Specialized Case-Control Genotype Misclassification Functions

Convenience functions for genotype-only case-control chi-square calculations under conditional model-based genotype frequencies and genotype misclassification. These functions are narrower than cc_mssn and cc_power: they compute only the genotype chi-square test for one specific misclassification model.

cc_chisq_mssn_genotype_misclassification_1p(
  power,
  alpha,
  prev,
  pd,
  R2,
  MOI = c("M", "D", "Rec"),
  k = 1,
  e = 0,
  verbose = TRUE
)

cc_chisq_power_genotype_misclassification_1p(
  N_case,
  alpha,
  prev,
  pd,
  R2,
  MOI = c("M", "D", "Rec"),
  k = 1,
  e = 0,
  verbose = TRUE
)

cc_chisq_mssn_genotype_misclassification_2p(
  power,
  alpha,
  prev,
  pd,
  R2,
  MOI = c("M", "D", "Rec"),
  k = 1,
  e1 = 0,
  e2 = 0,
  verbose = TRUE
)

cc_chisq_power_genotype_misclassification_2p(
  N_case,
  alpha,
  prev,
  pd,
  R2,
  MOI = c("M", "D", "Rec"),
  k = 1,
  e1 = 0,
  e2 = 0,
  verbose = TRUE
)

cc_chisq_mssn_genotype_misclassification_3p(
  power,
  alpha,
  prev,
  pd,
  R2,
  MOI = c("M", "D", "Rec"),
  k = 1,
  e01 = 0,
  e02 = 0,
  e03 = 0,
  verbose = TRUE
)

cc_chisq_power_genotype_misclassification_3p(
  N_case,
  alpha,
  prev,
  pd,
  R2,
  MOI = c("M", "D", "Rec"),
  k = 1,
  e01 = 0,
  e02 = 0,
  e03 = 0,
  verbose = TRUE
)

cc_chisq_mssn_genotype_misclassification_differential_3p(
  power,
  alpha,
  prev,
  pd,
  R2,
  MOI = c("M", "D", "Rec"),
  k = 1,
  case_e01 = 0,
  case_e02 = 0,
  case_e03 = 0,
  ctrl_e01 = 0,
  ctrl_e02 = 0,
  ctrl_e03 = 0,
  verbose = TRUE
)

cc_chisq_power_genotype_misclassification_differential_3p(
  N_case,
  alpha,
  prev,
  pd,
  R2,
  MOI = c("M", "D", "Rec"),
  k = 1,
  case_e01 = 0,
  case_e02 = 0,
  case_e03 = 0,
  ctrl_e01 = 0,
  ctrl_e02 = 0,
  ctrl_e03 = 0,
  verbose = TRUE
)

Arguments

power

Numeric in \((0,1)\). Desired target power for MSSN functions.

alpha

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

prev

Numeric in \((0,1)\). Disease prevalence.

pd

Numeric in \((0,1)\). Disease-allele frequency.

R2

Numeric \(> 0\). Homozygote relative risk.

MOI

Character. Mode of inheritance: "M", "D", or "Rec".

k

Numeric \(> 0\). Control-to-case ratio \(N_{ctrl}/N_{case}\).

e

Numeric in \([0,0.5]\). One-parameter symmetric error probability assigned to each adjacent off-diagonal call. The matrix diagonal is \(1-2e\); textbook Eq. 2.5 uses a total error parameter \(\epsilon=2e\).

verbose

Logical. If TRUE, prints a formatted summary.

N_case

Numeric \(> 0\). Number of cases for power functions.

e1, e2

Numeric. Two-parameter genotype misclassification rates.

e01, e02, e03

Numeric. Three-parameter non-differential genotype misclassification rates.

case_e01, case_e02, case_e03

Numeric. Case-specific three-parameter genotype misclassification rates for differential misclassification.

ctrl_e01, ctrl_e02, ctrl_e03

Numeric. Control-specific three-parameter genotype misclassification rates for differential misclassification.

Value

A list with class matching the function name. MSSN functions include target non-centrality parameter, case/control sample sizes, model parameters, penetrances, misclassification matrices, internal S values, and true and observed genotype frequencies. Power functions include case/control sample sizes, non-centrality parameter, power, model parameters, penetrances, misclassification matrices, internal S values, and true and observed genotype frequencies.

Details

These are specialized convenience functions retained for users who want a focused genotype-only calculation. The all-in-one case-control functions are recommended when combining model-free inputs, locus heterogeneity, trend tests, or multiple modifier choices in one call.

