score_log_semiparam {CommKern} | R Documentation |

## Semiparametric score function for distance-based kernel

### Description

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

### Usage

```
score_log_semiparam(outcome, covars, dist_mat, grid_gran = 5000)
```

### Arguments

`outcome` |
a numeric vector containing the binary outcome variable, 0/1 (in the same ID order as dist_mat) |

`covars` |
a dataframe 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 binary 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\left(\rho\right) = \frac{Q_{\tau}\left(\hat{\beta_0},\rho\right)-\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\left(z_{i}\right) + e_{i},`

where `h\left(\cdot\right)`

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 binary outcome taking
values in 0, 1.

The function returns an numeric p-value for the kernel score test of association.

### Value

the score function p-value

### 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_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.
`score_cont_semiparam`

for semiparametric 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_log_semiparam(
outcome = simasd_covars$dx_group,
covars = covars_df,
dist_mat = hamil_matrix,
grid_gran = 5000
)
```

*CommKern*version 1.0.1 Index]