A Comparison of Marginal Likelihood Computation Methods

In a Bayesian analysis, different models can be compared on the basis of theexpected or marginal likelihood they attain. Many methods have been devised to compute themarginal likelihood, but simplicity is not the strongest point of most methods. At the sametime, the precision of methods is often questionable.In this paper several methods are presented in a common framework. The explanation of thedifferences is followed by an application, in which the precision of the methods is testedon a simple regression model where a comparison with analytical results is possible

A New Bayesian Test to Test for the Intractability-Countering Hypothesis

We present a new test of hypothesis in which we seek the probability of the null conditioned on the data, where the null is a simplification undertaken to counter the intractability of the more complex model, that the simpler null model is nested within. With the more complex model rendered intractable, the null model uses a simplifying assumption that capacitates the learning of an unknown parameter vector given the data. Bayes factors are shown to be known only up to a ratio of unknown data-dependent constants--a problem that cannot be cured using prescriptions similar to those suggested to solve the problem caused to Bayes factor computation, by non-informative priors. Thus, a new test is needed in which we can circumvent Bayes factor computation. In this test, we undertake generation of data from the model in which the null hypothesis is true and can achieve support in the measured data for the null by comparing the marginalised posterior of the model parameter given the measured data, to that given such generated data. However, such a ratio of marginalised posteriors can confound interpretation of comparison of support in one measured data for a null, with that in another data set for a different null. Given an application in which such comparison is undertaken, we alternatively define support in a measured data set for a null by identifying the model parameters that are less consistent with the measured data than is minimally possible given the generated data, and realising that the higher the number of such parameter values, less is the support in the measured data for the null. Then, the probability of the null conditional on the data is given within an MCMC-based scheme, by marginalising the posterior given the measured data, over parameter values that are as, or more consistent with the measured data, than with the generated data.Comment: Accepted for publication in JAS

The Impact of Training on Productivity and Wages - Evidence from Belgian Firm Level Panel Data

This paper uses longitudinal data of more than 13,000 firms to analyze the effects of on-the-job training on firm level productivity and wages. Workers receiving training are on average more productive than workers not receiving training. This makes firms more productive. On-the-job training increases firm level measured productivity between 1 and 2%, compared to firms that do not provide training. The effect of training on wages is also positive, but much lower than the effect on productivity. Average wages increase only by 0.5%. Sectoral spillovers between firms that train workers are found, but only in firms active in the manufacturing sector. In non-manufacturing no spillovers seem to take place. The results are consistent with recent theories that explain on-the-job training, related to imperfect competition in the labor market, such as monopsony and union bargaining

Cell killing and resistance in pre-operative breast cancer chemotherapy

<p>Abstract</p> <p>Background</p> <p>Despite the recent development of technologies giving detailed images of tumours <it>in vivo</it>, direct or indirect ways to measure how many cells are actually killed by a treatment or are resistant to it are still beyond our reach.</p> <p>Methods</p> <p>We designed a simple model of tumour progression during treatment, based on descriptions of the key phenomena of proliferation, quiescence, cell killing and resistance, and giving as output the macroscopically measurable tumour volume and growth fraction. The model was applied to a database of the time course of volumes of breast cancer in patients undergoing pre-operative chemotherapy, for which the initial estimate of proliferating cells by the measure of the percentage of Ki67-positive cells was available.</p> <p>Results</p> <p>The analysis recognises different patterns of response to treatment. In one subgroup of patients the fitting implied drug resistance. In another subgroup there was a shift to higher sensitivity during the therapy. In the subgroup of patients where killing of cycling cells had the highest score, the drugs showed variable efficacy against quiescent cells.</p> <p>Conclusion</p> <p>The approach was feasible, providing items of information not otherwise available. Additional data, particularly sequential Ki67 measures, could be added to the system, potentially reducing uncertainty in estimates of parameter values.</p

Comparing methods to estimate treatment effects on a continuous outcome in multicentre randomized controlled trials: A simulation study

