Author
Listed:
- Thomas H. Scheike
- Torben Martinussen
- Brice Ozenne
Abstract
Direct regression for the cumulative incidence function (CIF) has become increasingly popular since the Fine and Gray model was suggested (Fine and Gray) due to its more direct interpretation on the probability risk scale. We here consider estimation within the Fine and Gray model using the theory of semiparametric efficient estimation. We show that the Fine and Gray estimator is semiparametrically efficient in the case without censoring. In the case of right-censored data, however, we show that the Fine and Gray estimator is no longer semiparametrically efficient and derive the semiparametrically efficient estimator. This estimation approach involves complicated integral equations, and we therefore also derive a simpler estimator as an augmented version of the Fine and Gray estimator with respect to the censoring nuisance space. While the augmentation term involves the CIF of the competing risk, it also leads to a robustness property: the proposed estimators remain consistent even if one of the models for the censoring mechanism or the CIF of the competing risk are misspecified. We illustrate this robustness property using simulation studies, comparing the Fine–Gray estimator and its augmented version. When the competing cause has a high cumulative incidence we see a substantial gain in efficiency from adding the augmentation term with a very reasonable computation time. Supplementary materials for this article are available online.
Suggested Citation
Thomas H. Scheike & Torben Martinussen & Brice Ozenne, 2023.
"Efficient Estimation in the Fine and Gray Model,"
Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(544), pages 2482-2490, October.
Handle:
RePEc:taf:jnlasa:v:118:y:2023:i:544:p:2482-2490
DOI: 10.1080/01621459.2022.2057860
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
Corrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:118:y:2023:i:544:p:2482-2490. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
We have no bibliographic references for this item. You can help adding them by using this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .
Please note that corrections may take a couple of weeks to filter through
the various RePEc services.