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                    "value": "Background: Competing mortality complicates estimation and interpretation of prostate cancer-specific death. Cause-specific Cox and Fine-Gray models answer related but different questions and should be selected according to the target estimand. Objective: To demonstrate, using a fully reproducible fixed synthetic dataset, how cause-specific and subdistribution hazard estimands differ in risk-set construction, regression interpretation, and relation to cumulative incidence. Methods: A single fixed dataset of 500 synthetic observations was generated using seed 123. Covariates, treatment indicators, follow-up time sampled from 1-60 months, and event status sampled with probabilities 0.20 for prostate cancer death, 0.20 for other-cause death, and 0.60 for censoring were mutually independent; therefore, no covariate or treatment effects were encoded. Multivariable cause-specific Cox and Fine-Gray models included 15 regression parameters. Cumulative incidence functions, proportionality diagnostics, event-per-parameter calculations, an exploratory other-cause Cox model, and comparison with the naive Kaplan-Meier complement were examined. Results: Within this single realization, the fitted hormonal-therapy estimates were below unity in both models (CSHR 0.568, 95% CI 0.381-0.849; SHR 0.605, 95% CI 0.405-0.903). Stage III versus stage I had estimates in the same direction and of comparable magnitude (CSHR 2.227, 95% CI 1.045-4.746; SHR 2.006, 95% CI 0.948-4.245), and the difference in p-value thresholds was not interpreted as model disagreement. Global proportionality tests were not significant for the primary cause-specific Cox (p = 0.605) or Fine-Gray (p = 0.550) model. At 60 months, the naive Kaplan-Meier complement exceeded the cumulative incidence estimate by 12.2 percentage points, although only seven observations remained at risk.",
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                        "doi": "10.1002/9781118033005",
                        "unstructured": "Lawless JF. Statistical Models and Methods for Lifetime Data. 2nd ed. Wiley; 2003. https://doi.org/10.1002/9781118033005"
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                        "key": "ref3",
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                        "unstructured": "Austin PC, Fine JP. Practical recommendations for reporting Fine-Gray model analyses for competing risk data. Stat Med. 2017;36(27):4391-4400. https://doi.org/10.1002/sim.7501"
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                        "doi": "10.1093/eurheartj/ehu131",
                        "unstructured": "Wolbers M, Koller MT, Stel VS, et al. Competing risks analyses: objectives and approaches. Eur Heart J. 2014;35(42):2936-2941. https://doi.org/10.1093/eurheartj/ehu131"
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                        "key": "ref9",
                        "doi": "10.1002/sim.5459",
                        "unstructured": "Gerds TA, Scheike TH, Andersen PK. Absolute risk regression for competing risks: interpretation, link functions, and prediction. Stat Med. 2012;31(29):3921-3930. https://doi.org/10.1002/sim.5459"
                    },
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