◆ Model calculation

PGT-mt × PGT-A model

Scenarios for joint selection using PGT-mt and preimplantation genetic testing for aneuploidy (PGT-A), and sensitivity to model assumptions

Model version: 2026-10-12

What the result means

P(≥1) is the model probability that at least one of N blastocysts meets both model criteria: euploid by PGT-A and with heteroplasmy at or below the chosen threshold. It is not the probability of pregnancy, of a live birth or of a healthy child, and not a prediction for an individual patient.

The input comprises 187 records from 12 publications: 79 are explicitly identified as blastocysts, and the developmental stage is unspecified for 57. For 43 results reported as not detected, no limit of detection is available. These are heterogeneous published observations, not complete, independent treatment cycles.

Additional denominator for m.14487T>C excluding the 3PN embryo: ≤18% — 5/25. The main dataset retains all published embryo values; a 3PN embryo is not a transfer candidate.

H — proportion at or below the selected threshold; E — assumed proportion of euploid blastocysts; ◆ model calculation.

With 1–2 women carrying a variant, the proportion describes those women, not the variant as a whole. Records are linked across publications only when the available information supports the match. Counts are reported separately for each publication; the same woman may appear in several papers, so the counts must not be summed.

ρ describes dependence in the binary outcome of meeting both criteria. It is a specified beta-binomial correlation, not an observed correlation between heteroplasmy percentages. The same scenario value is used for every variant.

Teaching example using current data: H = 41/88, E = 0.5, N = 6 gives 0.8 at ρ = 0 and 0.64 at ρ = 0.2. This is a scenario calculation, not an individual prediction.

• H is the proportion of published heteroplasmy values at or below the selected threshold. It describes the included series, not an individual patient.
• E is the assumed proportion of euploid blastocysts in the scenario. The scenario values are not assigned to specific ages. Reference: Volodyaev et al., 2025 doi:10.1016/j.xfnr.2024.100082 — Volodyaev et al. 2025, F S Rev 6:100082, doi:10.1016/j.xfnr.2024.100082: p. 2, “Incidence, parental origin, and age relation” (whole-chromosome aneuploidy 20–30% at ages 25–35, an almost linear increase of ≈6% per year after 35, and 80–90% at ages 42–44); p. 3, Fig. 2 (proportion of euploid blastocysts by age, data from Franasiak et al.). E values are scenario parameters: they are not assigned to specific ages or matched to points in the figure.

P(≥1) for all variants in the dataset

H = k/n is calculated from the included records for each variant. The full dataset includes cleavage-stage embryos, 3PN embryos and values reported only for transferred embryos (Hyslop 2025, Thorburn 2009). Selection for low heteroplasmy biases H upwards. The filter retains only explicitly identified blastocyst TE biopsy samples. Intervals are represented by their upper bounds; results reported as not detected are assumed to fall below the threshold. Wilson intervals ignore clustering.

Formulae

q = H × E · P(≥1) = 1 − (1 − q)^N

For 0 < ρ < 1, the shared probability Q follows a beta distribution with mean q. Embryos are conditionally independent given Q; integrating Q induces positive dependence. At ρ = 0, the binomial limit is used.

Q ~ Beta(α, β); α = q(1/ρ − 1), β = (1 − q)(1/ρ − 1)
P(≥1) = 1 − B(α, β + N) / B(α, β)

Model assumptions (unproven)

• q = H × E: heteroplasmy and chromosome status are assumed independent;
• at ρ = 0, blastocysts are independent trials with the same probability; N is a given number of blastocysts, not an oocyte count or mean cycle yield;
• at ρ > 0, embryos share a random probability of meeting both criteria. The selected ρ is a scenario parameter; it has not been estimated from Atlas data;
• H describes pooled published records from different developmental stages and analytical methods; E is an assumed proportion of euploid blastocysts.

Estimating family and variant effects requires complete, linked cycle data from several independent families. The scenario proportions of euploid blastocysts are not calibrated to age.

When heteroplasmy status and ploidy may be associated

The marginal proportions H and E determine only bounds on the joint probability q for one embryo. The table shows these bounds, not confidence intervals. They are conditional on the input proportions and do not describe dependence between embryos.

max(0, H + E − 1) ≤ q ≤ min(H, E)

Joint results from primary studies

The endpoint is fixed here: H≤18% and strict euploidy. Each denominator comprises blastocysts assessed by TE biopsy in one published series. These small series describe specific women carrying mtDNA variants; their proportions do not calibrate the scenario curves for other families.

Sallevelt 2017: 3/22 numerical records below 18% include a low value in a 3PN embryo. Confirmed diagnostic yield for 2PN is 2/23. Four analyses are inconclusive due to a positive blank control; accepting the other 19 classifications bounds the below-18% fraction at 2/23–6/23. These are incomplete-data bounds, not a confidence interval. Sallevelt et al., 2017 doi:10.1093/humrep/dew356 — pp. 700–701; Supplementary Table SI.

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