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Research article
Estimating restricted mean survival time and expected life-years lost in the presence of competing risks within flexible parametric survival models
Sarwar Islam Mozumder
University of Leicester
Corresponding Author
ORCiD: https://orcid.org/0000-0001-9644-7525
License:
This work is licensed under a CC BY 4.0 License. Read Full License
Background Royston-Parmar flexible parametric survival models (FPMs) can be fitted on either the cause-specific hazards or cumulative incidence scale in the presence of competing risks. An advantage of modelling within this framework for competing risks data is the ease at which alternative predictions to the (cause-specific or subdistribution) hazard ratio can be obtained. Restricted mean survival time (RMST) is one such measure. This has an attractive interpretation, especially when the proportionality assumption is violated. Compared to similar measures, fewer assumptions are required and it does not require extrapolation. Furthermore, one can easily obtain the expected number of life-years lost, or gained, due to a particular cause of death, which is a further useful prognostic measure as introduced by Andersen.
Methods We present various measures, including the expected life-years lost due to a cause of death, which can be predicted for a specific covariate pattern to facilitate interpretation in observational studies. Summaries are also provided at the population-level using standardisation to obtain marginal measures. RMST is obtained in the presence of competing risks using Royston-Parmar FPMs. Predictions are illustrated using English colorectal data and are obtained using the Stata post-estimation command, standsurv.
Results Reporting such measures facilitate interpretation of a competing risks analysis, particularly when the proportional hazards assumption is not appropriate. Standardisation provides a useful way to obtain marginal estimates to make absolute comparisons between two covariate groups. Predictions can be made at various time-points and presented visually for each cause of death to better understand the overall impact of different covariate groups.
Conclusions We describe estimation of RMST and expected life-years lost, both partitioned by each competing cause of death after fitting a single FPM on either the log-cumulative subdistribution, or cause-specific hazards scale. These can be used to facilitate interpretation of a competing risks analysis when the proportionality assumption is in doubt.
Keywords
competing risks, restricted mean survival time, restricted mean life time, flexible parametric model, life-years lost, survival analysis
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On 10 Jan, 2021
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On 22 Dec, 2020
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On 22 Dec, 2020
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Editorial decision: Major revision
On 08 Nov, 2020
Review #1 received
Received 01 Nov, 2020
Reviewers invited
Invitations sent on 13 Oct, 2020
Reviewer #1 agreed
On 13 Oct, 2020
Editor assigned
On 09 Oct, 2020
Editor invited
On 08 Oct, 2020
Submission checks complete
On 07 Oct, 2020
No comments provided
Editorial decision: Major revision
On 02 Sep, 2020
Review #2 received
Received 27 Aug, 2020
Review #1 received
Received 25 Mar, 2020
Reviewer #2 agreed
On 24 Feb, 2020
Reviewer #1 agreed
On 24 Feb, 2020
Reviewers invited
Invitations sent on 21 Feb, 2020
Editor assigned
On 14 Feb, 2020
Submission checks complete
On 13 Feb, 2020
Editor invited
On 13 Feb, 2020
First submitted
On 12 Feb, 2020
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Subject Areas
Health Economics & Outcomes Research
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This preprint is under consideration at BMC Medical Research Methodology. A preprint is a preliminary version of a manuscript that has not completed peer review at a journal. Research Square does not conduct peer review prior to posting preprints. The posting of a preprint on this server should not be interpreted as an endorsement of its validity or suitability for dissemination as established information or for guiding clinical practice.
Learn more about In Review
Research article
Estimating restricted mean survival time and expected life-years lost in the presence of competing risks within flexible parametric survival models
Sarwar Islam Mozumder
University of Leicester
Corresponding Author
ORCiD: https://orcid.org/0000-0001-9644-7525
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
Peer Review Timeline
CURRENT STATUS: Under Review
Version 3
Posted 07 Jan, 2021
No community comments so far
Reviewers invited
Invitations sent on 10 Jan, 2021
Reviewer #1 agreed
On 10 Jan, 2021
Editor assigned
On 22 Dec, 2020
Submission checks complete
On 22 Dec, 2020
Editor invited
On 22 Dec, 2020
No comments provided
Editorial decision: Major revision
On 08 Nov, 2020
Review #1 received
Received 01 Nov, 2020
Reviewers invited
Invitations sent on 13 Oct, 2020
Reviewer #1 agreed
On 13 Oct, 2020
Editor assigned
On 09 Oct, 2020
Editor invited
On 08 Oct, 2020
Submission checks complete
On 07 Oct, 2020
No comments provided
Editorial decision: Major revision
On 02 Sep, 2020
Review #2 received
Received 27 Aug, 2020
Review #1 received
Received 25 Mar, 2020
Reviewer #2 agreed
On 24 Feb, 2020
Reviewer #1 agreed
On 24 Feb, 2020
Reviewers invited
Invitations sent on 21 Feb, 2020
Editor assigned
On 14 Feb, 2020
Submission checks complete
On 13 Feb, 2020
Editor invited
On 13 Feb, 2020
First submitted
On 12 Feb, 2020
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Health Economics & Outcomes Research
License:
This work is licensed under a CC BY 4.0 License. Read Full License
Background Royston-Parmar flexible parametric survival models (FPMs) can be fitted on either the cause-specific hazards or cumulative incidence scale in the presence of competing risks. An advantage of modelling within this framework for competing risks data is the ease at which alternative predictions to the (cause-specific or subdistribution) hazard ratio can be obtained. Restricted mean survival time (RMST) is one such measure. This has an attractive interpretation, especially when the proportionality assumption is violated. Compared to similar measures, fewer assumptions are required and it does not require extrapolation. Furthermore, one can easily obtain the expected number of life-years lost, or gained, due to a particular cause of death, which is a further useful prognostic measure as introduced by Andersen.
Methods We present various measures, including the expected life-years lost due to a cause of death, which can be predicted for a specific covariate pattern to facilitate interpretation in observational studies. Summaries are also provided at the population-level using standardisation to obtain marginal measures. RMST is obtained in the presence of competing risks using Royston-Parmar FPMs. Predictions are illustrated using English colorectal data and are obtained using the Stata post-estimation command, standsurv.
Results Reporting such measures facilitate interpretation of a competing risks analysis, particularly when the proportional hazards assumption is not appropriate. Standardisation provides a useful way to obtain marginal estimates to make absolute comparisons between two covariate groups. Predictions can be made at various time-points and presented visually for each cause of death to better understand the overall impact of different covariate groups.
Conclusions We describe estimation of RMST and expected life-years lost, both partitioned by each competing cause of death after fitting a single FPM on either the log-cumulative subdistribution, or cause-specific hazards scale. These can be used to facilitate interpretation of a competing risks analysis when the proportionality assumption is in doubt.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the manuscript can be downloaded and accessed as a PDF.