Firth's logistic regression has become a standard approach for the analysis of binary outcomes with small samples. Whereas it reduces the bias in maximum likelihood estimates of coefficients, bias towards one-half is introduced in the predicted probabilities. The stronger the imbalance of the outcome, the more severe is the bias in the predicted probabilities. We propose two simple modifications of Firth's logistic regression resulting in unbiased predicted probabilities. The first corrects the predicted probabilities by a post hoc adjustment of the intercept. The other is based on an alternative formulation of Firth's penalization as an iterative data augmentation procedure. Our suggested modification consists in introducing an indicator variable that distinguishes between original and pseudo-observations in the augmented data. In a comprehensive simulation study, these approaches are compared with other attempts to improve predictions based on Firth's penalization and to other published penalization strategies intended for routine use. For instance, we consider a recently suggested compromise between maximum likelihood and Firth's logistic regression. Simulation results are scrutinized with regard to prediction and effect estimation. We find that both our suggested methods do not only give unbiased predicted probabilities but also improve the accuracy conditional on explanatory variables compared with Firth's penalization. While one method results in effect estimates identical to those of Firth's penalization, the other introduces some bias, but this is compensated by a decrease in the mean squared error. Finally, all methods considered are illustrated and compared for a study on arterial closure devices in minimally invasive cardiac surgery. Copyright © 2017 John Wiley & Sons, Ltd.

Trastuzumab deruxtecan is an antibody–drug conjugate with high extracranial activity in human epidermal growth factor receptor 2 (HER2)-positive metastatic breast cancer. We conducted the prospective, open-label, single-arm, phase 2 TUXEDO-1 trial. We enrolled patients aged ≥18 years with HER2-positive breast cancer and newly diagnosed untreated brain metastases or brain metastases progressing after previous local therapy, previous exposure to trastuzumab and pertuzumab and no indication for immediate local therapy. Patients received trastuzumab deruxtecan intravenously at the standard dose of 5.4 mg per kg bodyweight once every 3 weeks. The primary endpoint was intracranial response rate measured according to the response assessment in neuro-oncology brain metastases criteria. A Simon two-stage design was used to compare a null hypothesis of <26% response rate against an alternative of 61%. Fifteen patients were enrolled in the intention-to-treat population of patients who received at least one dose of study drug. Two patients (13.3%) had a complete intracranial response, nine (60%) had a partial intracranial response and three (20%) had stable disease as the best intracranial response, with a best overall intracranial response rate of 73.3% (95% confidential interval 48.1–89.1%), thus meeting the predefined primary outcome. No new safety signals were observed and global quality-of-life and cognitive functioning were maintained over the treatment duration. In the TUXEDO-1 trial (NCT04752059, EudraCT 2020-000981-41), trastuzumab deruxtecan showed a high intracranial response rate in patients with active brain metastases from HER2-positive breast cancer and should be considered as a treatment option in this setting.

Conditional logistic regression is used for the analysis of binary outcomes when subjects are stratified into several subsets, e.g. matched pairs or blocks. Log odds ratio estimates are usually found by maximizing the conditional likelihood. This approach eliminates all strata-specific parameters by conditioning on the number of events within each stratum. However, in the analyses of both an animal experiment and a lung cancer case-control study, conditional maximum likelihood (CML) resulted in infinite odds ratio estimates and monotone likelihood. Estimation can be improved by using Cytel Inc.'s well-known LogXact software, which provides a median unbiased estimate and exact or mid-p confidence intervals. Here, we suggest and outline point and interval estimation based on maximization of a penalized conditional likelihood in the spirit of Firth's (Biometrika 1993; 80:27-38) bias correction method (CFL). We present comparative analyses of both studies, demonstrating some advantages of CFL over competitors. We report on a small-sample simulation study where CFL log odds ratio estimates were almost unbiased, whereas LogXact estimates showed some bias and CML estimates exhibited serious bias. Confidence intervals and tests based on the penalized conditional likelihood had close-to-nominal coverage rates and yielded highest power among all methods compared, respectively. Therefore, we propose CFL as an attractive solution to the stratified analysis of binary data, irrespective of the occurrence of monotone likelihood. A SAS program implementing CFL is available at: http://www.muw.ac.at/msi/biometrie/programs.

Background Despite increased INSTI use, limited large-scale, real-life data exists on INSTI uptake and discontinuation. Setting International multicohort collaboration. Methods RESPOND participants starting dolutegravir (DTG), elvitegravir (EVG) or raltegravir (RAL) after 1/1/2012 were included. Predictors of INSTI used were assessed using multinomial logistic regression. Kaplan Meier and Cox proportional hazards models describe time to and factors associated with discontinuation. Results Overall, 9702 persons were included; 5051 (52.1%) starting DTG, 1933 (19.9%) EVG, 2718 (28.0%) RAL. The likelihood of starting RAL or EVG versus DTG decreased over time and was higher in Eastern and Southern Europe compared to Western Europe.

This is the first study to investigate the risk factors for development of CKD amongst Australian HIV-infected patients using cohort data. It highlights the need for awareness of renal risk factors, particularly amongst older patients or in those with pre-existing renal dysfunction. Further research is required to explore the discrepancy between patients who have acquired HIV through different means of exposure.