To tune or not to tune, a case study of ridge logistic regression in small or sparse datasets

Šinkovec, Hana (avtor), Heinze, Georg (avtor), Blagus, Rok (avtor), Geroldinger, Angelika (avtor)

Background: For finite samples with binary outcomes penalized logistic regression such as ridge logistic regression has the potential of achieving smaller mean squared errors (MSE) of coefficients and predictions than maximum likelihood estimation. There is evidence, however, that ridge logistic regression can result in highly variable calibration slopes in small or sparse data situations. Methods: In this paper, we elaborate this issue further by performing a comprehensive simulation study, investigating the performance of ridge logistic regression in terms of coefficients and predictions and comparing it to Firth's correction that has been shown to perform well in low-dimensional settings. In addition to tuned ridge regression where the penalty strength is estimated from the data by minimizing some measure of the out-of- sample prediction error or information criterion, we also considered ridge regression with pre-specified degree of shrinkage. We included "oracle" models in the simulation study in which the complexity parameter was chosen based on the true event probabilities (prediction oracle) or regression coefficients (explanation oracle) to demonstrate the capability of ridge regression if truth was known. Results: Performance of ridge regression strongly depends on the choice of complexity parameter. As shown in our simulation and illustrated by a data example, values optimized in small or sparse datasets are negatively correlated with optimal values and suffer from substantial variability which translates into large MSE of coefficients and large variability of calibration slopes. In contrast, in our simulations pre-specifying the degree of shrinkage prior to fitting led to accurate coefficients and predictions even in non-ideal settings such as encountered in the context of rare outcomes or sparse predictors. Conclusions: Applying tuned ridge regression in small or sparse datasets is problematic as it results in unstable coefficients and predictions. In contrast, determining the degree of shrinkage according to some meaningful prior assumptions about true effects has the potential to reduce bias and stabilize the estimates.

• Jezik: Angleški jezik
• Ključne besede: logistic regression, Firth's correction, statistics
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: BF - Biotehniška fakulteta
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2021
• Št. strani: 15 str.
• Številčenje: Vol. 21
• PID: 20.500.12556/RUL-153155
• UDK: 311
• ISSN pri članku: 1471-2288
• DOI: 10.1186/s12874-021-01374-y
• COBISS.SI-ID: 79125251
• Datum objave v RUL: 20.12.2023

Gradivo je del revije

• Naslov: BMC medical research methodology
• Skrajšan naslov: BMC Med Res Methodol
• Založnik: BioMed Central
• ISSN: 1471-2288
• COBISS.SI-ID: 2441236

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: logistična regresija, Firthov popravek, statistika