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Bring more data!—a good advice? : removing separation in logistic regression by increasing sample size
ID
Šinkovec, Hana
(
Author
),
ID
Geroldinger, Angelika
(
Author
),
ID
Heinze, Georg
(
Author
)
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https://www.mdpi.com/1660-4601/16/23/4658
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Abstract
The parameters of logistic regression models are usually obtained by the method of maximum likelihood (ML). However, in analyses of small data sets or data sets with unbalanced outcomes or exposures, ML parameter estimates may not exist. This situation has been termed ‘separation’ as the two outcome groups are separated by the values of a covariate or a linear combination of covariates. To overcome the problem of non-existing ML parameter estimates, applying Firth’s correction (FC) was proposed. In practice, however, a principal investigator might be advised to ‘bring more data’ in order to solve a separation issue. We illustrate the problem by means of examples from colorectal cancer screening and ornithology. It is unclear if such an increasing sample size (ISS) strategy that keeps sampling new observations until separation is removed improves estimation compared to applying FC to the original data set. We performed an extensive simulation study where the main focus was to estimate the cost-adjusted relative efficiency of ML combined with ISS compared to FC. FC yielded reasonably small root mean squared errors and proved to be the more efficient estimator. Given our findings, we propose not to adapt the sample size when separation is encountered but to use FC as the default method of analysis whenever the number of observations or outcome events is critically low.
Language:
English
Keywords:
maximum likelihood estimation
,
logistic regression
,
Firth’s correction
,
separation
,
penalized likelihood
,
bias
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
BF - Biotechnical Faculty
Publication status:
Published
Publication version:
Version of Record
Year:
2019
Number of pages:
12 str.
Numbering:
Vol. 16, no. 23
PID:
20.500.12556/RUL-153007
UDC:
61
ISSN on article:
1660-4601
DOI:
10.3390/ijerph16234658
COBISS.SI-ID:
177404163
Publication date in RUL:
14.12.2023
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848
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26
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Record is a part of a journal
Title:
International journal of environmental research and public health
Shortened title:
Int. j. environ. res. public health
Publisher:
MDPI
ISSN:
1660-4601
COBISS.SI-ID:
1818965
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