SPPcomb (version 0.1)

DA_FDN2M1M2_inside: Internal calculation of estimating equation for DA_FDN2M1M2

Description

The internal function to solve the estimating equations constructed by combining pair (N2,M1) and (N2,M2). Since there is just one case data, no selection bias needed. Since it's a internal function for function DA_FDN2M1M2, thus it's not a necessary or important function.

Usage

DA_FDN2M1M2_inside(beta, CASEZ_2, CASEZhat_2, CASEZhat_22, CONTZ_1, CONTZhat_1, CONTZhat_2, CONTZhat_22, prob_case_2, prob_case_22, prob_cont_1, prob_cont_2, p, J, V, subset_2, subset_4, pwt_cont_2)

Arguments

beta

Parameter $\beta$.

CASEZ_2, CASEZhat_2, CASEZhat_22

CTR data(N2), details please see definition in the help of realdata_covariates.

CONTZ_1, CONTZhat_1

control data(M1) from case-control study, details please see definition in the help of realdata_covariates.

CONTZhat_2, CONTZhat_22

BRFSS data(M2), details please see definition in the help of realdata_covariates.

prob_cont_1, prob_cont_2, prob_case_2, prob_case_22, pwt_cont_2

please see definition in the help of realdata_alpha.

p

Number of parameters, a constant value of 8.

J

The derivative of the estimating equation.

V

The variance of the estimating equation.

subset_2

A vector of 1:(p-2).

subset_4

A vector of 1:(p-2).

Value

A list of (f,J,V)

1. f The final form of the estimating equation after adjusting eta.
2. J The derivative of the estimating equation.
3. V The variance of the estimating equation.

Details

The function solves estimating equation based on (N2,M1) and (N2, M2) with handling selection bias. It also accounts for the uncertainty due to the estimated value of eta. The function will output the estimating equation at current input value beta. Hence it can be used in "nleqslv" to solve for $\beta$. Because the function also outputs J and V, the asymptotic variance of $\beta$ can be calculated in a straightforward way. $\hat{Z}_l$ may be highly correlated with Z_d, so it is removed in the estimation.