Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

A zero-augmented gamma mixed model for longitudinal data with many zeros

In many occupational safety interventions, the objective is to reduce the injury incidence as well as the mean claims cost once injury has occurred. The claims cost data within a period typically contain a large proportion of zero observations (no claim). The distribution thus comprises a point mass at 0 mixed with a non-degenerate parametric component. Essentially, the likelihood function can be factorized into two orthogonal components. These two components relate respectively to the effect of covariates on the incidence of claims and the magnitude of claims, given that claims are made. Furthermore, the longitudinal nature of the intervention inherently imposes some correlation among the observations. This paper introduces a zero-augmented gamma random effects model for analysing longitudinal data with many zeros. Adopting the generalized linear mixed model (GLMM) approach reduces the original problem to the fitting of two independent GLMMs. The method is applied to evaluate the effectiveness of a workplace risk assessment teams program, trialled within the cleaning services of a Western Australian public hospital.

Transitional dynamics of an endogenous growth model with an erosion effect

The convergence features of an Endogenous Growth model with Physical capital, Human Capital and R&D have been studied. We add an erosion effect (supported by empirical evidence) to this model, and fully characterize its convergence properties. The dynamics is described by a fourth-order system of differential equations. We show that the model converges along a one-dimensional stable manifold and that its equilibrium is saddle-path stable. We also argue that one of the implications of considering this “erosion effect” is the increase in the adherence of the model to data.

The Effect of Four-Lane to Three-Lane Conversion on the Number of Crashes and Crash Rates in Iowa Roads, June 2005

We analyze crash data collected by the Iowa Department of Transportation using Bayesian methods. The data set includes monthly crash numbers, estimated monthly traffic volumes, site length and other information collected at 30 paired sites in Iowa over more than 20 years during which an intervention experiment was set up. The intervention consisted in transforming 15 undivided road segments from four-lane to three lanes, while an additional 15 segments, thought to be comparable in terms of traffic safety-related characteristics were not converted. The main objective of this work is to find out whether the intervention reduces the number of crashes and the crash rates at the treated sites. We fitted a hierarchical Poisson regression model with a change-point to the number of monthly crashes per mile at each of the sites. Explanatory variables in the model included estimated monthly traffic volume, time, an indicator for intervention reflecting whether the site was a “treatment” or a “control” site, and various interactions. We accounted for seasonal effects in the number of crashes at a site by including smooth trigonometric functions with three different periods to reflect the four seasons of the year. A change-point at the month and year in which the intervention was completed for treated sites was also included. The number of crashes at a site can be thought to follow a Poisson distribution. To estimate the association between crashes and the explanatory variables, we used a log link function and added a random effect to account for overdispersion and for autocorrelation among observations obtained at the same site. We used proper but non-informative priors for all parameters in the model, and carried out all calculations using Markov chain Monte Carlo methods implemented in WinBUGS. We evaluated the effect of the four to three-lane conversion by comparing the expected number of crashes per year per mile during the years preceding the conversion and following the conversion for treatment and control sites. We estimated this difference using the observed traffic volumes at each site and also on a per 100,000,000 vehicles. We also conducted a prospective analysis to forecast the expected number of crashes per mile at each site in the study one year, three years and five years following the four to three-lane conversion. Posterior predictive distributions of the number of crashes, the crash rate and the percent reduction in crashes per mile were obtained for each site for the months of January and June one, three and five years after completion of the intervention. The model appears to fit the data well. We found that in most sites, the intervention was effective and reduced the number of crashes. Overall, and for the observed traffic volumes, the reduction in the expected number of crashes per year and mile at converted sites was 32.3% (31.4% to 33.5% with 95% probability) while at the control sites, the reduction was estimated to be 7.1% (5.7% to 8.2% with 95% probability). When the reduction in the expected number of crashes per year, mile and 100,000,000 AADT was computed, the estimates were 44.3% (43.9% to 44.6%) and 25.5% (24.6% to 26.0%) for converted and control sites, respectively. In both cases, the difference in the percent reduction in the expected number of crashes during the years following the conversion was significantly larger at converted sites than at control sites, even though the number of crashes appears to decline over time at all sites. Results indicate that the reduction in the expected number of sites per mile has a steeper negative slope at converted than at control sites. Consistent with this, the forecasted reduction in the number of crashes per year and mile during the years after completion of the conversion at converted sites is more pronounced than at control sites. Seasonal effects on the number of crashes have been well-documented. In this dataset, we found that, as expected, the expected number of monthly crashes per mile tends to be higher during winter months than during the rest of the year. Perhaps more interestingly, we found that there is an interaction between the four to three-lane conversion and season; the reduction in the number of crashes appears to be more pronounced during months, when the weather is nice than during other times of the year, even though a reduction was estimated for the entire year. Thus, it appears that the four to three-lane conversion, while effective year-round, is particularly effective in reducing the expected number of crashes in nice weather.

