estimateQ function

Initial Estimation of Q portion of the Likelihood

An internal function called by the tmle function to obtain an initial estimate of the $Q$ portion of the likelihood based on user-supplied matrix values for predicted values of (counterfactual outcomes) Q(0,W),Q(1,W), or a user-supplied regression formula, or based on a data-adaptively selected SuperLearner fit. In the absence of user-supplied values, a user-supplied regression formula takes precedence over data-adaptive super-learning. The default is to return cross-validated predictions.

estimateQ(Y, Z, A, W, Delta, Q, Qbounds, Qform, maptoYstar, SL.library, cvQinit, 
    family, id, V, verbose, discreteSL, obsWeights)

Arguments

• Y: continuous or binary outcome variable
• Z: optional binary indicator for intermediate covariate for conrolled direct effect estimation
• A: binary treatment indicator, 1 - treatment, 0 - control
• W: vector, matrix, or dataframe containing baseline covariates
• Delta: indicator of missing outcome. 1 - observed, 0 - missing
• Q: 3-column matrix (Q(A,W), Q(0,W), Q(1,W))
• Qbounds: Bounds on predicted values for Q, set to alpha for logistic fluctuation, or range(Y) if not user-supplied
• Qform: regression formula of the form Y~A+W
• maptoYstar: if TRUE indicates continuous Y values should be shifted and scaled to fall between (0,1)
• SL.library: specification of prediction algorithms, default is (SL.glm , SL.glmnet , tmle.SL.dbarts2 ). In practice, including more prediction algorithms in the library improves results.
• cvQinit: logical, whether or not to estimate cross-validated values for initial Q, default=TRUE
• family: family specification for regressions, generally gaussian for continuous oucomes, binomial for binary outcomes
• id: subject identifier
• V: Number of cross-validation folds for Super Learning
• verbose: status message printed if set to TRUE
• discreteSL: If true, returns discrete SL estimates, otherwise ensemble estimates. Ignored when SL is not used.
• obsWeights: sampling weights

Returns

• Q: $nx3$ matrix, columns contain the initial estimate of $[Q(A,W)=E(Y|A=a,W), Q(0,W)=E(Y|A=0,W), Q(1,W)=E(Y|A=1,W)]$. For controlled direct estimation, $nx5$ matrix, $E(Y|Z,A,W)$, evaluated at $(z,a), (0,0), (0,1), (1,0), (1,1)$ on scale of linear predictors

• Qfamily: binomial for targeting with logistic fluctuation, gaussian for linear fluctuation

• coef: coefficients for each term in working model used for initial estimation of Q if glm used.

• type: type of estimation procedure

Author(s)

Susan Gruber

See Also

tmle, estimateG, calcParameters, tmleMSM, calcSigma