R/targetQ2.R

In benkeser/drinf: Computes doubly-robust estimators and doubly-robust confidence intervals

#' targetQ2
#' 
#' Function that targets Q2n in two steps. First solving original equations, then
#' solving sum of two new equations. 
#' 
#' @param A0 A \code{vector} treatment delivered at baseline.
#' @param A1 A \code{vector} treatment deliver after \code{L1} is measured.
#' @param L2 A \code{vector} outcome of interest. 
#' @param Qn A \code{list} of current estimates of Q2n and Q1n
#' @param gn A \code{list} of current estimates of g1n and g0n
#' @param Qnr.gnr A \code{list} of current estimates of reduced dim. regressions
#' @param abar A \code{vector} of length 2 indicating the treatment assignment 
#' that is of interest. 
#' @param tolg A \code{numeric} indicating the truncation level for conditional treatment probabilities. 
#' @param tolQ A \code{numeric}
#' @param return.models  A \code{boolean} indicating whether the fluctuation model should be 
#' returned with the output.  
#' @param tol.coef A \code{numeric} indicating the coefficient above which the minimization along the
#' submodel using \code{glm} is deemed to be unreasonable. In these cases \code{optim} is used 
#' instead to perform the fluctuation along the same submodel. 
#' @importFrom SuperLearner trimLogit
#' 
#' @return A list with named entries corresponding to the estimators of the 
#' fluctuated nuisance parameters evaluated at the observed data values. If 
#' \code{return.models = TRUE} output also includes the fitted fluctuation model. 

targetQ2 <- function(
    A0, A1, L2, Qn, gn, Qnr.gnr, 
    # Q2n, Q1n, g1n, g0n, Q2nr.obsa, Q2nr.seta, Q1nr, g0nr, g1nr, h0nr, h1nr, hbarnr, 
    abar, tolg, tolQ, return.models, tol.coef = 1e2, ...
){
    #-------------------------------------------
    # making outcomes for logistic fluctuation
    #-------------------------------------------
    # length of output
    n <- length(gn$g0n)
    
    # scale L2, Q2n, Q1n to be in (0,1)
    L2.min <- min(L2); L2.max <- max(L2)
    # scale L2
    L2s <- (L2 - L2.min)/(L2.max - L2.min)
    # scale Q2n,Q1n
    Q2ns <- (Qn$Q2n - L2.min)/(L2.max - L2.min)

    #-------------------------------------------
    # making offsets for logistic fluctuation
    #-------------------------------------------
    flucOff <- c(
        SuperLearner::trimLogit(Q2ns, trim = tolQ)
    )
    
    #-------------------------------------------
    # making covariates for fluctuation
    #-------------------------------------------
    # the original "clever covariates"
    combinedPropensity <- gn$g0n * gn$g1n
    combinedPropensity[combinedPropensity < tolg] <- tolg
    flucCov1 <- c(
        as.numeric(A0==abar[1] & A1==abar[2])/(combinedPropensity) # the usual guy
        # (L2.max - L2.min) * as.numeric(A0==abar[1] & A1==abar[2])/(gn$g0n * gn$g1n) # the usual guy
    )
    # the new "clever covariates" for Q
    flucCov2 <- c(
        # the sum of the extra two terms for targeting Q2n
        # (L2.max - L2.min) * as.numeric(A0==abar[1] & A1==abar[2]) *  
        #     ((Qnr.gnr$gnr$hbarnr + Qnr.gnr$gnr$h1nr)/Qnr.gnr$gnr$g1nr)
        as.numeric(A0==abar[1] & A1==abar[2]) *  
            ((Qnr.gnr$gnr$hbarnr + Qnr.gnr$gnr$h1nr)/Qnr.gnr$gnr$g1nr)
    )

    #-------------------------------------------
    # making covariates for prediction
    #-------------------------------------------
    # getting the values of the clever covariates evaluated at 
    # \bar{A} = abar
    predCov1 <- c(
        # (L2.max - L2.min)/(gn$g0n * gn$g1n)  # all c(A0,A1) = abar
        1/combinedPropensity  # all c(A0,A1) = abar
    )
    
    predCov2 <- c(
        # (L2.max - L2.min) * (Qnr.gnr$gnr$hbarnr + Qnr.gnr$gnr$h1nr)/Qnr.gnr$gnr$g1nr  # all c(A0,A1) = abar
        (Qnr.gnr$gnr$hbarnr + Qnr.gnr$gnr$h1nr)/Qnr.gnr$gnr$g1nr  # all c(A0,A1) = abar
    )
    
    #-------------------------------------------
    # fitting fluctuation submodel
    #-------------------------------------------
    # second fluctuation submodel to solve new equations
    flucmod2 <- suppressWarnings(glm(
        formula = "out ~ -1 + offset(fo) + fc1",
        data = data.frame(out = L2s, fo = flucOff, 
                          fc1 = flucCov2),
        family = binomial(), start = 0
    ))

    
    if(abs(flucmod2$coefficients) < tol.coef){
        # get predictions 
        tmp <- predict(
            flucmod2, 
            newdata = data.frame(out = 0, fo = flucOff,
                                 fc1 = predCov2),
            type = "response"
        )
    }else{
        # use optim to try the minimization along intercept only submodel if glm 
        # looks wonky
        flucmod2 <- optim(
            par = 0, fn = wnegloglik, gr = gradient.wnegloglik,
            method = "L-BFGS-B", lower = -tol.coef, upper = tol.coef,
            control = list(maxit = 10000),
            Y = L2s, offset = flucOff, weight = flucCov2
        )
        epsilon <- flucmod2$par
        tmp <- plogis(flucOff +  epsilon)
    }
    
    # new offset 
    flucOff <- c(
        SuperLearner::trimLogit(tmp, trim = tolQ)
    )
    
    # first fluctuation submodel to solve original equations
    flucmod1 <- suppressWarnings(glm(
        formula = "out ~ -1 + offset(fo) + fc1",
        data = data.frame(out = L2s, fo = flucOff, 
                          fc1 = flucCov1),
        family = binomial(), start = 0
    ))
    # see if the fluctuation coefficient is reasonable
    if(abs(flucmod1$coefficients) < tol.coef){
        # get predictions 
        Q2nstar <- predict(
            flucmod1, 
            newdata = data.frame(out = 0, fo = flucOff,
                                 fc1 = predCov1),
            type = "response"
        )*(L2.max - L2.min) + L2.min
    }else{
        # use optim to try the minimization along submodel if glm 
        # looks wonky
        flucmod1 <- optim(
                par = 0, fn = offnegloglik, gr = gradient.offnegloglik,
                method = "L-BFGS-B", lower = -tol.coef, upper = tol.coef,
                control = list(maxit = 10000),
                Y = L2s, offset = flucOff, weight = flucCov1
            )
        epsilon <- flucmod1$par
        Q2nstar <- stats::plogis(flucOff + predCov1 * epsilon)*(L2.max - L2.min) + L2.min
    }

    #--------------
    # output 
    #-------------
    out <- list(
        Q2nstar = Q2nstar,
        flucmod = NULL
    )
    if(return.models){
        out$flucmod = list(flucmod1, flucmod2)
    }
    return(out)
}