Asymptotic Relative Efficiency of Parametric and Nonparametric Survival Estimators
The dominance of non- and semi-parametric methods in survival analysis is not without criticism. Several studies have highlighted the decrease in efficiency compared to parametric methods. We revisit the problem of Asymptotic Relative Efficiency (<inline-formula><math xmlns="http://www...
| Published in: | Stats |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-10-01
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| Subjects: | |
| Online Access: | https://www.mdpi.com/2571-905X/6/4/72 |
| Summary: | The dominance of non- and semi-parametric methods in survival analysis is not without criticism. Several studies have highlighted the decrease in efficiency compared to parametric methods. We revisit the problem of Asymptotic Relative Efficiency (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>R</mi><mi>E</mi></mrow></semantics></math></inline-formula>) of the Kaplan–Meier survival estimator compared to parametric survival estimators. We begin by generalizing Miller’s approach and presenting a formula that enables the estimation (numerical or exact) of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>R</mi><mi>E</mi></mrow></semantics></math></inline-formula> for various survival distributions and types of censoring. We examine the effect of follow-up time and censoring on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>R</mi><mi>E</mi></mrow></semantics></math></inline-formula>. The article concludes with a discussion about the reasons behind the lower and time-dependent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>R</mi><mi>E</mi></mrow></semantics></math></inline-formula> of the Kaplan–Meier survival estimator. |
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| ISSN: | 2571-905X |