Initial.estimates {SynDI}

Internal estimation

Description

Calculate the initial estimates for external populations.

Usage

Initial.estimates(datan, gamma.I, X, B, beta, Btype)

Arguments

datan

internal data only

gamma.I

regression estimates using internal data only (datan)

X

a vector of predictor that were used in the external study, e.g. X = c('X1','X2','X3')

B

a vector of covariates that were not used in the external study, e.g. B=c('X4','B1','B2')

beta

a vector of external model estimates, the vector order should be the same as listed in X, e.g. names(beta) = c("int", "X1", "X2", "X3")

Btype

a vector of type of B, either continuous or binary. If "continuous", linear regression will be used; if "binary", logistic regression will be used. More types can be implemented manually.

Value

a numeric vector of estimated coefficients of the target model for the given external population. Assume the internal data contains p predictors. The vector is of dimension (p+1), including the estimates of the intercept.

References

Neuhaus, J. and Jewell, N. (1993). A geometric approach to assess bias due to omitted covariates in generalized linear models. Biometrika 80,807–815.

Gu, T., Taylor, J.M.G. and Mukherjee, B. (2021) Regression inference for multiple populations by integrating summary-level data using stacked imputations https://arxiv.org/abs/2106.06835.

Examples

#' data(initial_estimates_example)

datan = initial_estimates_example$datan
gamma.I = initial_estimates_example$gamma.I
beta = initial_estimates_example$beta

# calculate the initial gamma for population S=1
gamma.S1.origin = Initial.estimates(datan = datan, gamma.I = gamma.I, 
    X = c('X1', 'X2', 'X3'), B = c('X4', 'B1', 'B2'), 
    beta = beta, Btype = c('continuous', 'continuous', 'binary'))