Predicting frequency distributions of biopsied genotypes by their discrete cohort size using the binomial theorem

How are blastocyst biopsy genotypes distributed as a function of cohort size, and how well does the binomial theorem predict the specific distribution of euploid genotypes across different cohort sizes? This retrospective observational study included 1065 autologous blastocyst biopsies from 206 consecutive biopsy cases at a single centre. Cohorts were classified into three mutually exclusive categories: euploid+ (containing at least one euploid), euploid-mosaic/segmental+ and meiotic (containing whole chromosome errors alone), stratified by patient age (<37 years versus ≥37 years) and cohort size (10 discrete groups). 'Observed' distributions of individual euploid blastocysts/cohort were compared with binomially 'expected' distributions using the overall probability for euploidy for each age group. For patients aged <37 years, cohorts were predominantly euploid+ (85.7%). The odds of being euploid increased for each 1-unit increase in cohort size. For each size group, the observed distribution of euploid blastocysts/cohort was closely concordant with distributions predicted binomially in the largest three cohort size quartiles. In contrast, cohort categories in the smallest quartile showed greater discordance. For patients aged ≥37 years, 48.5% of cohorts were euploid+ cohorts. While the odds of being euploid also increased for each 1-unit increase in cohort size, the observed peak number of euploid blastocysts/cohort was lower than predicted binomially in all size quartiles. The binomial theorem can predict the probability distributions of euploid genotypes in cohort sizes exceeding four in patients aged <37 years without a biopsy. However, in smaller cohort sizes for patients aged >37 years and all cohort sizes in patients aged ≥37 years, there were fewer euploid blastocysts/cohort than predicted binomially; thus, untransferred mosaic/segmental genotypes represent a repository of pregnancy potential.