Minimum Sample Size for a Threshold-Selected Genotype Chi-Square Test

Calculates the minimum selected case and control sample sizes after deriving their genotype distributions from a single-trait Falconer threshold model.

qtl_threshold_chisq_mssn(
  power,
  alpha,
  qtl_var,
  tau,
  pd,
  x_upper,
  x_lower,
  k = 1,
  verbose = TRUE
)

Arguments

power: Target power in \((0,1)\).
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_mssn" containing selected MSSN values, target NCP, internal S, thresholds, penetrances, prevalences, conditional frequencies, Falconer parameters, and separately labelled expected population screening counts.

Details

The primary MSSN is the selected case-control sample size used by the association test. The separately reported screening quantities are expected population counts needed to obtain those selected samples under simple population sampling; they are not statistical MSSN values. Genotype-specific distributions and threshold selection follow Eqs. 6.1 and 6.3–6.5 (pp. 324–326). The downstream genotype-test NCP is Eq. 1.22 (p. 26). The function solves for selected cases and controls; expected screening counts are reported separately and are not rounded MSSNs.

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