<p>Abstract</p> <p>Background</p> <p>Multicentre randomized controlled trials (RCTs) routinely use randomization and analysis stratified by centre to control for differences between centres and to improve precision. No consensus has been reached on how to best analyze correlated continuous outcomes in such settings. Our objective was to investigate the properties of commonly used statistical models at various levels of clustering in the context of multicentre RCTs.</p> <p>Methods</p> <p>Assuming no treatment by centre interaction, we compared six methods (ignoring centre effects, including centres as fixed effects, including centres as random effects, generalized estimating equation (GEE), and fixed- and random-effects centre-level analysis) to analyze continuous outcomes in multicentre RCTs using simulations over a wide spectrum of intraclass correlation (ICC) values, and varying numbers of centres and centre size. The performance of models was evaluated in terms of bias, precision, mean squared error of the point estimator of treatment effect, empirical coverage of the 95% confidence interval, and statistical power of the procedure.</p> <p>Results</p> <p>While all methods yielded unbiased estimates of treatment effect, ignoring centres led to inflation of standard error and loss of statistical power when within centre correlation was present. Mixed-effects model was most efficient and attained nominal coverage of 95% and 90% power in almost all scenarios. Fixed-effects model was less precise when the number of centres was large and treatment allocation was subject to chance imbalance within centre. GEE approach underestimated standard error of the treatment effect when the number of centres was small. The two centre-level models led to more variable point estimates and relatively low interval coverage or statistical power depending on whether or not heterogeneity of treatment contrasts was considered in the analysis.</p> <p>Conclusions</p> <p>All six models produced unbiased estimates of treatment effect in the context of multicentre trials. Adjusting for centre as a random intercept led to the most efficient treatment effect estimation across all simulations under the normality assumption, when there was no treatment by centre interaction.</p

A semiparametric Bayesian proportional hazards model for interval censored data with frailty effects

<p>Abstract</p> <p>Background</p> <p>Multivariate analysis of interval censored event data based on classical likelihood methods is notoriously cumbersome. Likelihood inference for models which additionally include random effects are not available at all. Developed algorithms bear problems for practical users like: matrix inversion, slow convergence, no assessment of statistical uncertainty.</p> <p>Methods</p> <p>MCMC procedures combined with imputation are used to implement hierarchical models for interval censored data within a Bayesian framework.</p> <p>Results</p> <p>Two examples from clinical practice demonstrate the handling of clustered interval censored event times as well as multilayer random effects for inter-institutional quality assessment. The software developed is called survBayes and is freely available at CRAN.</p> <p>Conclusion</p> <p>The proposed software supports the solution of complex analyses in many fields of clinical epidemiology as well as health services research.</p

Random effects diagonal metric multidimensional scaling models

By assuming a distribution for the subject weights in a diagonal metric (INDSCAL) multidimensional scaling model, the subject weights become random effects. Including random effects in multidimensional scaling models offers several advantages over traditional diagonal metric models such as those fitted by the INDSCAL, ALSCAL, and other multidimensional scaling programs. Unlike traditional models, the number of parameters does not increase with the number of subjects, and, because the distribution of the subject weights is modeled, the construction of linear models of the subject weights and the testing of those models is immediate. Here we define a random effects diagonal metric multidimensional scaling model, give computational algorithms, describe our experiences with these algorithms, and provide an example illustrating the use of the model and algorithms.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45758/1/11336_2005_Article_BF02295730.pd

Internally coupled ears in living mammals.

It is generally held that the right and left middle ears of mammals are acoustically isolated from each other, such that mammals must rely on neural computation to derive sound localisation cues. There are, however, some unusual species in which the middle ear cavities intercommunicate, in which case each ear might be able to act as a pressure-difference receiver. This could improve sound localisation at lower frequencies. The platypus Ornithorhynchus is apparently unique among mammals in that its tympanic cavities are widely open to the pharynx, a morphology resembling that of some non-mammalian tetrapods. The right and left middle ear cavities of certain talpid and golden moles are connected through air passages within the basicranium; one experimental study on Talpa has shown that the middle ears are indeed acoustically coupled by these means. Having a basisphenoid component to the middle ear cavity walls could be an important prerequisite for the development of this form of interaural communication. Little is known about the hearing abilities of platypus, talpid and golden moles, but their audition may well be limited to relatively low frequencies. If so, these mammals could, in principle, benefit from the sound localisation cues available to them through internally coupled ears. Whether or not they actually do remains to be established experimentally.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s00422-015-0675-