Case-Control Minimum Sample Size for Conditional Genotype Frequencies

Computes the minimum sample size necessary (MSSN) for case-control association tests using conditional genotype frequencies. The function supports model-based genotype frequencies, model-free genotype frequencies, optional locus heterogeneity, optional phenotype misclassification, optional genotype misclassification, genotype chi-square tests, and genotype trend tests.

cc_mssn(
  power,
  alpha,
  input_mode = c("model_based", "model_free"),
  prev = NULL,
  pd = NULL,
  R2 = NULL,
  MOI = c("M", "D", "Rec"),
  g1 = NULL,
  g0 = NULL,
  locus_het = FALSE,
  pi = 1,
  pheno_misclass = FALSE,
  theta = 0,
  phi = 0,
  k = 1,
  w = c(0, 1, 2),
  geno_misclass = c("none", "1p", "2p", "3p", "diff3p"),
  e = 0,
  e1 = 0,
  e2 = 0,
  e01 = 0,
  e02 = 0,
  e03 = 0,
  case_e01 = 0,
  case_e02 = 0,
  case_e03 = 0,
  ctrl_e01 = 0,
  ctrl_e02 = 0,
  ctrl_e03 = 0,
  diff_source = c("explicit", "case", "ctrl"),
  diff_multiplier = 1,
  verbose = TRUE
)

Arguments

power: Numeric in \((0,1)\). Desired target power.
alpha: Numeric in \((0,1)\). Significance level.
input_mode: Character. One of "model_based" or "model_free". See Details.
prev: Numeric in \((0,1)\). Disease prevalence for input_mode = "model_based".
pd: Numeric in \((0,1)\). Disease-allele frequency for input_mode = "model_based".
R2: Numeric \(> 0\). Homozygote relative risk for input_mode = "model_based".
MOI: Character. Mode of inheritance for model-based frequencies: "M" for multiplicative, "D" for dominant, or "Rec" for recessive.
g1, g0: Numeric vectors of length 3 for input_mode = "model_free". g1 gives case genotype frequencies and g0 gives control genotype frequencies, each ordered as c(g0, g1, g2) and summing to 1.
locus_het: Logical. If TRUE, requests a separate locus- heterogeneity sensitivity scenario starting from the baseline frequencies.
pi: Numeric in \([0,1]\). Locus-homogeneity fraction used when locus_het = TRUE. When locus_het = FALSE, pi must remain at its default value of 1.
pheno_misclass: Logical. If TRUE, requests a separate phenotype-misclassification sensitivity scenario starting from baseline.
theta: Numeric in \([0,1)\). Probability that a truly affected individual is classified as a control.
phi: Numeric in \([0,1)\). Probability that a truly unaffected individual is classified as a case.
k: Numeric \(> 0\). Control-to-case sample size ratio \(N_{ctrl} / N_{case}\).
w: Numeric vector of length 3. Genotype trend-test scores. The three weights cannot all be equal.
geno_misclass: Character. Genotype misclassification model: "none", "1p", "2p", "3p", or "diff3p".
e: Numeric in \([0,0.5]\). For geno_misclass = "1p", the probability assigned to each adjacent off-diagonal genotype call; the diagonal probability is \(1-2e\). Thus the \(\epsilon\) in textbook Eq. 2.5 equals \(2e\); see Details.
e1, e2: Numeric. Two-parameter misclassification rates for geno_misclass = "2p".
e01, e02, e03: Numeric. Non-differential three-parameter misclassification rates for geno_misclass = "3p".
case_e01, case_e02, case_e03: Numeric. Case-specific three-parameter misclassification rates for geno_misclass = "diff3p".
ctrl_e01, ctrl_e02, ctrl_e03: Numeric. Control-specific three-parameter misclassification rates for geno_misclass = "diff3p".
diff_source: Character. For geno_misclass = "diff3p", one of "explicit", "case", or "ctrl". See Details.
diff_multiplier: Numeric \(\ge 0\). Multiplier used when diff_source = "case" or diff_source = "ctrl".
verbose: Logical. If TRUE, prints a clean formatted summary.

Value

An object of class "cc_mssn", containing:

alpha, target_power: Requested significance level and power.
input_mode, k, w, locus_het: Input mode, control-to-case ratio, trend scores, and locus-heterogeneity settings.
errors: Genotype-error model and matrices, plus phenotype-error settings and intermediate frequencies.
model_info: Model-based penetrances and risk-model inputs, or model-free identifying information.
scenarios: Named independent results. no_error always exists; requested modifiers add phenotype_misclassification, heterogeneity, and genotype_misclassification. Each contains scenario frequencies, modifier metadata, and genotype/trend MSSN results.
tests, freqs, compatibility_scenario: Compatibility fields. With zero or one modifier, they mirror the sole design previously returned. With several modifiers, they explicitly mirror no_error; use scenarios for each sensitivity result.