Conditional genotype probabilities are constructed from prevalence, allele frequency, and relative risks using Chapter 1, Section 1.4.2 and Eqs. 1.6–1.7 (p. 13) of Gordon, Finch, and Kim (2020). The genotype test uses the two-degree-of-freedom NCP in Eq. 1.22 (p. 26). The error matrices are the one-, two-, and three-parameter families in Eqs. 2.5, 2.6, and 2.7 (pp. 57–58). Douglas et al. (2002) and Sobel et al. (2002) support the corresponding error-model families; Gordon et al. (2002) supports their use in case-control power and sample-size calculations.

For the 1p functions, package e is the probability in each adjacent off-diagonal cell, and the diagonal is \(1-2e\). Textbook Eq. 2.5 instead writes each off-diagonal as \(\epsilon/2\) and the diagonal as \(1-\epsilon\); therefore \(\epsilon=2e\).

Differential 3p functions use separate Eq. 2.7-family matrices for cases and controls, as discussed in Chapter 2, Section 2.5.2 (pp. 61–69). Their power is nominal asymptotic power, and their MSSN is nominal MSSN, evaluated with the usual chi-square critical value. Different case and control error mechanisms can distort the null distribution and inflate type I error. These functions do not independently recalibrate the null distribution for arbitrary differential genotyping error.

The returned objects keep internal effect-size components such as S and, for differential misclassification, per-genotype components, for validation and debugging.

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. doi:10.1007/978-3-030-61121-7 .

Gordon, D., Finch, S. J., Nothnagel, M., & Ott, J. (2002). Power and sample size calculations for case-control genetic association tests when errors are present: application to single nucleotide polymorphisms. Human Heredity, 54(1), 22–33. doi:10.1159/000066696 .

Douglas, J. A., Skol, A. D., & Boehnke, M. (2002). Probability of detection of genotyping errors and mutations as inheritance inconsistencies in nuclear-family data. American Journal of Human Genetics, 70(2), 487–495. doi:10.1086/338919 .

Sobel, E., Papp, J. C., & Lange, K. (2002). Detection and integration of genotyping errors in statistical genetics. American Journal of Human Genetics, 70(2), 496–508. doi:10.1086/338920 .

Ahn, K., Gordon, D., & Finch, S. J. (2009). Increase of rejection rate in case-control studies with the differential genotyping error rates. Statistical Applications in Genetics and Molecular Biology, 8(1), Article 25. doi:10.2202/1544-6115.1429 .

See also

cc_power, cc_mssn, case_control_locus_heterogeneity, and case_control_phenotype_misclassification.

Examples

cc_chisq_mssn_genotype_misclassification_1p(
  power = 0.8, alpha = 0.05, prev = 0.1, pd = 0.3, R2 = 1.8,
  MOI = "D", e = 0.02, verbose = FALSE
)

cc_chisq_power_genotype_misclassification_1p(
  N_case = 500, alpha = 0.05, prev = 0.1, pd = 0.3, R2 = 1.8,
  MOI = "D", e = 0.02, verbose = FALSE
)

cc_chisq_mssn_genotype_misclassification_2p(
  power = 0.8, alpha = 0.05, prev = 0.1, pd = 0.3, R2 = 1.8,
  MOI = "D", e1 = 0.02, e2 = 0.01, verbose = FALSE
)

cc_chisq_power_genotype_misclassification_2p(
  N_case = 500, alpha = 0.05, prev = 0.1, pd = 0.3, R2 = 1.8,
  MOI = "D", e1 = 0.02, e2 = 0.01, verbose = FALSE
)

cc_chisq_mssn_genotype_misclassification_3p(
  power = 0.8, alpha = 0.05, prev = 0.1, pd = 0.3, R2 = 1.8,
  MOI = "D", e01 = 0.02, e02 = 0.01, e03 = 0.005,
  verbose = FALSE
)

cc_chisq_power_genotype_misclassification_3p(
  N_case = 500, alpha = 0.05, prev = 0.1, pd = 0.3, R2 = 1.8,
  MOI = "D", e01 = 0.02, e02 = 0.01, e03 = 0.005,
  verbose = FALSE
)

cc_chisq_mssn_genotype_misclassification_differential_3p(
  power = 0.8, alpha = 0.05, prev = 0.1, pd = 0.3, R2 = 1.8,
  MOI = "D",
  case_e01 = 0.02, case_e02 = 0.01, case_e03 = 0.005,
  ctrl_e01 = 0.01, ctrl_e02 = 0.005, ctrl_e03 = 0.002,
  verbose = FALSE
)

cc_chisq_power_genotype_misclassification_differential_3p(
  N_case = 500, alpha = 0.05, prev = 0.1, pd = 0.3, R2 = 1.8,
  MOI = "D",
  case_e01 = 0.02, case_e02 = 0.01, case_e03 = 0.005,
  ctrl_e01 = 0.01, ctrl_e02 = 0.005, ctrl_e03 = 0.002,
  verbose = FALSE
)