R/tdt_functions.R
tdt_mssn_phenotype_misclassification_from_ncp.RdComputes the expected transmissions (\(gT^*\)) and non-transmissions (\(gNT^*\)) as well as the required number of trios (\(N^*\)) for a specified non-centrality parameter (\(\lambda^*\)) under a misclassification model. Implements Eq. 5.26 and Eqs. 5.27a–b (Chapter 5, Section 5.2.6, pp. 284–285) of Gordon, Finch, and Kim (2020). Eq. 5.28a–b is the book's numerical worked example.
tdt_mssn_phenotype_misclassification_from_ncp(
lambda_star,
pd,
prev,
R1,
R2,
delta_prime = 1,
pi01 = 0,
digits = 5
)Numeric. Non-centrality parameter (\(\lambda^*\)) derived from
desired power (e.g., from tdt_mssn_from_model()).
Numeric. Frequency of the disease-associated allele.
Numeric. Disease prevalence (\(\phi_1\)).
Numeric. Relative risk for heterozygotes.
Numeric. Relative risk for homozygotes.
Numeric. Linkage disequilibrium scale parameter (\(D'\)) (default = 1).
Numeric. Misclassification rate for controls (default = 0).
Integer. Number of digits to round intermediate printed results (default = 5).
A list containing:
Expected transmission probability.
Expected non-transmission probability.
Required number of trios (\(N^*\)).
Non-centrality parameter.
Intermediate derived values used in Eq. 5.26.
This function adjusts the Transmission Disequilibrium Test (TDT) for possible phenotype misclassification. When \(\pi_{01} > 0\), a fraction of unaffected individuals are incorrectly classified as affected, inflating the apparent transmission probability. The expected transmission (\(gT^*\)) and non-transmission (\(gNT^*\)) are calculated as:
$$gT^* = p_d p_+ + \frac{D(p_T - \theta_1)C(1 - \pi_{01})}{\phi_1 + \pi_{01}\phi_0}$$ $$gNT^* = p_d p_+ + \frac{D(p_A - \theta_1)C(\pi_{01} - 1)}{\phi_1 + \pi_{01}\phi_0}$$
The required number of trios is then: $$N^* = \frac{\lambda^* (gT^* + gNT^*)}{2 (gT^* - gNT^*)^2}$$
Setting \(\pi_{01} = 0\) reproduces the standard (non-misclassified) TDT.
Buyske, S., Yang, G., Matise, T. C., & Gordon, D. (2009). When a case is not a case: Effects of phenotype misclassification on power and sample size requirements for the transmission disequilibrium test with affected child trios. Human Heredity, 67(4), 287–292. doi:10.1159/000194981 . PMID: 19172087.
Gordon, D., Finch, S. J., & Kim, W. (2020). Heterogeneity in Statistical Genetics: How to Assess, Address, and Account for Mixtures in Association Studies. Springer. doi:10.1007/978-3-030-61121-7 .
# Example: Compute N* with misclassification adjustment (pi01 = 0.1)
tdt_mssn_phenotype_misclassification_from_ncp(
lambda_star = 7.8488,
pd = 0.25, prev = 0.005,
R1 = 2, R2 = 2,
delta_prime = 1,
pi01 = 0.1
)
#>
#> --- Transmission Disequilibrium Test (Trios) with Misclassification ---
#> Implements Eq. 5.26 (gT_star, gNT_star) and Eq. 5.27b for N_star
#> -----------------------------------------------------------------------
#> Parameters
#> Misclassification Rate (pi01): 0.100
#> Allele Frequency (p_d): 0.250 | Prevalence (phi1): 0.005
#> Relative Risks (R1,R2): 2, 2
#> LD scale c (delta_prime): 1.000
#> -----------------------------------------------------------------------
#> Derived
#> p_plus (transmitting allele freq): 0.75000 | phi0: 0.99500
#> f0: 0.00348 | f1: 0.00696 | f2: 0.00696
#> C: 0.00261 | DpT: 0.14062 | DpA: 0.04688
#> -----------------------------------------------------------------------
#> Expectations
#> gT_star: 0.19066
#> gNT_star: 0.18645
#> -----------------------------------------------------------------------
#> lambda_star (TDT): 7.84880
#> Required Number of Trios (N_star): 83395
#> -----------------------------------------------------------------------