Event

Prob [Down Syndrome | Parents' Ages]: Statistical Sudoku and Analyses of Penrose's Data (J. Genetics 1933)

Wednesday, November 22, 2023 15:30to16:30

James Hanley

Professor | Department of Epidemiology, Biostatistics and Occupational Health
McGill University

Supratik Roy

Lecturer in Statistics | Department of Statistics
University College Cork, Ireland

WHEN: Wednesday, November 22, 2023, from 3:30 to 4:30 p.m.

WHERE: Hybrid | 2001 McGill College, Rm 1140 | Zoom &

Note: Dr. J. Hanley will present in-person & Dr. S. Roy will present from Ireland

Abstract

As for their “relative aetiological importance,” Lionel Penrose's analysis of “150 sibships, containing each at least one” [child] with Down syndrome[...], “indicated that paternal age is not a significant factor, while maternal age is to be regarded as very important.” In hindsight, his data analyses, even with the help of Ronald Fisher, seem rudimentary. Moreover, it appears that they were limited to the (2-D) 42 x 2 frequency table of fathers' ages x Down/Normal children, the corresponding 31 x 2 table involving mothers' ages, and the 42 x 31 table of fathers' ages x mothers' ages. These three marginal distributions, derived from the total of 727 children, were provided in the article.

We describe how, in what we think of as Statistical Sudoku, we used linear programming, as well as the statistics reported in the text, to reconstruct a full 3-D 42 x 31 x 2 frequency table describing the full joint distribution. We then use these (non-unique) 3-D frequencies, and a number of statistical methods developed since 1933, to re-consider Penrose's conclusions, and to draw some lessons re data disclosure.

We briefly mention how Fisher helped Penrose to then study the effects of maternal age and birth order.