Computes prospective analytic power for a single-variant TDT1-NGS study of complete father-mother-affected-child trios. The implementation uses the published latent-state, sequencing-read-count likelihood rather than hard genotype calls.
tdt_ngs_power(
N,
pd,
R1,
coverage = NULL,
seq_error = NULL,
alpha = 0.05,
verbose = TRUE,
father_coverage = coverage,
mother_coverage = coverage,
child_coverage = coverage,
epsilon0 = seq_error,
epsilon1 = seq_error,
pheno_misclass = FALSE,
prev = NULL,
pi01 = 0,
locus_het = FALSE,
heter_rate = 0
)A single finite integer greater than or equal to 1. Number of complete father-mother-affected-child trios.
A single finite disease/risk-allele frequency strictly between 0
and 1. The null information is reflection-symmetric in pd and
1 - pd; the supplied allele labeling is retained.
A single finite positive heterozygote genotype relative risk under the multiplicative model. The homozygote relative risk is \(R_2 = R_1^2\).
A single finite integer greater than or equal to 2. Common fixed-depth shorthand for the father, mother, and affected child. It may be omitted when all three member-specific depths are supplied.
A single finite symmetric per-read sequencing-error
probability in \([0,0.5)\). Internally, the directional error parameters
default to \(\epsilon_0 = \epsilon_1 =\) seq_error. It may be
omitted when both directional parameters are supplied.
A single finite significance level in \((0,1)\). Defaults to 0.05.
Logical scalar. If TRUE, print a concise result
summary.
Optional fixed depths
for each trio member. An explicitly supplied member depth overrides
coverage; otherwise that member inherits coverage.
Directional probability that a reference-allele read is
observed as the alternative allele. Defaults to seq_error.
Directional probability that an alternative-allele read is
observed as the reference allele. Defaults to seq_error.
Logical scalar. If TRUE, add a phenotype-
misclassification sensitivity scenario using the ordinary-TDT NCP bridge.
Disease prevalence in \((0,1)\). Required when either phenotype misclassification or locus heterogeneity is requested. It is used only by the ordinary-TDT bridges and does not alter the raw-read likelihood.
Probability that an unaffected individual is misclassified or
ascertained as affected, in \([0,1)\). It must be zero unless
pheno_misclass = TRUE.
Logical scalar. If TRUE, add an independent locus-
heterogeneity sensitivity scenario using the ordinary-TDT NCP bridge.
Heterogeneous trio fraction in \([0,1]\). The ordinary-
TDT linked/homogeneous fraction is \(\pi=1-\)heter_rate. It must
be zero unless locus_het = TRUE.
Invisibly, an object of class "tdt_ngs_power" containing the
design inputs, power and NCP, multiplicative-model parameters, efficient
information, the 11 by 11 information matrix, compact numerical
diagnostics, effective member-specific coverage and directional-error
metadata, model metadata, and a scenarios list that always contains
sequencing_only and, when requested,
phenotype_misclassification and heterogeneity. Modifier
scenarios record their ordinary-TDT bridge inputs, coefficients,
attenuation factor, and confirmation that the raw-read likelihood was not
modified. Legacy coverage and seq_error fields retain the
supplied common shorthand values.
TDT1-NGS is evaluated for one biallelic variant under Hardy-Weinberg parental genotype frequencies, random mating, a multiplicative disease model, fixed member-specific coverage, and common directional sequencing error. With \(t = R_1/(1+R_1)\), the transmission parameter is \(\delta = \log\{t/(1-t)\} = \log(R_1)\) and \(R_2 = R_1^2\).
Kim's Appendix B noncentrality parameter is $$\lambda = N \delta^2 I_{eff},$$ where \(I_{eff}\) is the nuisance-adjusted per-trio information evaluated under the null from raw sequencing read-count probabilities and the 15 latent Mendelian trio states. Power is the upper-tail probability beyond the central one-degree-of-freedom chi-square critical value under a noncentral chi-square distribution with NCP \(\lambda\).
When requested, phenotype misclassification is a sensitivity bridge rather than a phenotype-aware sequencing likelihood. Let \(c=2(g_T-g_{NT})^2/(g_T+g_{NT})\) be the ordinary-TDT per-trio NCP coefficient. The bridge computes $$r_{pheno}=c_{pheno}/c_{noerror}$$ from the ordinary-TDT expected transmission and nontransmission probabilities, using the fixed assumptions \(R_2=R_1^2\), \(\delta'=1\), and \(\theta_1=p_d\). It then reports \(\lambda_{pheno}=\lambda_{NGS}r_{pheno}\). Kim's raw-read likelihood, information matrix, and efficient information remain unchanged.
Locus heterogeneity uses the analogous independent bridge
$$r_{het}=c_{heterogeneity}/c_{noerror},\qquad
\lambda_{het}=\lambda_{NGS}r_{het}.$$
The ordinary-TDT expected counts are evaluated at one trio using
\(\pi=1\) for the homogeneous reference and
\(\pi=1-\)heter_rate for the requested sensitivity scenario.
It uses the same fixed \(R_2\), \(\delta'\), and \(\theta_1\)
assumptions as the phenotype bridge. If both modifiers are requested, they
are reported separately against the same sequencing-only baseline; their
factors are never multiplied and no combined result is calculated.
The existing directional read model is $$q_G=\epsilon_0 + (1-\epsilon_0-\epsilon_1)G/2,$$ for genotype \(G\in\{0,1,2\}\). Thus \(q_0=\epsilon_0\), \(q_2=1-\epsilon_1\), and \(q_1=(1+\epsilon_0-\epsilon_1)/2\); the heterozygote probability is one-half in the symmetric case. The effective errors must be nonnegative and sum to less than one.
Coverage 1 is unsupported under the full published nuisance model. Its eight observable read-count triples provide at most seven independent probability dimensions for an 11-parameter information model, so efficient information is not identifiable without changing the model or using a generalized inverse.
This prospective calculation performs no simulation or EM fitting. It does not implement TDT2-NGS, conventional genotype misclassification/TDTae, a joint modifier likelihood, or multi-locus testing. Coverage is fixed for each member rather than random or sample-specific.
Kim, W. (2015). Transmission disequilibrium tests based on read counts for low-coverage next-generation sequence data. Human Heredity, 80(1), 36–49. doi:10.1159/000434645 .
Buyske, S., Yang, G., Matise, T. C., & Gordon, D. (2009). When a case is not a case: Effects of phenotype misclassification on power and sample size requirements for the transmission disequilibrium test with affected child trios. Human Heredity, 67(4), 287–292. doi:10.1159/000194981 .
Chen, C., Yang, G., Buyske, S., Matise, T., Finch, S. J., & Gordon, D. (2009). Transmission disequilibrium test power and sample size in the presence of locus heterogeneity. Statistical Applications in Genetics and Molecular Biology, 8, Article 44. doi:10.2202/1544-6115.1501 .
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 .
tdt_ngs_power(
N = 5000, pd = 0.325, R1 = 1.2,
coverage = 12, seq_error = 0.005,
alpha = 5e-8, verbose = FALSE
)
tdt_ngs_power(
N = 5000, pd = 0.325, R1 = 1.2, coverage = 12, seq_error = 0.005,
locus_het = TRUE, prev = 0.01, heter_rate = 0.25,
alpha = 5e-8, verbose = FALSE
)
tdt_ngs_power(
N = 5000, pd = 0.325, R1 = 1.2, coverage = 12, seq_error = 0.005,
pheno_misclass = TRUE, prev = 0.01, pi01 = 0.05,
alpha = 5e-8, verbose = FALSE
)