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- Review by Adam Pendleton and Madison Johnson
- The authors are to be commended for using a Bayesian approach for making inferences from logistic regression models
- The Bayesian approach allowed the authors to calculate direct probabilities of interesting things, unlike P-values which are probabilities of getting results more impressive than the observed results if nothing interesting is going on
- The paper computes posterior probabilities of being a risk factor
- Credible intervals are given for effects of regressors; these are the Bayesian analogs of confidence intervals but have a much simpler interpretation

- Bayes allows one to make exact inference, unlike traditional frequentist inference in which everything outside of ordinary regression uses approximations
- The authors used a wide distribution (Cauchy) as the prior distribution for each regression coefficient, after arbitrary scaling of the covariate
- They used the R
`arm`

package for the calculations. This package actually uses a rough approximation to full Bayes analysis by assuming that regression coefficients from an ordinary logistic model fit have a multivariate normal distribution. For logistic regression, such approximations are poor. The authors should have used exact Bayesian methods (e.g., the R package`MCMCpack`

). - They used model averaging which was not needed at all in this context
- The authors are confused about statistical terminology.
*Multivariate*was used to refer to multivariable (adjusted) analyses but should be reserved to refer only to the case where one is simulatneously analyzing multiple dependent variables

- Variation in glycohemoglobin explained by various risk factors. From
*Regression Modeling Strategies, second edition*by FE Harrell, 2015:

`size`

entry sums the influence of leg length, subscapular skinfold thickness, tricep skinfold thickness, and waist circumference. `re`

is a combined race + ethnicity multiple degree of freedom effect. Here the measure of explained variation is the Wald chi-square statistic minus the number of degrees of freedom required to achieve that chi-square. The subtraction is to level the playing field so that risk factors having many categories do not get more changes to explain variation in the outcome variable. I | Attachment | Action | Size | Date | Who | Comment |
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html | pendletonJohnsonReview.html | manage | 33.8 K | 21 Oct 2015 - 06:45 | FrankHarrell | Review of Am J Psychiatry March 2015 by Pendleton and Johnson |

png | anova.png | manage | 18.0 K | 18 Oct 2015 - 10:12 | FrankHarrell | Variation in glycohemoglobin explained by various risk factors |

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