The Statistical Analysis of Doubly Truncated Data. Prof Carla Moreira

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X"/> is right truncated by the age at blood sampling
, and it is left truncated by
(age in years). Clark et al. (2011) considered only the right‐truncation issue, but ignored left‐truncation. Both truncation limits were taken into account however in several re‐analyses of the PD data, including Austin et al. (2014) and Mandel et al. (2018).

      The Parkinson's Disease Data are used in Chapters 2 and 4. Access to this dataset is possible through the DTDA package, which includes the data frames PDearly and PDlate, for the early and late onset groups, respectively.

      

      1.4.6 Acute Coronary Syndrome Data

and mean (and standard deviation, SD) for the age at diagnosis (years). STEMI: ST‐segment elevation myocardial infarction; NSTEMI: non‐ST‐segment elevation myocardial infarction.

Mean (SD)
Sex Men 697 62.86 (12.63)
Women 242 69.83 (12.59)
Diagnosis STEMI 359 61.47 (12.82)
NSTEMI 580 66.61 (12.69)

      The age at diagnosis

, ranging from 29.42 to 94.09 years old, was doubly truncated by (
), where
stands for the elapsed time (in years) between birth and end of the study (December 2014), and
.

      The ACS Data are used in Chapters 2 and 3. This dataset can be obtained from ACS (complete dataset) or ACSred (reduced dataset) in the DTDA package.

      1 Araújo C, Laszczyńska O, Viana M, Melão F, Henriques A, Borges A, Severo M, Maciel MJ, Moreira I, Azevedo A 2018 Sex differences in presenting symptoms of acute coronary syndrome: the EPIHeart cohort study. BMJ Open 8, e018798.

      2 Austin MD, Simon DK, Betensky RA 2014 Computationally simple estimation and improved efficiency for special cases of double truncation. Lifetime Data Analysis 20, 335–354.

      3 Beyersmann J, Allignol A, Schumacher M 2012 Competing Risks and Multistate Models with R . Springer.

      4 Bilker WB, Wang MC 1996 A semiparametric extension of the Mann‐Whitney test for randomly truncated data. Biometrics 52, 10–20.

      5 Clark J, Reddy S, Zheng K, Betensky RA, Simon DK 2011 Association of PGC‐1alphapolymorphisms with age of onset and risk of Parkinson's disease. BMC Medical Genetics 12, 69.

      6 de Uña‐Álvarez J 2020 Nonparametric estimation of the cumulative incidences of competing risks under double truncation. Biometrical Journal 62, 852–867.

      7 Efron B, Petrosian V 1999 Nonparametric methods for doubly truncated data. Journal of the American Statistical Association 94, 824–834.

      8 Kalbfleisch JD, Lawless JF 1989 Inference based on retrospective ascertainment: An analysis of the data on transfusion‐related AIDS. Journal of the American Statistical Association 84, 360–372.

      9 Kaplan EL, Meier P 1958 Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53, 457–481.

      10 Klein JP, Moeschberger ML 2003 Survival Analysis. Techniques for Censored and Truncated Data (2nd Edition). Springer.

      11 Lynden‐Bell D 1971 A method of allowing for known observational selection in small samples applied to 3CR quasars. Monthly Notices of the Royal Astronomical Society 155, 95–118.

      12 Mandel M, de Uña‐Álvarez J, Simon DK, Betensky RA 2018 Inverse probability weighted Cox regression for doubly truncated data. Biometrics 74, 481–487.

      13 Moreira C, de Uña‐Álvarez J 2010 Bootstrapping the NPMLE for doubly truncated data. Journal of Nonparametric Statistics 22, 567–583.

      14 Moreira C, de Uña‐Álvarez J, Crujeiras RM 2021a DTDA: Doubly Truncated Data Analysis. R package version 3.0.

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