{
  "title": "Draft familial disease risk reductions for five potential live births",
  "method": "Direct integration of Lencz et al. 2021 Appendix 48,52,54,55; same posterior as original risk_reduction_lowest_family_history R function",
  "paper": "https://www.orzuk.org/publications/Lencz_Utility_eLife.pdf",
  "code_reference": "https://github.com/scarmi/embryo_selection/blob/master/EmbryoSelectionAnalysis_Lowest.R",
  "inputs_sha256": "b5822b2c1eacb1030346bb3efdbf239160668600a31f4f048d6eb0b81505c94a",
  "inputs_filename": "family-history-all-conditions.csv",
  "retrieved_date": "2026-10-13",
  "numerical_method": "120-point Gaussian-Hermite per parent and 180-point Gaussian-Legendre minimum-order-statistic integration over [-10,10]; compared with 80 parent nodes",
  "assumptions": [
    "5 sibling embryos capable of live birth; no IVF attrition or transfer failure adjustment.",
    "Optimize one condition at a time; reductions cannot be claimed simultaneously for a multi-condition index.",
    "Independent parental genotypes/random mating; additive normal genetic liability.",
    "No family-shared environmental covariance or age-specific parental ascertainment model.",
    "One affected parent means the other lifetime unaffected for non-sex-limited diseases. Alternative other-unknown estimates are retained in data.",
    "Sex-limited one-parent scenarios use affected father for prostate/testicular and affected mother for breast cancer; the other genetic parent is unobserved in the corresponding sex-specific liability model.",
    "Breast/prostate/testicular two-parent scenarios are not estimated; no fabricated numeric points.",
    "Current external R2 assumed to reflect direct within-family performance; no attenuation or embryo-genotyping correction.",
    "All h2 point inputs are candidates; numeric integration accuracy does not resolve input or model uncertainty.",
    "Four illustrative input pairings are marked: POAG transport, gout male h2/pooled inputs, BCC proxy h2, and testicular assumed K=0.004.",
    "R2 interval fields transform supplied R2 confidence endpoints holding K and h2 fixed; they are not total-uncertainty intervals and are not plotted as such."
  ],
  "provisional_inputs": {
    "Glaucoma": "POAG/Taiwan h2 with current target-population inputs",
    "Gout": "Male Taiwan h2 with pooled R2/K; sex/population pairing assumed",
    "Basal cell carcinoma": "Nonmelanoma skin-cancer h2 proxy",
    "Testicular cancer": "K=0.004 assumed; K used to derive reported R2 remains unreconciled"
  },
  "definitions": {
    "baseline": "Risk of a randomly selected embryo from the same parental-status group",
    "selected": "Risk of the lowest-PRS embryo among five sibling embryos",
    "relative": "100*(1-selected/baseline), percent",
    "absolute": "100*(baseline-selected), percentage points"
  },
  "audit": {
    "lencz_published_example": {
      "r2": 0.1,
      "h2": 0.4,
      "K": 0.05,
      "n": 5,
      "parents": [
        "affected",
        "unaffected"
      ],
      "baseline": 0.10002225414777768,
      "selected": 0.058158023460892286
    },
    "checks": [
      "n=1: zero reduction for four parental configurations",
      "R2=0: zero reduction",
      "parental-status weighted mixture reproduces population K and previously computed selected risk",
      "parent exchange symmetry",
      "independent truncated-parent-liability Monte Carlo agrees within five standard errors for three cases"
    ],
    "quadrature_convergence_max_absolute_probability_error": 2.7755575615628914e-15
  },
  "elapsed_seconds": 76.83668337482959
}