In contrast to most previous studies using nonparametric estimates, we find a positive and significant price of risk in our semiparametric setting.     

The challenges of evaluating dose response in flexible‐dose trials using marginal structural models

Assessing dose response from flexible‐dose clinical trials is problematic. The true dose effect may be obscured and even reversed in observed data because dose is related to both previous and subsequent outcomes. To remove selection bias, we propose marginal structural models, inverse probability of treatment‐weighting (IPTW) methodology. Potential clinical outcomes are compared across dose groups using a marginal structural model (MSM) based on a weighted pooled repeated measures analysis (generalized estimating equations with robust estimates of standard errors), with dose effect represented by current dose and recent dose history, and weights estimated from the data (via logistic regression) and determined as products of (i) inverse probability of receiving dose assignments that were actually received and (ii) inverse probability of remaining on treatment by this time. In simulations, this method led to almost unbiased estimates of true dose effect under various scenarios. Results were compared with those obtained by unweighted analyses and by weighted analyses under various model specifications. The simulation showed that the IPTW MSM methodology is highly sensitive to model misspecification even when weights are known. Practitioners applying MSM should be cautious about the challenges of implementing MSM with real clinical data. Clinical trial data are used to illustrate the methodology. Copyright © 2012 John Wiley & Sons, Ltd.     

Model fusion and multiple testing in the likelihood paradigm: shrinkage and evidence supporting a point null hypothesis

ABSTRACT

According to the general law of likelihood, the strength of statistical evidence for a hypothesis as opposed to its alternative is the ratio of their likelihoods, each maximized over the parameter of interest. Consider the problem of assessing the weight of evidence for each of several hypotheses. Under a realistic model with a free parameter for each alternative hypothesis, this leads to weighing evidence without any shrinkage toward a presumption of the truth of each null hypothesis. That lack of shrinkage can lead to many false positives in settings with large numbers of hypotheses. A related problem is that point hypotheses cannot have more support than their alternatives. Both problems may be solved by fusing the realistic model with a model of a more restricted parameter space for use with the general law of likelihood. Applying the proposed framework of model fusion to data sets from genomics and education yields intuitively reasonable weights of evidence.     

Exact likelihood inference for two exponential populations based on a joint generalized Type-I hybrid censored sample

Following the work of Chen and Bhattacharyya [Exact confidence bounds for an exponential parameter under hybrid censoring. Comm Statist Theory Methods. 1988;17:1857–1870], several results have been developed regarding the exact likelihood inference of exponential parameters based on different forms of censored samples. In this paper, the conditional maximum likelihood estimators (MLEs) of two exponential mean parameters are derived under joint generalized Type-I hybrid censoring on the two samples. The moment generating functions (MGFs) and the exact densities of the conditional MLEs are obtained, using which exact confidence intervals are then developed for the model parameters. We also derive the means, variances, and mean squared errors of these estimates. An efficient computational method is developed based on the joint MGF. Finally, an example is presented to illustrate the methods of inference developed here.     

Bayesian exponential random graph models with nodal random effects

We extend the well-known and widely used exponential random graph model (ERGM) by including nodal random effects to compensate for heterogeneity in the nodes of a network. The Bayesian framework for ERGMs proposed by Caimo and Friel (2011) yields the basis of our modelling algorithm. A central question in network models is the question of model selection and following the Bayesian paradigm we focus on estimating Bayes factors. To do so we develop an approximate but feasible calculation of the Bayes factor which allows one to pursue model selection. Three data examples and a small simulation study illustrate our mixed model approach and the corresponding model selection.     

On the application of statistical learning approaches to construct inverse probability weights in marginal structural Cox models: Hedging against weight-model misspecification

The marginal structural Cox model (MSCM) estimates can be highly sensitive to weight-model misspecification. We assess the performance of various popular statistical learners, such as LASSO, support vector machines, CART, bagged CART, and boosted CART, in estimating MSCM weights. When weight-models are misspecified, we find that the weights computed from boosted CART generally lead to less MSE and better coverage for the MSCM estimates. This study is motivated by the investigation of the impact of beta-interferon treatment on disability progression in subjects with multiple sclerosis from British Columbia, Canada (1995–2008).