Lower Bounds on Bayes Factors for Multinomial Distributions, with Application to Chi-Squared Tests of Fit

Delampady, Mohan; Berger, James O.

doi:10.1214/aos/1176347750

Cited by 40 publications

(24 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Bayes factors actually provide a more direct measure of the strength of evidence than do p values. (30) The polymorphisms that exhibited strong evidence of association by Bayes factors in our data were a subset of the same ones that had significant (p < 0.05) associations.…”

Section: Discussionmentioning

confidence: 62%

“…Although several SNPs had a significant association (p < 0.05) with this PC, Bayes factors did not indicate strong evidence of association. SN-38 elimination (PC 8, k 30 in Figure 1) was associated with a SNP in the ABCC2 gene. A SNP in the SLCO1 gene and one in the ABCC1 gene had a significant association with this PC (p<0.05).…”

Section: Statistical Modelmentioning

confidence: 99%

“…One compartment corresponded to plasma, and two compartments (bile and gut) characterized EHR. Specifically, k SN (1/hr) described the formation of SN-38 from irinotecan, and k 30 (1/hr) described the elimination of SN-38. The transition of SN-38 from plasma to bile is described by k 3B (1/hr), and k BG +k BG1 (1/hr) characterizes the transition of SN-38 from the bile to the gut.…”

Section: Pharmacokineticsmentioning

confidence: 99%

See 2 more Smart Citations

Pharmacogenetic Pathway Analysis of Irinotecan

Rosner

Panetta

Innocenti

et al. 2008

Clin Pharmacol Ther

View full text Add to dashboard Cite

Irinotecan, a chemotherapeutic agent for various solid tumors, is a prodrug requiring activation to SN-38. Irinotecan's complex pharmacokinetics allows for potentially many genetic sources of variability. We explored relationships between pharmacokinetic pathways and polymorphisms in genes associated with irinotecan's metabolism and transport. We fit a seven-compartment pharmacokinetic model with enterohepatic recirculation to concentrations of irinotecan and metabolites SN-38, SN-38G (glucuronide), and APC. Principal component analysis (PCA) of patientspecific parameter estimates produced measures interpretable along pathways. Nine principal components characterized overall variation well. Polymorphisms in genes UGT1A1, UGT1A7, and UGT1A9 had strong associations with a component corresponding to the irinotecan-to-SN-38 pathway and SN-38 recirculation and to a component relating to SN-38-to-SN-38G conversion and SN-38G's elimination. The component characterizing irinotecan's compartments was associated with HNF1α and ABCC2 polymorphisms. The exploratory analysis with PCA in this pharmacogenetic analysis identified known associations and may have allowed identification of previously uncharacterized functional polymorphisms.

show abstract

Section: Discussionmentioning

confidence: 62%

Section: Statistical Modelmentioning

confidence: 99%

Section: Pharmacokineticsmentioning

confidence: 99%

See 1 more Smart Citation

Pharmacogenetic Pathway Analysis of Irinotecan

Rosner

Panetta

Innocenti

et al. 2008

Clin Pharmacol Ther

View full text Add to dashboard Cite

show abstract

“…Sedransk, Monahan, and Chiu (1985) considered estimation of multinomial probabilities under the constraint π 1 ≤ ... ≤ π k ≥ π k+1 ≥ ... ≥ π c , using a truncated Dirichlet prior and possibly a prior on k if it is unknown. Delampady and Berger (1990) derived lower bounds on Bayes factors in favor of the null hypothesis of a point multinomial probability, and related them to P -values in chi-squared tests. Bernardo and Ramón (1998) illustrated Bernardo's reference analysis approach by applying it to the problem of estimating the ratio π i /π j of two multinomial parameters.…”

Section: Bayesian Estimation Of Multinomial Parametersmentioning

confidence: 99%

Bayesian inference for categorical data analysis

Agresti

Hitchcock

2005

JISS

133

View full text Add to dashboard Cite

This article surveys Bayesian methods for categorical data analysis, with primary emphasis on contingency table analysis. Early innovations were proposed by Good (1953Good ( , 1956Good ( , 1965 for smoothing proportions in contingency tables and by Lindley (1964) for inference about odds ratios. These approaches primarily used conjugate beta and Dirichlet priors. Altham (1969Altham ( , 1971 presented Bayesian analogs of small-sample frequentist tests for 2×2 tables using such priors. An alternative approach using normal priors for logits received considerable attention in the 1970s by Leonard and others (e.g., Leonard 1972). Adopted usually in a hierarchical form, the logit-normal approach allows greater flexibility and scope for generalization. The 1970s also saw considerable interest in loglinear modeling. The advent of modern computational methods since the mid-1980s has led to a growing literature on fully Bayesian analyses with models for categorical data, with main emphasis on generalized linear models such as logistic regression for binary and multi-category response variables.

show abstract

“…However, the P-value can be highly misleading as a measure of the evidence provided by the data against the null hypothesis. This was demonstrated by Edwards, Lindman and Savage (1963), Berger and Sellke (1987), Berger and Delampady (1987) and Delampady and Berger (1990) who have reviewed the practicality of the P-value and explored the dramatic conflict between the P-value and other data dependent measures of evidence.…”

mentioning

confidence: 99%

Properties of Unified Bayesian-Frequentist Tests

Berger

Boukai

Wang

1997

Advances in Statistical Decision Theory and Applications

View full text Add to dashboard Cite

The modified Bayesian-Frequentist test of Berger, Brown and Wolpert (1994) is considered here in the context of normal hypothesis testing. We focus attention on the testing of a precise null hypothesis versus a composite alternative, either the one-sided or the two-sided type. We study the properties of the corresponding modified Bayesian-Frequentist test and in particular the large-sample behavior of its no decision region under two different classes of prior distributions, viz., the shifted conjugate class and a domain-restricted noninformative class. It is shown that under these prior classes, the size of the no-decision region of the test is rather small, compared to the relevant sample size. A lower bound on the conditional probability of the type I error is also provided.

show abstract

Lower Bounds on Bayes Factors for Multinomial Distributions, with Application to Chi-Squared Tests of Fit

Cited by 40 publications

References 0 publications

Pharmacogenetic Pathway Analysis of Irinotecan

Pharmacogenetic Pathway Analysis of Irinotecan

Bayesian inference for categorical data analysis

Properties of Unified Bayesian-Frequentist Tests

Contact Info

Product

Resources

About