Comparative Study on Estimation Methods of Proportional Hazard Models for Interval-Censored Data
DOI:
https://doi.org/10.6000/1929-6029.2023.12.27Keywords:
Breslow’s method, Cox model, Efron’s method, Finkelstein’s method, Imputation methodAbstract
Purpose: In this study, we compare the estimation methods of interval-censored data using both simulated and real data. Many past studies have used fixed sample sizes in their simulation studies. We performed the best possible simulation study.
Method: The methods include Finkelstein’s method with Piecewise and Spline and imputation methods (i.e., Efron’s method in the Cox model).
Results: If the interval-censored data do not overlap, the same estimation results are obtained regardless of the assignment point for the estimation of the Cox model. The overlapping data also did not significantly affect the accuracy of the estimation. On the other hand, Finkelstein’s method showed differences in estimation depending on the two estimation methods of the baseline survival function. Although it was not possible to determine which method had better power, the Spline method had a smaller absolute error than the Finkelstein method. A comparison of Cox’s and Finkelstein’s methods showed that Finkelstein’s method was superior in terms of power.
Conclusion: Interval-censored data is a form of data that can be found in a variety of fields. In this study, we compared estimation methods for interval-censored data, and the usefulness of Finkelstein’s method can be seen from simulation studies.
References
Peto R. Experimental survival curves for interval-censored data. Journal of the Royal Statistical Society Series C 1973; 22(1): 86-91. https://doi.org/10.2307/2346307 DOI: https://doi.org/10.2307/2346307
Turnbull BW. The empirical distribution function with arbitrarily grouped, censored and truncated data. Journal of the Royal Statistical Society Series B 1976; 38(3): 290-295. https://doi.org/10.1111/j.2517-6161.1976.tb01597.x DOI: https://doi.org/10.1111/j.2517-6161.1976.tb01597.x
Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 1958; 53(282): 457-481. https://doi.org/10.1080/01621459.1958.10501452 DOI: https://doi.org/10.1080/01621459.1958.10501452
Nishikawa M, Tango T. Behavior of the Kaplan–Meier estimator for deterministic imputations to interval-censored data and the Turnbull estimator. Japanese Journal of Biometrics 2003; 24(2): 71-94. https://doi.org/10.5691/jjb.24.71 DOI: https://doi.org/10.5691/jjb.24.71
Cox DR. Regression models and life-tables. Journal of the Royal Statistical Society Series B 1972; 34(2): 187-220. https://doi.org/10.1111/j.2517-6161.1972.tb00899.x DOI: https://doi.org/10.1111/j.2517-6161.1972.tb00899.x
Finkelstein MD. A proportional hazards model for interval-censored failure time data. Biometrics 1986; 42(4): 845-854. https://doi.org/10.2307/2530698 DOI: https://doi.org/10.2307/2530698
Sun X, Chen C. Comparison of Finkelstein’s method with the conventional approach for interval-censored data analysis. Statistics in Biopharmaceutical Research 2010; 2(1): 97-108. https://doi.org/10.1198/sbr.2010.09013 DOI: https://doi.org/10.1198/sbr.2010.09013
Breslow N. Covariance analysis of censored survival data. Biometrics 1974; 30(1): 89-99. https://doi.org/10.2307/2529620 DOI: https://doi.org/10.2307/2529620
Efron B. The efficiency of Cox’s likelihood function for censored data. Journal of the American Statistical Association 1977; 72(359): 557-565. https://doi.org/10.1080/01621459.1977.10480613 DOI: https://doi.org/10.1080/01621459.1977.10480613
Hertz-Picciotto I, Rockhill B. Validity and efficiency of approximation methods for tied survival times in Cox regression. Biometrics 1997; 53(3): 1151-1156. https://doi.org/10.2307/2533573 DOI: https://doi.org/10.2307/2533573
Royston P, Parmar MKB. Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine 2002; 21: 2175-2197. https://doi.org/10.1002/sim.1203 DOI: https://doi.org/10.1002/sim.1203
Beadle GF, Silver B, Botnick L, Hellman S, Harris JR. Cosmetic results following primary radiation therapy for early breast cancer. Cancer 1984a; 54(12): 2911-2918. https://doi.org/10.1002/1097-0142(19841215)54:12<2911::AID-CNCR2820541216>3.0.CO;2-V DOI: https://doi.org/10.1002/1097-0142(19841215)54:12<2911::AID-CNCR2820541216>3.0.CO;2-V
Beadle GF, Come S, Henderson C, Silver B, Hellman S, Harris JR. The effect of adjuvant chemotherapy on the cosmetic results after primary radiation treatment for early stage breast cancer. International Journal of Radiation Oncology Biology Physics 1984b; 10(11): 2131-2137. https://doi.org/10.1016/0360-3016(84)90213-X DOI: https://doi.org/10.1016/0360-3016(84)90213-X
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Policy for Journals/Articles with Open Access
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are permitted and encouraged to post links to their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work
Policy for Journals / Manuscript with Paid Access
Authors who publish with this journal agree to the following terms:
- Publisher retain copyright .
- Authors are permitted and encouraged to post links to their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work .
