Additional file 1: of A statistical measure for the skewness of X chromosome inactivation based on family trios

Appendix A. Derivation of P(FMC| D) in Table 1. Appendix B. Choice of initial value of θ (θ0) and MLE of θ (θ0) using family trios with missing parental genotypes. Appendix C. Inapplicability of ECM algorithm when using only single daughters. Appendix D. Contribution of single daughters to estimate of θ in ECM algorithm. Appendix E. Effect of different initial values of θ (θ0) on ECM algorithm. Tables S1–S3. The conditional probabilities and conditional expectations for seven types of possible mother-daughter pairs, four types of possible father-daughter pairs and three types of possible single daughters, respectively. Tables S4–S5. Statistical properties of likelihood-based confidence interval of γ against missing pattern (MP) and γ with ρ=0.05, (pm, pf) = (0.30, 0.30), (0.25, 0.30) and (0.30, 0.25), and λ2=1.5 and 2, respectively. Tables S6–S9. Statistical properties of likelihood-based confidence interval of γ against missing pattern (MP) and γ with (pm, pf)= (0.20, 0.20), (0.15, 0.20) and (0.20, 0.15), ρ=0 and 0.05, and λ2=1.5 and 2, respectively. Table S10. Averages of absolute differences of each element of θ ̂ $$ \widehat{\theta} $$ and ln L θ ̂ $$ \ln L\left(\widehat{\theta}\right) $$ between ECM1 and ECM1000 with ρ=0, λ2= 1.5 and (pm, pf) = (0.30, 0.30) under MP1-MP6. Table S11. Averages of absolute differences of each element of θ ˜ 0 $$ {\tilde{\theta}}_0 $$ and ln L θ ˜ 0 $$ \ln L\left({\tilde{\theta}}_0\right) $$ between ECM1/ECM10 and ECM1000 with ρ=0, λ2= 1.5 and (pm, pf) = (0.30, 0.30) under MP1-MP6. Figures S1–S2. Medians of point estimates of γ against MP for different pm, pf and λ2 values with ρ=0 and 0.05, respectively. Figures S3–S6. Estimated powers of LRT against γ with ρ=0.05 and (pm, pf) being (0.30, 0.30), (0.25, 0.30) and (0.30, 0.25) under MP1–MP4 and MP5–MP6, and λ2=1.5 and 2, respectively. Figures S7–S14. Estimated powers of LRT against γ with (pm, pf) being (0.20, 0.20), (0.15, 0.20) and (0.20, 0.15) under MP1–MP4 and MP5–MP6, ρ=0 and 0.05, and λ2=1.5 and 2, respectively. (PDF 2328 kb)