Transmission Disequilibrium Test (TDT) Power from Expected Transmissions and Non-Transmissions

Computes the statistical power of the Transmission Disequilibrium Test (TDT) given the expected number of transmissions (ET) and non-transmissions (ENT) under a specified significance level. Implements Eq. 1.25 (Chapter 1, Section 1.6.1.3, p. 27) of Gordon, Finch, and Kim (2020).

tdt_power_from_expected_counts(ET, ENT, alpha = 0.05)

Arguments

ET

Numeric. Expected number of transmissions.

ENT

Numeric. Expected number of non-transmissions.

alpha

Numeric. Significance level (default = 0.05).

Value

A list containing:

lambda

Non-centrality parameter.

power

Computed power at the given alpha level.

ET

Expected transmissions.

ENT

Expected non-transmissions.

Details

The function calculates the non-centrality parameter and statistical power for the TDT using the chi-square distribution with 1 degree of freedom. ET and ENT are expected counts, not probabilities, and must refer to the same affected-trio design.

The non-centrality parameter is computed as: $$\lambda = \frac{(ET - ENT)^2}{ET + ENT}$$

Power is then obtained as: $$1 - P(\chi^2_{1,\lambda} < q_{\chi^2_{1,1-\alpha}})$$

References

Spielman, R. S., McGinnis, R. E., & Ewens, W. J. (1993). Transmission test for linkage disequilibrium: the insulin gene region and insulin-dependent diabetes mellitus. American Journal of Human Genetics, 52(3), 506–516. PMID: 8447318; PMCID: PMC1682161.

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 .

See also

tdt_power and tdt_power_from_model.

Examples

# Example: compute power for ET = 140 and ENT = 100
tdt_power_from_expected_counts(ET = 140, ENT = 100, alpha = 0.05)
#> 
#> --- Transmission Disequilibrium Test (TDT) ---
#> Equation: 1.25  |  Input: Expected Transmissions and Non-Transmissions
#> -----------------------------------------------------------
#> Expected Transmissions (ET):             140.0000
#> Expected Non-Transmissions (ENT):        100.0000
#> Non-Centrality Parameter (lambda):         6.6667
#> Power at alpha = 0.05:                     0.7330
#> -----------------------------------------------------------