Competing risks analysis with missing cause-of-failure-penalized likelihood estimation of cause-specific Cox models

Serigne N Lô; Jun Ma; Maurizio Manuguerra; Margarita Moreno-Betancur; Richard A Scolyer; John F Thompson

doi:10.1177/09622802211070254

Competing risks analysis with missing cause-of-failure-penalized likelihood estimation of cause-specific Cox models

Stat Methods Med Res. 2022 May;31(5):978-994. doi: 10.1177/09622802211070254. Epub 2022 Jan 17.

Authors

Serigne N Lô^{1

2

3}, Jun Ma⁴, Maurizio Manuguerra⁴, Margarita Moreno-Betancur^{5

6}, Richard A Scolyer^{1

2

7

8}, John F Thompson^{1

2

9}

Affiliations

¹ Melanoma Institute Australia, 4334The University of Sydney, Sydney, NSW, Australia.
² Faculty of Medicine and Health, 4334The University of Sydney, Sydney, NSW, Australia.
³ Institute for Research and Medical Consultations (IRMC), 577330Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia.
⁴ Department of Mathematics and Statistics, 7788Macquarie University, NSW, Australia.
⁵ Clinical Epidemiology and Biostatistics Unit, Department of Paediatrics, 2281University of Melbourne, VIC, Australia.
⁶ Clinical Epidemiology and Biostatistics Unit, 34361Murdoch Children's Research Institute, VIC, Australia.
⁷ Tissue Pathology and Diagnostic Oncology, 2205Royal Prince Alfred Hospital and NSW Health Pathology, Sydney, NSW, Australia.
⁸ Charles Perkins Centre, 4334The University of Sydney, NSW, Sydney, Australia.
⁹ Department of Melanoma and Surgical Oncology, 2205Royal Prince Alfred Hospital, Sydney, NSW, Australia.

PMID: 35037794
DOI: 10.1177/09622802211070254

Abstract

Competing risks models are attractive tools to analyze time-to-event data where several causes of an event are competing. However, a complexity may arise when, for instance, some subjects experience the event of interest but the causes are not known. Assuming that unknown causes of events are missing at random, we developed a novel constrained maximum penalized likelihood method for fitting semi-parametric cause-specific Cox regression models. Here, penalty functions were used to smooth the baseline hazards. An appealing feature of this approach is that all the relevant estimands in competing risks models are estimated including cause-specific hazard ratios, cause-specific baseline hazards, and cumulative incidence functions. Asymptotic results for these estimators were also developed, allowing for direct inferences. The proposed method was compared with some existing methods through a simulation study. A real data example was analyzed using the new method to evaluate the association of age at diagnosis with melanoma-death and non-melanoma-death in patients diagnosed with thin melanoma (tumour thickness $\leq$ 1.0 mm). An R function for our proposed method is currently available on GitHub and will be included in the R package "survivalMPL" at CRAN.

Keywords: Competing risks; cause-specific Cox model; constrained optimization; missing cause of failure; penalized likelihood estimation.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Computer Simulation
Humans
Likelihood Functions
Melanoma*
Models, Statistical
Proportional Hazards Models
Risk Assessment