aids

The data is from a 3-year study on the effects of AZT in slowing the
development of AIDS symptoms. 338 veterans whose immune systems
were beginning to falter after infection with the AIDS virus were
randomly assigned either to receive AZT immediately or to wait
until their T cells showed severe immune weakness.

datasets

Estimation and inference from generalized linear models based on various methods for bias reduction and maximum penalized likelihood with powers of the Jeffreys prior as penalty. The 'brglmFit' fitting method can achieve reduction of estimation bias by solving either the mean bias-reducing adjusted score equations in Firth (1993) <doi:10.1093/biomet/80.1.27> and Kosmidis and Firth (2009) <doi:10.1093/biomet/asp055>, or the median bias-reduction adjusted score equations in Kenne et al. (2017) <doi:10.1093/biomet/asx046>, or through the direct subtraction of an estimate of the bias of the maximum likelihood estimator from the maximum likelihood estimates as in Cordeiro and McCullagh (1991) <https://www.jstor.org/stable/2345592>. See Kosmidis et al (2020) <doi:10.1007/s11222-019-09860-6> for more details. Estimation in all cases takes place via a quasi Fisher scoring algorithm, and S3 methods for the construction of of confidence intervals for the reduced-bias estimates are provided. In the special case of generalized linear models for binomial and multinomial responses (both ordinal and nominal), the adjusted score approaches to mean and media bias reduction have been found to return estimates with improved frequentist properties, that are also always finite, even in cases where the maximum likelihood estimates are infinite (e.g. complete and quasi-complete separation; see Kosmidis and Firth, 2020 <doi:10.1093/biomet/asaa052>, for a proof for mean bias reduction in logistic regression).

Ioannis Kosmidis

brglm2

Bias Reduction in Generalized Linear Models

Kjell Konis

Nicola Sartori

aids function

A data frame with 4 rows and 4 variables:<ul>
<li><code>symptomatic</code>: counts of veterans showing AIDS symptoms during the 3-year study</li>
<li><code>asymptomatic</code>: counts of veterans not showing AIDS symptoms during the 3-year study</li>
<li><code>race</code>: the race of the veterans with levels <code>"White"</code> and <code>"Black"</code></li>
<li><code>AZT_use</code>: whether the veterans received AZT immediately (<code>"Yes"</code>)
or waited until their T cells showed severe immune weakness (<code>"No"</code>)</li>
</ul>

aids: The effects of AZT in slowing the development of AIDS symptoms

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