Specialized Case-Control Locus-Heterogeneity Functions

Convenience functions for case-control association calculations under locus heterogeneity. These focused functions compute genotype chi-square or genotype trend calculations one test at a time. The all-in-one case-control functions remain the recommended interface when multiple tests or modifiers are needed in one call.

cc_chisq_mssn_locus_heterogeneity(
  power,
  alpha,
  g_case_assoc,
  g_ctrl,
  pi,
  k = 1,
  verbose = TRUE
)

cc_chisq_power_locus_heterogeneity(
  N_case,
  alpha,
  g_case_assoc,
  g_ctrl,
  pi,
  k = 1,
  verbose = TRUE
)

cc_trend_mssn_locus_heterogeneity(
  power,
  alpha,
  g_case_assoc,
  g_ctrl,
  pi,
  k = 1,
  w = c(0, 1, 2),
  verbose = TRUE
)

cc_trend_power_locus_heterogeneity(
  N_case,
  alpha,
  g_case_assoc,
  g_ctrl,
  pi,
  k = 1,
  w = c(0, 1, 2),
  verbose = TRUE
)

Arguments

power

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

alpha

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

g_case_assoc

Numeric vector of length 3. Case genotype frequencies under the associated-locus model, ordered as c(g0, g1, g2) and summing to 1.

g_ctrl

Numeric vector of length 3. Control genotype frequencies, ordered as c(g0, g1, g2) and summing to 1.

pi

Numeric in \([0,1]\). Locus-homogeneity fraction. The adjusted case genotype frequencies are \(\pi g_{case,assoc} + (1 - \pi) g_{ctrl}\).

k

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

verbose

Logical. If TRUE, prints a formatted summary.

N_case

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

w

Numeric vector of length 3. Trend-test genotype scores. The three weights cannot all be equal.

Value

A list with class matching the function name. MSSN functions include target non-centrality parameter, sample sizes, internal S values, and adjusted frequencies. Power functions include sample sizes, non-centrality parameter, power, internal S values, and adjusted frequencies. Trend functions additionally return the trend numerator and denominator.

Details

The associated case distribution is mixed with the control distribution as \(\pi g_{case,assoc} + (1-\pi)g_{ctrl}\), following textbook Eq. 2.16 (p. 88). Thus pi is the homogeneous/associated fraction and \(1-\pi\) is the heterogeneous fraction. The adjusted probabilities are then passed to either the genotype chi-square NCP in Eq. 1.22 (p. 26) or the trend-test NCP in Eq. 1.24 (p. 27). The trend construction under locus heterogeneity is given more specifically by Eqs. 5.29a–b (pp. 287–288).

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 .

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 .

See also

cc_power, cc_mssn, and case_control_genotype_misclassification.

Examples

cc_chisq_mssn_locus_heterogeneity(
  power = 0.8, alpha = 0.05,
  g_case_assoc = c(0.25, 0.50, 0.25),
  g_ctrl = c(0.36, 0.48, 0.16),
  pi = 0.8,
  verbose = FALSE
)

cc_chisq_power_locus_heterogeneity(
  N_case = 500, alpha = 0.05,
  g_case_assoc = c(0.25, 0.50, 0.25),
  g_ctrl = c(0.36, 0.48, 0.16), pi = 0.8, verbose = FALSE
)

cc_trend_mssn_locus_heterogeneity(
  power = 0.8, alpha = 0.05,
  g_case_assoc = c(0.25, 0.50, 0.25),
  g_ctrl = c(0.36, 0.48, 0.16), pi = 0.8, verbose = FALSE
)

cc_trend_power_locus_heterogeneity(
  N_case = 500, alpha = 0.05,
  g_case_assoc = c(0.25, 0.50, 0.25),
  g_ctrl = c(0.36, 0.48, 0.16),
  pi = 0.8,
  verbose = FALSE
)