Some Bayesian and Non-Bayesian Procedures for the Analysis of Comparative Experiments and for Small-Area Estimation: Computational Aspects, Frequentist Properties, and Relationships

Hulting, Frederick L.; Harville, David A.

doi:10.2307/2290383

Cited by 10 publications

(16 citation statements)

References 21 publications

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“…In some configurations of our simulations, we observed a zero estimate almost 40% of the time (see Web Table 1). In these cases, a Bayesian procedure may produce more sensible results (Hulting and Harville, 1991; Harville and Carriquiry, 1992). We investigated a hybrid approach with initial (nonzero) Bayesian estimation of the variance component followed by pseudo‐likelihood estimation of the fixed and random effects using the Bayesian variance component estimator.…”

Section: Methodsmentioning

confidence: 99%

Hierarchical Modeling for Estimating Relative Risks of Rare Genetic Variants: Properties of the Pseudo-Likelihood Method

Capanu

Begg

2010

Biometrics

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SummaryMany major genes have been identified that strongly influence the risk of cancer. However, there are typically many different mutations that can occur in the gene, each of which may or may not confer increased risk. It is critical to identify which specific mutations are harmful, and which ones are harmless, so that individuals who learn from genetic testing that they have a mutation can be appropriately counseled. This is a challenging task, since new mutations are continually being identified, and there is typically relatively little evidence available about each individual mutation.In an earlier article we employed hierarchical modeling (Capanu et al. 2008) using the pseudolikelihood and Gibbs sampling methods to estimate the relative risks of individual rare variants using data from a case-control study and showed that one can draw strength from the aggregating power of hierarchical models to distinguish the variants that contribute to cancer risk. However, further research is needed to validate the application of asymptotic methods to such sparse data. In this article we use simulations to study in detail the properties of the pseudo-likelihood method for this purpose. We also explore two alternative approaches: pseudo-likelihood with correction for the variance component estimate as proposed by Lin and Breslow (1996) and a hybrid pseudolikelihood approach with Bayesian estimation of the variance component. We investigate the validity of these hierarchical modeling techniques by looking at the bias and coverage properties of the estimators as well as at the efficiency of the hierarchical modeling estimates relative to that of the maximum likelihood estimates. The results indicate that the estimates of the relative risks of very sparse variants have small bias, and that the estimated 95% confidence intervals are typically anti-conservative, though the actual coverage rates are generally above 90 per cent. The widths of the confidence intervals narrow as the residual variance in the second-stage model is reduced. The results also show that the hierarchical modeling estimates have shorter confidence intervals relative to estimates obtained from conventional logistic regression, and that these relative improvements increase as the variants become more rare.

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Section: Methodsmentioning

confidence: 99%

Hierarchical Modeling for Estimating Relative Risks of Rare Genetic Variants: Properties of the Pseudo-Likelihood Method

Capanu

Begg

2010

Biometrics

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“…Thus, the prediction intervals for the specific underlying relative risk of a subregion can be constructed using the normal distribution to set the boundaries. However, θ must be replaced by in g 1 j ( θ ) and g 2 j ( θ ), therefore the estimator of the MSE might be biased and a Student's t ‐distribution would be more appropriate (Hulting and Harville, 1991); , where p is the number of parameters to be estimated in the model. Thus, the proposal for the adjusted SE is given by SE 1 = (MSE 1 ) 1/2 .…”

Section: Detection Of Extreme Risksmentioning

confidence: 99%

“…Booth and Hobert (1998) also provide a bias correction using bootstrap methodology for GLMM. We took the bias induced in our study into account by implementing prediction intervals using a Student's t ‐distribution instead of the normal approximation, which provides wider intervals (Hulting and Harville, 1991).…”

Section: Final Remarks and Conclusionmentioning

confidence: 99%

Detection of Significant Disease Risks Using a Spatial Conditional Autoregressive Model

