Prof Carla Moreira - The Statistical Analysis of Doubly Truncated Data

Table 1.5Parkinson's Disease Data: age of onset for genetic groups. Early onset: 35–55 years; late onset: 63–87 years. Sample size and mean (and standard deviation, SD) for the age of onset (years).

Group	SNP	Alleles		Mean (SD)
Early onset	A10398G	A	76	46.93
		G	21	47.14
	PGC‐1a	A	8	50.00
		AG	50	47.18
		G	39	46.10
Late onset	A10398G	A	73
		G	27	75.33
	PGC‐1a	A	10	74.00
		AG	37	76.49
		G	53	74.49

In order to remove the selection bias related to survival, the study was limited to patients diagnosed from PD who had their DNA sample taken within 8 years after onset. Consequently, the age of onset 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).

Clark et al. (2011) divided the cases into an earlier age of onset group (35–55 years) with 99 patients, and a later age of onset group (63–87 years) with 100 patients. The genetic information of these cases, together with basic statistics on the age of onset, is reported in Table 1.5. The early onset group have two patients with missing data on A10398G SNP and on age at sampling, and these are excluded from the analysis.

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

We also consider data on the age at diagnosis of acute coronary syndrome (ACS). In Portugal, with a population of 10.3 million inhabitants, there are 38 public hospitals with resources for structured care of patients with ACS, out of which 16 have catheterization laboratory facilities. Public hospitals provide treatment for the majority of the acute coronary events and the number of patients submitted to primary percutaneous coronary intervention increased by 37.0% from 2009 to 2013, although at the regional level access to this procedure varied. The EPIHeart study (Araújo et al., 2018) is a study assembled between August 2013 and December 2014 by the Cardiology Department of two tertiary hospitals in two regions in Northern Portugal: Hospital de São João, Porto, covering the metropolitan area of Porto in the coast; and Hospital de São Pedro, Vila Real, covering the interior, northeastern region. The inclusion criteria to the cohort were admission with confirmed diagnosis of type 1 (primary spontaneous) ACS, aged 18 years or older, and living in the catchment area of the referred hospitals (Porto, Vila Real, Bragança or Viseu). Data were collected through structured interviews within the first 48 hours after admission. Of the 1297 patients initially considered, 939 were included in the cohort due the inclusion criteria (Moreira et al., 2021b). Some descriptive statistics can be found in Table 1.6.

Table 1.6Descriptive statistics for the ACS Data. Sample size 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 2and 3. This dataset can be obtained from ACS(complete dataset) or ACSred(reduced dataset) in the DTDApackage.

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.