Designs and model effects definitions in the initial stage of a plant breeding program

The objective of this work was to compare the relative efficiency of initial selection and genetic parameter estimation, using augmented blocks design (ABD), augmented blocks twice replicated design (DABD) and group of randomised block design experiments with common treatments (ERBCT), by simulations, considering fixed effect model and mixed model with regular treatment effects as random. For the simulations, eight different conditions (scenarios) were considered. From the 600 simulations in each scenario, the mean percentage selection coincidence, the Pearsons´s correlation estimates between adjusted means for the fixed effects model, and the heritability estimates for the mixed model were evaluated. DABD and ERBCT were very similar in their comparisons and slightly superior to ABD. Considering the initial stages of selection in a plant breeding program, ABD is a good alternative for selecting superior genotypes, although none of the designs had been effective to estimate heritability in all the different scenarios evaluated.

Random regression models to estimate genetic parameters for milk production of Guzerat cows using orthogonal Legendre polynomials

The objective of this work was to compare random regression models for the estimation of genetic parameters for Guzerat milk production, using orthogonal Legendre polynomials. Records (20,524) of test-day milk yield (TDMY) from 2,816 first-lactation Guzerat cows were used. TDMY grouped into 10-monthly classes were analyzed for additive genetic effect and for environmental and residual permanent effects (random effects), whereas the contemporary group, calving age (linear and quadratic effects) and mean lactation curve were analized as fixed effects. Trajectories for the additive genetic and permanent environmental effects were modeled by means of a covariance function employing orthogonal Legendre polynomials ranging from the second to the fifth order. Residual variances were considered in one, four, six, or ten variance classes. The best model had six residual variance classes. The heritability estimates for the TDMY records varied from 0.19 to 0.32. The random regression model that used a second-order Legendre polynomial for the additive genetic effect, and a fifth-order polynomial for the permanent environmental effect is adequate for comparison by the main employed criteria. The model with a second-order Legendre polynomial for the additive genetic effect, and that with a fourth-order for the permanent environmental effect could also be employed in these analyses.

Bayesian analysis of an inverse Gaussian correlated frailty model

In survival analysis frailty is often used to model heterogeneity between individuals or correlation within clusters. Typically frailty is taken to be a continuous random effect, yielding a continuous mixture distribution for survival times. A Bayesian analysis of a correlated frailty model is discussed in the context of inverse Gaussian frailty. An MCMC approach is adopted and the deviance information criterion is used to compare models. As an illustration of the approach a bivariate data set of corneal graft survival times is analysed. (C) 2006 Elsevier B.V. All rights reserved.

Estimation of genetic parameters for partial egg production periods by means of random regression models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Variance component estimates applying random regression models for test-day milk yield in Caracu heifers (Bos taurus Artiodactyla, Bovidae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The effect of refuge on Dermestes ater (Coleoptera : Dermestidae) predation on Musca domestica (Diptera : Muscidae): Refuge for prey or the predator?

It is believed that habitat heterogeneity can change the extent of predator-prey interactions. Therefore, in this study we examined the effect of habitat heterogeneity (characterized here as an addition of refuge) on D. ater predation on M. domestica. Predation of D. ater on M. domestica larvae was carried out in experimental habitats with and without refuge, and examined at different prey densities. The number of prey eaten by beetles over 24 h of predator-prey interaction was recorded, and we investigated the strength of interaction between prey and predator in both experimental habitats by determining predator functional response. The mean number of prey eaten by beetles in the presence of refuge was significantly higher than in the absence of refuge. Females had greater weight gains than males. Logistic regression analyses revealed the type II functional response for both experimental habitats, even though data did not fit well into the random predator model. Results suggest that the addition of refuge in fact enhanced predation, as prey consumption increased in the presence of refuge. Predators kept in the presence of refuge also consumed more prey at high prey densities. Thus, we concluded that the addition of refuge was an important component mediating D. ater-M. domestica population interactions. Refuge actually acted as a refuge for predators from prey, since prey behaviors detrimental to predators were reduced in this case.

The effect of adhesive and flowable composite on postoperative sensitivity: 2-Week results

