Prospective Power for an LRTae Design — lrtae

Computes prospective power for the likelihood-ratio test allowing for error (LRTae). The function uses lrtae_ncp() and the corrected LRTae information matrix; it does not perform an observed-data hypothesis test.

lrtae_power(
  true_control_genotype_frequencies,
  true_case_genotype_frequencies,
  true_sampling_proportions,
  phenotype_misclassification_matrix,
  genotype_misclassification_matrix,
  n_fallible,
  n_pheno_validated,
  n_geno_validated,
  n_both_validated,
  alpha
)

Arguments

true_control_genotype_frequencies: Numeric vector of true genotype frequencies among controls.
true_case_genotype_frequencies: Numeric vector of true genotype frequencies among cases, in the same category order as true_control_genotype_frequencies.
true_sampling_proportions: Numeric vector of length two containing the true control and case sampling proportions, in that order.
phenotype_misclassification_matrix: Numeric two-by-two matrix whose rows are true phenotype categories (control, case) and whose columns are observed phenotype categories (control, case).
genotype_misclassification_matrix: Numeric square matrix whose rows are true genotype categories and whose columns are observed genotype categories, in the genotype-frequency order.
n_fallible: Number sampled with fallible phenotype and genotype measurements only.
n_pheno_validated: Number whose phenotype is validated while genotype is measured fallibly.
n_geno_validated: Number whose genotype is validated while phenotype is measured fallibly.
n_both_validated: Number whose phenotype and genotype are both validated.
alpha: Significance level, strictly between zero and one.

Value

An object of class lrtae_power, containing power, ncp, df, alpha, critical_value, the four sampling-tier counts, and N_total.

Details

For k genotype categories, the asymptotic reference distribution has k - 1 degrees of freedom. The rejection threshold is the upper alpha quantile of the central chi-square distribution, and power is the corresponding upper-tail probability from a noncentral chi-square distribution with the NCP returned by lrtae_ncp().

Examples

lrtae_power(
  true_control_genotype_frequencies = c(0.81, 0.18, 0.01),
  true_case_genotype_frequencies = c(0.64, 0.32, 0.04),
  true_sampling_proportions = c(0.5, 0.5),
  phenotype_misclassification_matrix = matrix(
    c(0.95, 0.05, 0.05, 0.95), 2, byrow = TRUE
  ),
  genotype_misclassification_matrix = matrix(
    c(0.950, 0.050, 0.000,
      0.025, 0.950, 0.025,
      0.000, 0.050, 0.950),
    3, byrow = TRUE
  ),
  n_fallible = 700,
  n_pheno_validated = 100,
  n_geno_validated = 100,
  n_both_validated = 100,
  alpha = 0.05
)
#> $power
#> [1] 0.998997
#> 
#> $ncp
#> [1] 29.17305
#> 
#> $df
#> [1] 2
#> 
#> $alpha
#> [1] 0.05
#> 
#> $critical_value
#> [1] 5.991465
#> 
#> $n_fallible
#> [1] 700
#> 
#> $n_pheno_validated
#> [1] 100
#> 
#> $n_geno_validated
#> [1] 100
#> 
#> $n_both_validated
#> [1] 100
#> 
#> $N_total
#> [1] 1000
#> 
#> attr(,"class")
#> [1] "lrtae_power"