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Analyses were carried out for the estimation of (co)variance components and genetic parameters for birth weight (BWT), 6-month weight (6WT), 12-month weight (12WT), 18-month weight (18WT), 24-month weight (24WT), 30-month weight (30WT), 36-month weight (36WT), weight at first service (WFS), and weight at first calving(WFC) in Sahiwal cattle. Data for 802 lifetime records (raw data) were collected over a period of 30 years (1990-2019) for various growth traits in the herd for Sahiwal cows maintained at the livestock farm unit of ICAR-NDRI Karnal, Haryana, India. Bayesian estimates using the multi-trait Gibbs sampling animal model approach were calculated in the present study. Total heritability for BWT, 6WT, 12WT, 18WT, 24WT, 30WT, 36WT, WFS, and WFC by Bayesian modeling was estimated as 0.22 ± 0.0052, 0.47 ± 0.0037, 0.30 ± 0.0025, 0.65 ± 0.0021, 0.32 ± 0.0039, 0.33 ± 0.0027, 0.39 ± 0.0031, 0.49 ± 0.0020, and 0.57 ± 0.0023, respectively, along with its Monte Carlo error in Sahiwal cattle. Direct genetic covariances between body weight traits were ranging from - 2762.5 for 18WT and WFC to 4739.6 between WFS and WFC. Environmental covariances were ranging from - 169.98 for 30WT and 36WT to 4539.4 between WFS and WFC. Family relationships as well as the existing interaction effects between two or more traits in opposite direction effect lead to negative estimates for genetic covariances between some of the combinations with various growth traits. Although most of the estimates for posteriori were somewhat skewed, the marginalization effect enabled them to fit into the Gaussian distribution, by comparing the mean, mode, and median with each other. Results suggest that genetic progress through growth traits can be achieved if the selection is carried out for highly heritable 18-month weight as well as for the selection of pubertal and fertility traits, viz., 24WT, 30WT, 36WT, WFS, and WFC with a balanced feeding and optimum management.

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This paper concerns Kalman filtering when the measurements of the process are censored. The censored measurements are addressed by the Tobit model of Type I and are one-dimensional with two censoring limits, while the (hidden) state vectors are multidimensional. For this model, Bayesian estimates for the state vectors are provided through a recursive algorithm of Kalman filtering type. Experiments are presented to illustrate the effectiveness and applicability of the algorithm. The experiments show that the proposed method outperforms other filtering methodologies in minimizing the computational cost as well as the overall Root Mean Square Error (RMSE) for synthetic and real data sets.

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Nonlinear mixed-effects modeling is one of the most popular tools for analyzing repeated measurement data, particularly for applications in the biomedical fields. Multiple integration and nonlinear optimization are the two major challenges for likelihood-based methods in nonlinear mixed-effects modeling. To solve these problems, approaches based on empirical Bayesian estimates have been proposed by breaking the problem into a nonlinear mixed-effects model with no covariates and a linear regression model without random effect. This approach is time-efficient as it involves no covariates in the nonlinear optimization. However, covariate effects based on empirical Bayesian estimates are underestimated and the bias depends on the extent of shrinkage. Marginal correction method has been proposed to correct the bias caused by shrinkage to some extent. However, the marginal approach appears to be suboptimal when testing covariate effects on multiple model parameters, a situation that is often encountered in real-world data analysis. In addition, the marginal approach cannot correct the inaccuracy in the associated p-values. In this paper, we proposed a simultaneous correction method (nSCEBE), which can handle the situation where covariate analysis is performed on multiple model parameters. Simulation studies and real data analysis showed that nSCEBE is accurate and efficient for both effect-size estimation and p-value calculation compared with the existing methods. Importantly, nSCEBE can be >2000 times faster than the standard mixed-effects models, potentially allowing utilization for high-dimension covariate analysis for longitudinal or repeated measured outcomes.

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Genome-wide association studies (GWAS) using longitudinal phenotypes collected over time is appealing due to the improvement of power. However, computation burden has been a challenge because of the complex algorithms for modeling the longitudinal data. Approximation methods based on empirical Bayesian estimates (EBEs) from mixed-effects modeling have been developed to expedite the analysis. However, our analysis demonstrated that bias in both association test and estimation for the existing EBE-based methods remains an issue. We propose an incredibly fast and unbiased method (simultaneous correction for EBE, SCEBE) that can correct the bias in the naive EBE approach and provide unbiased P-values and estimates of effect size. Through application to Alzheimer's Disease Neuroimaging Initiative data with 6 414 695 single nucleotide polymorphisms, we demonstrated that SCEBE can efficiently perform large-scale GWAS with longitudinal outcomes, providing nearly 10 000 times improvement of computational efficiency and shortening the computation time from months to minutes. The SCEBE package and the example datasets are available at https://github.com/Myuan2019/SCEBE.