Objective: To measure 2-week postoperative sensitivity in Class II composite restorations placed with a self-etching adhesive (Clearfil SE Bond) or a total-etch adhesive (Prime&Bond NT) with or without a flowable composite as cervical increment. Method and materials: Upon approval by the University of Guarulhos Committee on Human Subjects, 100 restorations were inserted in 46 patients who required Class II restorations in their molars and premolars. Enamel and dentin walls were conditioned with a self-etching primer (for Clearfil SE Bond) or etched with 34% phosphoric acid (for Prime&Bond NT). A 1- to 2-mm-thick increment of a flowable composite (Filtek Flow) was used in the proximal box in 50% of the restorations of each adhesive. Preparations were restored with a packable composite (Surefil). The restorations were evaluated preoperatively and 2 weeks postoperatively for sensitivity to cold, air, and masticatory forces using a visual analog scale. Marginal integrity of the accessible margins was also evaluated. Statistical analysis used a mixed linear model with subject as a random effect. Results: Ninety-eight teeth from 44 subjects were observed at 2 weeks. The type of adhesive and use of flowable composite had no significant effects or interaction for any of the four outcomes of interest, ie, change from baseline to 2 weeks in sensitivity and response time for the cold or air stimulus. For the air stimulus, the overall average change from baseline was not significant for either sensitivity or response time. For the cold stimulus, the overall average change from baseline was significant for both sensitivity and response time. No case of sensitivity to masticatory forces was observed. Conclusion: No differences in postoperative sensitivity were observed between a self-etch adhesive and a total-etch adhesive at 2 weeks. The use of flowable composite did not decrease postoperative sensitivity.

Random regression models to estimate genetic parameters for milk production of Guzerat cows using orthogonal Legendre polynomials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Multilevel Model with Time Series Components for the Analysis of Tribal Art Prices

In the present work we perform an econometric analysis of the Tribal art market. To this aim, we use a unique and original database that includes information on Tribal art market auctions worldwide from 1998 to 2011. In Literature, art prices are modelled through the hedonic regression model, a classic fixed-effect model. The main drawback of the hedonic approach is the large number of parameters, since, in general, art data include many categorical variables. In this work, we propose a multilevel model for the analysis of Tribal art prices that takes into account the influence of time on artwork prices. In fact, it is natural to assume that time exerts an influence over the price dynamics in various ways. Nevertheless, since the set of objects change at every auction date, we do not have repeated measurements of the same items over time. Hence, the dataset does not constitute a proper panel; rather, it has a two-level structure in that items, level-1 units, are grouped in time points, level-2 units. The main theoretical contribution is the extension of classical multilevel models to cope with the case described above. In particular, we introduce a model with time dependent random effects at the second level. We propose a novel specification of the model, derive the maximum likelihood estimators and implement them through the E-M algorithm. We test the finite sample properties of the estimators and the validity of the own-written R-code by means of a simulation study. Finally, we show that the new model improves considerably the fit of the Tribal art data with respect to both the hedonic regression model and the classic multilevel model.

Effect of initial treatment strategy on survival of patients with advanced-stage Hodgkin's lymphoma: a systematic review and network meta-analysis

BACKGROUND Several treatment strategies are available for adults with advanced-stage Hodgkin's lymphoma, but studies assessing two alternative standards of care-increased dose bleomycin, etoposide, doxorubicin, cyclophosphamide, vincristine, procarbazine, and prednisone (BEACOPPescalated), and doxorubicin, bleomycin, vinblastine, and dacarbazine (ABVD)-were not powered to test differences in overall survival. To guide treatment decisions in this population of patients, we did a systematic review and network meta-analysis to identify the best initial treatment strategy. METHODS We searched the Cochrane Library, Medline, and conference proceedings for randomised controlled trials published between January, 1980, and June, 2013, that assessed overall survival in patients with advanced-stage Hodgkin's lymphoma given BEACOPPbaseline, BEACOPPescalated, BEACOPP variants, ABVD, cyclophosphamide (mechlorethamine), vincristine, procarbazine, and prednisone (C[M]OPP), hybrid or alternating chemotherapy regimens with ABVD as the backbone (eg, COPP/ABVD, MOPP/ABVD), or doxorubicin, vinblastine, mechlorethamine, vincristine, bleomycin, etoposide, and prednisone combined with radiation therapy (the Stanford V regimen). We assessed studies for eligibility, extracted data, and assessed their quality. We then pooled the data and used a Bayesian random-effects model to combine direct comparisons with indirect evidence. We also reconstructed individual patient survival data from published Kaplan-Meier curves and did standard random-effects Poisson regression. Results are reported relative to ABVD. The primary outcome was overall survival. FINDINGS We screened 2055 records and identified 75 papers covering 14 eligible trials that assessed 11 different regimens in 9993 patients, providing 59 651 patient-years of follow-up. 1189 patients died, and the median follow-up was 5·9 years (IQR 4·9-6·7). Included studies were of high methodological quality, and between-trial heterogeneity was negligible (τ(2)=0·01). Overall survival was highest in patients who received six cycles of BEACOPPescalated (HR 0·38, 95% credibility interval [CrI] 0·20-0·75). Compared with a 5 year survival of 88% for ABVD, the survival benefit for six cycles of BEACOPPescalated is 7% (95% CrI 3-10)-ie, a 5 year survival of 95%. Reconstructed individual survival data showed that, at 5 years, BEACOPPescalated has a 10% (95% CI 3-15) advantage over ABVD in overall survival. INTERPRETATION Six cycles of BEACOPPescalated significantly improves overall survival compared with ABVD and other regimens, and thus we recommend this treatment strategy as standard of care for patients with access to the appropriate supportive care.