Power for a Threshold-Selected Genotype Chi-Square Test

Source: R/falconer_threshold.R

Calculates power for the 2-df genotype chi-square test after a quantitative trait is converted into upper-tail cases and lower-tail controls.

qtl_threshold_chisq_power(
  N_case,
  alpha,
  qtl_var,
  tau,
  pd,
  x_upper,
  x_lower,
  k = 1,
  verbose = TRUE
)

Arguments

N_case

Positive number of selected cases.

alpha

Significance level in \((0,1)\).

qtl_var

Variance in the standardized trait attributable to the QTL. Must be in \((0,1)\).

tau

Finite dominance-to-additivity ratio \(\delta/a\).

pd

Frequency of the increaser allele. Must be in \((0,1)\).

x_upper

Percentage selected from the upper population tail in percentile mode.

x_lower

Percentage selected from the lower population tail in percentile mode.

k

Positive control-to-case ratio \(N_{control}/N_{case}\).

verbose

Logical. If TRUE, prints a concise summary.

Value

An object of class "qtl_threshold_chisq_power" containing selected sample sizes, power, non-centrality parameter, internal effect component S, thresholds, penetrances, prevalences, conditional genotype frequencies, and Falconer parameters.

Details

Genotype-specific normal means and the common residual variance follow the mixture in Eq. 6.1. Upper-tail cases and lower-tail controls are constructed with Eqs. 6.3–6.5 (pp. 324–326); the middle of the trait distribution is excluded. The resulting conditional genotype probabilities are compared by the two-degree-of-freedom genotype chi-square test using Eq. 1.22 (p. 26). N_case and k * N_case are selected case and control counts, not numbers screened from the source population.

References

Gordon, D., Finch, S. J., & Kim, W. (2020). Heterogeneity in Statistical Genetics: How to Assess, Address, and Account for Mixtures in Association Studies. Springer, Eqs. 1.22, 6.1, and 6.3–6.5, pp. 26 and 324–326. doi:10.1007/978-3-030-61121-7 .

Examples

qtl_threshold_chisq_power(
  N_case = 126, alpha = 0.0001,
  qtl_var = 0.025, tau = 0.5, pd = 0.15,
  x_upper = 5, x_lower = 5, verbose = FALSE
)