2008

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The conditional autoregressive (CAR) model is widely used to describe the geographical distribution of a specific disease risk in lattice mapping. Successful developments based on frequentist and Bayesian procedures have been extensively applied to obtain two-stage disease risk predictions at the subregional level. Bayesian procedures are preferred for making inferences, as the posterior standard errors (SE) of the two-stage prediction account for the variability in the variance component estimates; however, some recent work based on frequentist procedures and the use of bootstrap adjustments for the SE has been undertaken. In this article we investigate the suitability of an analytical adjustment for disease risk inference that provides accurate interval predictions by using the penalized quasilikelihood (PQL) technique to obtain model parameter estimates. The method is a first-order approximation of the naive SE based on a Taylor expansion and is interpreted as a conditional measure of variability providing conditional calibrated prediction intervals, given the data. We conduct a simulation study to demonstrate how the method can be used to estimate the specific subregion risk by interval. We evaluate the proposed methodology by analyzing the commonly used example data set of lip cancer incidence in the 56 counties of Scotland for the period 1975-1980. This evaluation reveals a close similarity between the solutions provided by the method proposed here and those of its fully Bayesian counterpart.

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“…Following Hulting and Harville (1991), let us consider a subset of the data in Table 2 of Westlake (1974). These data are from a comparative bioavailability study in which each of 12 patients received one of four formulations of lithium carbonate (A, B, C or D) on Day 1 and a second one of the four on Day 8.…”

Section: Example: Lithium Carbonate Bioequivalence Studymentioning

confidence: 99%

“…However, for purposes of illustration, it is supposed that patients 2, 5, 6 and 9 dropped out of the study prior to Day 8, thereby destroying the balance. With this Following Hulting and Harville (1991), we focus on inference about the mean hectares of corn per segment for the 12 counties represented in the sample. Let represent the reported hectares of corn for the jth segment in the ith county, and let xi^j and X2ij represent the number of satellite pixels in that segment clas sified as corn and soybeans, respectively.…”

Section: Example: Lithium Carbonate Bioequivalence Studymentioning

confidence: 99%

Inference about the fixed and random effects in a mixed-effects linear model: an approximate Bayesian approach

Zimmermann

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A.2 Proof of Identity 2.3 A.3 Integrating/3 out of s I y) 130 A.4 Derivation of Expression (2.24) modification, the data are those presented in Table 1.1. Let yj^j represent the natural logarithm of the serum level of lithium in the blood of the jth patient subsequent to receiving the ith formulation. Following Hulting and Harville (1991), the model is taken to be Vij = M + /5i + + Pj + e^j, where m equals 1 or 2 depending on whether the j'th patient received the ith formu lation on Day 1 or Day 8. The formulation effects ... ,/3^) and day effects and ^2) s-re considered fixed, while the patient effects are considered random. Thus, ...,P22 ^re normally distributed random variables that are statistically indepen dent of each other and of the ejj's and that have mean 0 and variance and the ejj's are normally and independently distributed with mean 0 and variance cr^. This model (when appropriately reparameterized) is expressible as a special case of model (1.1). Formulation D was the standard formulation, while A, B, and C were new formu lations. The objective of the experiment was to make inferences about the contrasts A vs. D, B vs. D, and C vs. D, that is, about Pi-/?2-P4., and (3^-Note that each of these is a linear combination of the fixed effects only. 1.1.2 Example: Crop area prediction This example was first considered by Battese, Harter, and Fuller (1988), and was later considered by Hulting and Harville (1991). The general problem is one of small-area estimation. The data consist of two determinations of the area planted to corn and soybeans for a sample of land segments in 12 north-central Iowa counties.

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Some Bayesian and Non-Bayesian Procedures for the Analysis of Comparative Experiments and for Small-Area Estimation: Computational Aspects, Frequentist Properties, and Relationships

Cited by 10 publications

References 21 publications

Hierarchical Modeling for Estimating Relative Risks of Rare Genetic Variants: Properties of the Pseudo-Likelihood Method

Hierarchical Modeling for Estimating Relative Risks of Rare Genetic Variants: Properties of the Pseudo-Likelihood Method

Detection of Significant Disease Risks Using a Spatial Conditional Autoregressive Model

Inference about the fixed and random effects in a mixed-effects linear model: an approximate Bayesian approach

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