score_cont_semiparam: Semiparametric score function for distance-based kernel and...

In CommKern: Network-Based Communities and Kernel Machine Methods

Semiparametric score function for distance-based kernel and continuous outcome.

Description

Description of the semiparametric score function for distance-based kernel function and continuous outcome.

Usage

score_cont_semiparam(outcome, covars, dist_mat, grid_gran = 5000)

Arguments

outcome	a numeric vector containing the continuous outcome variable (in the same ID order as dist_mat)
covars	a data frame containing the covariates to be modeled parametrically (should NOT include an ID variable)
dist_mat	a square distance matrix
grid_gran	a numeric value specifying the grid search length, preset to 5000

Details

This is the main function that calculates the p-value associated with a semiparametric kernel test of association between the kernel and continuous outcome variable. A null model (where the kernel is not associated with the outcome) is initially fit. Then, the variance of Y_i | X_i is used as the basis for the score test,

S(rho) = (Q_tau(beta_0, rho)-mu_Q) / (sigma_Q).

However, because rho disappears under the null hypothesis, we run a grid search over a range of values of rho (the bounds of which were derived by Liu et al. in 2008). This grid search gets the upper bound for the score test's p-value. This function is tailored for the underlying model

y_i = x_i^T beta + h(z_i) + e_i,

where h(.) is the kernel function, z_i is a multidimensional array of variables, x_i is a vector or matrix of covariates, beta is a vector of regression coefficients, and y_i is a continuous outcome taking values in the real numbers.

Value

the score function p-value for the kernel score test of association.

References

Liu D, Ghosh D, and Lin X (2008) "Estimation and testing for the effect of a genetic pathway on a disease outcome using logistic kernel machine regression via logistic mixed models." BMC Bioinformatics, 9(1), 292. ISSN 1471-2105. doi: 10.1186/1471-2105-9-292.

See Also

hms, ext_distance, ham_distance score_log_semiparam for semiparametric score function of distance-based kernel functions and binary outcome. score_log_nonparam for nonparametric score function of distance-based kernel functions and binary outcome. score_cont_nonparam for nonparametric score function of distance-based kernel function and continuous outcome.

Examples

data(simasd_hamil_df)
data(simasd_covars)

hamil_matrix <- ham_distance(simasd_hamil_df)
covars_df <- simasd_covars[,3:4]


score_cont_semiparam(
  outcome   = simasd_covars$verbal_IQ,
  covars    = covars_df,
  dist_mat  = hamil_matrix,
  grid_gran = 5000
  )

CommKern documentation built on Sept. 23, 2022, 5:07 p.m.