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In social research, investigating sensitive, highly personal or embarrassing issues by means of standard survey techniques based on direct questioning leads to refusals to answer or false responses which, generally, flaw the validity of the analyses and produce incorrect inferences. To correct biases induced by nonresponse or underreporting of sensitive matters, Warner (1965) introduced an indirect questioning approach, known as the randomized response technique, which allows researchers to estimate the proportion of individuals with sensitive attributes or behaviors, while ensuring respondents' privacy protection. In this article, we consider the randomized response model proposed by Christofides (2003) and, through a simulation and an empirical study, compare different estimation methods for the prevalence of a sensitive attribute. Specifically, we discuss how the model has been implemented in a pilot study to collect data and derive maximum likelihood and Bayesian estimates for the proportion of non-heterosexuals aged 20 years or older for the Taiwanese population and for some subgroups of it by sex and age. Our analysis, and in particular the Bayesian approach, seems to meet the expectation of social researchers and experts of sexual behaviors. In fact, the produced estimates are higher than official findings in Taiwan obtained by direct questioning in face-to-face interviews and provide a more reliable picture of sexual identity in the country. Moreover, Bayesian estimates appear more accurate than those produced by the method of moment and the maximum likelihood method.

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In time-to-event studies it is common the presence of a fraction of individuals not expecting to experience the event of interest; these individuals who are immune to the event or cured for the disease during the study are known as long-term survivors. In addition, in many studies it is observed two lifetimes associated to the same individual, and in some cases there exists a dependence structure between them. In these situations, the usual existing lifetime distributions are not appropriate to model data sets with long-term survivors and dependent bivariate lifetimes. In this study, it is proposed a bivariate model based on a Weibull standard distribution with a dependence structure based on fifteen different copula functions. We assumed the Weibull distribution due to its wide use in survival data analysis and its greater flexibility and simplicity, but the presented methods can be adapted to other continuous survival distributions. Three examples, considering real data sets are introduced to illustrate the proposed methodology. A Bayesian approach is assumed to get the inferences for the parameters of the model where the posterior summaries of interest are obtained using Markov Chain Monte Carlo simulation methods and the Openbugs software. For the data analysis considering different real data sets it was assumed fifteen different copula models from which is was possible to find models with satisfactory fit for the bivariate lifetimes in presence of long-term survivors.

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In medical studies, the monotone partial likelihood is frequently encountered in the analysis of time-to-event data using the Cox model. For example, with a binary covariate, the subjects can be classified into two groups. If the event of interest does not occur (zero event) for all the subjects in one of the groups, the resulting partial likelihood is monotone and consequently, the covariate effects are difficult to estimate. In this article, we develop both Bayesian and frequentist approaches using a data-dependent Jeffreys-type prior to handle the monotone partial likelihood problem. We first carry out an in-depth examination of the conditions of the monotone partial likelihood and then characterize sufficient and necessary conditions for the propriety of the Jeffreys-type prior. We further study several theoretical properties of the Jeffreys-type prior for the Cox model. In addition, we propose two variations of the Jeffreys-type prior: the shifted Jeffreys-type prior and the Jeffreys-type prior based on the first risk set. An efficient Markov-chain Monte Carlo algorithm is developed to carry out posterior computation. We perform extensive simulations to examine the performance of parameter estimates and demonstrate the applicability of the proposed method by analyzing real data from the SEER prostate cancer study.

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In the United States, diabetes is common and costly. Programs to prevent new cases of diabetes are often carried out at the level of the county, a unit of local government. Thus, efficient targeting of such programs requires county-level estimates of diabetes incidence-the fraction of the non-diabetic population who received their diagnosis of diabetes during the past 12 months. Previously, only estimates of prevalence-the overall fraction of population who have the disease-have been available at the county level. Counties with high prevalence might or might not be the same as counties with high incidence, due to spatial variation in mortality and relocation of persons with incident diabetes to another county. Existing methods cannot be used to estimate county-level diabetes incidence, because the fraction of the population who receive a diabetes diagnosis in any year is too small. Here, we extend previously developed methods of Bayesian small-area estimation of prevalence, using diffuse priors, to estimate diabetes incidence for all U.S. counties based on data from a survey designed to yield state-level estimates. We found high incidence in the southeastern United States, the Appalachian region, and in scattered counties throughout the western U.S. Our methods might be applicable in other circumstances in which all cases of a rare condition also must be cases of a more common condition (in this analysis, "newly diagnosed cases of diabetes" and "cases of diabetes"). If appropriate data are available, our methods can be used to estimate proportion of the population with the rare condition at greater geographic specificity than the data source was designed to provide.