sleev (version 1.1.6)

linear2ph: Sieve maximum likelihood estimator (SMLE) for two-phase linear regression problems

Description

Performs efficient semiparametric estimation for general two-phase measurement error models when there are errors in both the outcome and covariates. See pacakge vigenette for code examples.

Usage

linear2ph(
  y_unval = NULL,
  y = NULL,
  x_unval = NULL,
  x = NULL,
  z = NULL,
  data = NULL,
  hn_scale = 1,
  se = TRUE,
  tol = 1e-04,
  max_iter = 1000,
  verbose = FALSE
)

Value

linear2ph() returns an object of class "linear2ph". The function coef() is used to obtain the coefficients of the fitted model. The function summary() is used to obtain and print a summary of results.

An object of class "linear2ph" is a list containing at least the following components:

call

the matched call.

coefficients

A named vector of the linear regression coefficient estimates.

sigma

The residual standard error.

covariance

The covariance matrix of the linear regression coefficient estimates.

converge

In parameter estimation, if the EM algorithm converges, then converge = TRUE. Otherwise, converge = FALSE.

converge_cov

In variance estimation, if the EM algorithm converges, then converge_cov = TRUE. Otherwise, converge_cov = FALSE.

Arguments

y_unval

Column name of the error-prone or unvalidated continuous outcome. Subjects with missing values of y_unval are omitted from the analysis. This argument is required.

y

Column name that stores the validated value of y_unval in the second phase. Subjects with missing values of y are considered as those not selected in the second phase. This argument is required.

x_unval

Specifies the columns of the error-prone covariates. Subjects with missing values of x_unval are omitted from the analysis. This argument is required.

x

Specifies the columns that store the validated values of x_unval in the second phase. Subjects with missing values of x are considered as those not selected in the second phase. This argument is required.

z

Specifies the columns of the accurately measured covariates. Subjects with missing values of z are omitted from the analysis. This argument is optional.

data

Specifies the name of the dataset. This argument is required.

hn_scale

Specifies the scale of the perturbation constant in the variance estimation. For example, if hn_scale = 0.5, then the perturbation constant is \(0.5n^{-1/2}\), where \(n\) is the first-phase sample size. The default value is 1. This argument is optional.

se

If FALSE, then the variances of the parameter estimators will not be estimated. The default value is TRUE. This argument is optional.

tol

Specifies the convergence criterion in the EM algorithm. The default value is 1E-4. This argument is optional.

max_iter

Maximum number of iterations in the EM algorithm. The default number is 1000. This argument is optional.

verbose

If TRUE, then show details of the analysis. The default value is FALSE.

Details

Models for linear2ph() are specified through the arguments. The dataset input should at least contain columns for unvalidated error-prone outcome, validated error-prone outcome, unvalidated error-prone covariate(s), validated error-prone covariate(s), and B-spline basis. B-spline basis can be generated from splines::bs() function, with argument x being the unvalidated error-prone covariate(s). See vignette for options in tuning the B-spline basis.

References

Tao, R., Mercaldo, N. D., Haneuse, S., Maronge, J. M., Rathouz, P. J., Heagerty, P. J., & Schildcrout, J. S. (2021). Two-wave two-phase outcome-dependent sampling designs, with applications to longitudinal binary data. Statistics in Medicine, 40(8), 1863–1876. https://doi.org/10.1002/sim.8876

See Also

cv_linear2ph() to calculate the average predicted log likelihood of this function.

Examples

if (FALSE) {
# Regression model: CD4 ~ VL + Sex. CD4 and VL are partially validated.
data("mock.vccc")
sn <- 20
data.linear <- spline2ph(x = "VL_unval", data = mock.vccc, size = sn,
                         degree = 3,  group = "Sex")
res_linear <- linear2ph(y_unval = "CD4_unval", y = "CD4_val",
                        x_unval = "VL_unval", x = "VL_val",
                        z = "Sex", data = data.linear,  hn_scale = 1,
                        se = TRUE, tol = 1e-04, max_iter = 1000,
                        verbose = FALSE)
}