Details

The no-error scenario is always calculated from the baseline conditional case and control genotype frequencies. Each requested modifier is evaluated independently from that same baseline:

no error: baseline -> tests;
phenotype misclassification: baseline -> phenotype misclassification -> tests;
locus heterogeneity: baseline -> locus heterogeneity -> tests;
genotype misclassification: baseline -> genotype misclassification -> tests.

Supplying several modifiers requests several independent sensitivity scenarios. Ordinary cc_mssn() does not combine modifiers. Specialized joint-error methods such as LRTae and LTTae are separate methods and are not implemented here.

With input_mode = "model_based", conditional case and control genotype frequencies are derived from prev, pd, R2, and MOI using Chapter 1, Section 1.4.2, Eqs. 1.6–1.7 (p. 13) of Gordon, Finch, and Kim (2020). With input_mode = "model_free", the user supplies g1 and g0 directly; when phenotype misclassification is enabled, g1 is treated as the true affected genotype distribution and g0 is treated as the true unaffected genotype distribution.

Phenotype misclassification requires prev in both input modes because disease prevalence is used to mix the baseline affected and unaffected genotype distributions into observed case and control distributions. Locus heterogeneity uses \(g_{case,het} = \pi g_{case,base} + (1 - \pi) g_{ctrl,base}\) and leaves controls unchanged. Genotype misclassification matrices are likewise applied directly to baseline case and control frequencies.

The genotype misclassification models are: "none" for identity matrices, "1p" for one symmetric error rate, "2p" for adjacent homozygote/heterozygote and heterozygote error rates, "3p" for a non-differential three-parameter matrix, and "diff3p" for separate case and control three-parameter matrices. The one-, two-, and three-parameter matrices correspond to textbook Eqs. 2.5, 2.6, and 2.7 (pp. 57–58). For "1p", package e is the probability in each adjacent off-diagonal cell and the diagonal is \(1-2e\); textbook Eq. 2.5 uses off-diagonal \(\epsilon/2\), so \(\epsilon=2e\).

The genotype test uses Eq. 1.22 (p. 26). The trend test is defined by Eqs. 1.20–1.21 (p. 24) and uses the NCP in Eq. 1.24 (p. 27). Locus heterogeneity follows Eq. 2.16 (p. 88): pi is the homogeneous fraction and \(1-\pi\) is the heterogeneous fraction. Its trend-test construction corresponds to Eqs. 5.29a–b (pp. 287–288).

For geno_misclass = "diff3p", diff_source = "explicit" uses the case and control error parameters exactly as supplied. With diff_source = "case", control parameters are computed by multiplying the case parameters by diff_multiplier. With diff_source = "ctrl", case parameters are computed by multiplying the control parameters by diff_multiplier.

With geno_misclass = "diff3p", returned MSSNs are nominal, asymptotic values evaluated with the usual chi-square critical value. Different case and control error mechanisms can distort the null distribution and inflate type I error. This function does not independently recalibrate that null distribution for arbitrary differential genotyping error.

Internal effect-size components S are retained in the returned object for validation and debugging, but are not printed in the clean verbose output.

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 .

Armitage, P. (1955). Tests for linear trends in proportions and frequencies. Biometrics, 11(3), 375–386. doi:10.2307/3001775 .

Slager, S. L., & Schaid, D. J. (2001). Case-control studies of genetic markers: power and sample size approximations for Armitage's test for trend. Human Heredity, 52(3), 149–153. doi:10.1159/000053370 .

Edwards, B. J., Haynes, C., Levenstien, M. A., Finch, S. J., & Gordon, D. (2005). Power and sample size calculations in the presence of phenotype errors for case/control genetic association studies. BMC Genetics, 6, 18. doi:10.1186/1471-2156-6-18 .

Examples

cc_mssn(
  power = 0.8, alpha = 0.05,
  input_mode = "model_free",
  g1 = c(0.25, 0.50, 0.25),
  g0 = c(0.36, 0.48, 0.16),
  geno_misclass = "none",
  verbose = FALSE
)

cc_mssn(
  power = 0.8, alpha = 0.05,
  input_mode = "model_free",
  g1 = c(0.25, 0.50, 0.25),
  g0 = c(0.36, 0.48, 0.16),
  locus_het = TRUE, pi = 0.8,
  verbose = FALSE
)

cc_mssn(
  power = 0.8, alpha = 0.05,
  input_mode = "model_free",
  g1 = c(0.25, 0.50, 0.25),
  g0 = c(0.36, 0.48, 0.16),
  locus_het = TRUE, pi = 0.8,
  geno_misclass = "3p", e01 = 0.02, e02 = 0.01, e03 = 0.005,
  verbose = FALSE
)

cc_mssn(
  power = 0.8, alpha = 0.05,
  input_mode = "model_free",
  g1 = c(0.25, 0.50, 0.25),
  g0 = c(0.36, 0.48, 0.16),
  prev = 0.05,
  pheno_misclass = TRUE, theta = 0.05, phi = 0.01,
  verbose = FALSE
)