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Regression analysis of general mixed recurrent event data

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Abstract

In modern biomedical datasets, it is common for recurrent outcomes data to be collected in an incomplete manner. More specifically, information on recurrent events is routinely recorded as a mixture of recurrent event data, panel count data, and panel binary data; we refer to this structure as general mixed recurrent event data. Although the aforementioned data types are individually well-studied, there does not appear to exist an established approach for regression analysis of the three component combination. Often, ad-hoc measures such as imputation or discarding of data are used to homogenize records prior to the analysis, but such measures lead to obvious concerns regarding robustness, loss of efficiency, and other issues. This work proposes a maximum likelihood regression estimation procedure for the combination of general mixed recurrent event data and establishes the asymptotic properties of the proposed estimators. In addition, we generalize the approach to allow for the existence of terminal events, a common complicating feature in recurrent event analysis. Numerical studies and application to the Childhood Cancer Survivor Study suggest that the proposed procedures work well in practical situations.

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References

  • Brewster D, Clark D, Hopkins L, Bauer J, Wild S, Edgar A, Wallace W (2014) Subsequent hospitalisation experience of 5-year survivors of childhood, adolescent, and young adult cancer in scotland: a population based, retrospective cohort study. Brit J Cancer 110(5):1342–1350

    Article  Google Scholar 

  • Bycroft C, Freeman C, Petkova D, Band G, Elliott LT, Sharp K, Motyer A, Vukcevic D, Delaneau O, O’Connell J et al (2018) The UK Biobank resource with deep phenotyping and genomic data. Nature 562(7726):203–209

    Article  Google Scholar 

  • Casillas J, Castellino SM, Hudson MM, Mertens AC, Lima IS, Liu Q, Zeltzer LK, Yasui Y, Robison LL, Oeffinger KC (2011) Impact of insurance type on survivor-focused and general preventive health care utilization in adult survivors of childhood cancer: the childhood cancer survivor study (ccss). Cancer 117(9):1966–1975

    Article  Google Scholar 

  • Castellino SM, Casillas J, Hudson MM, Mertens AC, Whitton J, Brooks SL, Zeltzer LK, Ablin A, Castleberry R, Hobbie W et al (2005) Minority adult survivors of childhood cancer: a comparison of long-term outcomes, health care utilization, and health-related behaviors from the childhood cancer survivor study. J Clin Oncol 23(27):6499–6507

    Article  Google Scholar 

  • Cook RJ, Lawless J (2007) Cancer Epidemiology and Prevention Biomarkers. Springer Science & Business Media

    Google Scholar 

  • Kirchhoff AC, Fluchel MN, Wright J, Ying J, Sweeney C, Bodson J, Stroup AM, Smith KR, Fraser A, Kinney AY (2014) Risk of hospitalization for survivors of childhood and adolescent cancer. Cancer Epidemiol Prev Biomark 23(7):1280–1289

    Article  Google Scholar 

  • Kurt BA, Nolan VG, Ness KK, Neglia JP, Tersak JM, Hudson MM, Armstrong GT, Hutchinson RJ, Leisenring WM, Oeffinger KC et al (2012) Hospitalization rates among survivors of childhood cancer in the childhood cancer survivor study cohort. Pediat Blood Cancer 59(1):126–132

    Article  Google Scholar 

  • Liu L, Huang X, Yaroshinsky A, Cormier JN (2016) Joint frailty models for zero-inflated recurrent events in the presence of a terminal event. Biometrics 72(1):204–214. https://doi.org/10.1111/biom.12376

    Article  MathSciNet  MATH  Google Scholar 

  • Mueller EL, Park ER, Kirchhoff AC, Kuhlthau K, Nathan PC, Perez GK, Rabin J, Hutchinson R, Oeffinger KC, Robison LL et al (2018) Insurance, chronic health conditions, and utilization of primary and specialty outpatient services: a childhood cancer survivor study report. J Cancer Surviv 12(5):639–646

    Article  Google Scholar 

  • Robison LL, Armstrong GT, Boice JD, Chow EJ, Davies SM, Donaldson SS, Green DM, Hammond S, Meadows AT, Mertens AC et al (2009) The childhood cancer survivor study: a national cancer institute-supported resource for outcome and intervention research. J Clin Oncol 27(14):2308

    Article  Google Scholar 

  • Rosenberg SM, Moskowitz CS, Ford JS, Henderson TO, Frazier AL, Diller LR, Hudson MM, Stanton AL, Chou JF, Smith S et al (2015) Health care utilization, lifestyle, and emotional factors and mammography practices in the childhood cancer survivor study. Cancer Epidemiol Prev Biomark 24(11):1699–1706

    Article  Google Scholar 

  • Sun J, Zhao X (2013) Statistical Analysis of Panel Count Data. Springer-Verlag, New York https://doi.org/10.1007/978-1-4614-8715-9

  • Wellner JA, Zhang Y (2000) Two estimators of the mean of a counting process with panel count data. Ann Stat 28(3):779–814

    Article  MathSciNet  MATH  Google Scholar 

  • Wellner JA, Zhang Y (2007) Two likelihood-based semi- parametric estimation methods for panel count data with covariates. Ann Stat 35(1):2106–2142

    MATH  Google Scholar 

  • Yu G, Zhu L, Li Y, Sun J, Robison LL (2017) Regression analysis of mixed panel count data with dependent terminal events. Stat Med 36(10):1669–1680. https://doi.org/10.1002/sim.7217

    Article  MathSciNet  Google Scholar 

  • Yu G, Li Y, Zhu L, Zhao H, Sun J, Robison LL (2019) An additive-multiplicative mean model for panel count data with dependent observation and dropout processes. Scand J Stat 46(2):414–431

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu L, Tong X, Zhao H, Sun J, Srivastava DK, Leisenring W, Robison LL (2013) Statistical analysis of mixed recurrent event data with application to cancer survivor study. Stat Med 32(11):1954–1963

    Article  MathSciNet  Google Scholar 

  • Zhu L, Tong X, Sun J, Chen M, Srivastava DK, Leisenring W, Robison LL (2014) Regression analysis of mixed recurrent-event and panel-count data. Biostatistics 15(3):555–568. https://doi.org/10.1093/biostatistics/kxu009

    Article  Google Scholar 

  • Zhu L, Zhao H, Sun J, Leisenring W, Robison LL (2015) Regression analysis of mixed recurrent-event and panel-count data with additive rate models. Biometrics 71(1):71–79

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu L, Zhang Y, Li Y, Sun J, Robison LL (2018) A semiparametric likelihood-based method for regression analysis of mixed panel-count data. Biometrics 74(2):488–497. https://doi.org/10.1111/biom.12774

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu L, Choi S, Li Y, Huang X, Sun J, Robison LL (2020) Statistical analysis of clustered mixed recurrent-event data with application to a cancer survivor study. Lifetime Data Anal 26(4):820–832

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors thank the Editor-in-Chief, Dr. Mei-Ling Ting Lee, the Associate Editor, and two referees for their careful reviews and many insightful comments that have significantly improved the paper. The authors also gratefully acknowledge the support of NIH grant R03-DE029238.

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Correspondence to Ryan Sun.

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Sun, R., Sun, D., Zhu, L. et al. Regression analysis of general mixed recurrent event data. Lifetime Data Anal 29, 807–822 (2023). https://doi.org/10.1007/s10985-023-09604-9

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