Treatment effect: Part 2

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Presentation transcript:

Treatment effect: Part 2 Date: 2017.08.29 Presenter: Ryan Chen

REF: Introduction to treatment effects in Stata®: Part 1

REF: Introduction to treatment effects in Stata®: Part 1

Treatment-effects estimators: RA: Regression adjustment IPW: Inverse probability weighting IPWRA: Inverse probability weighting with regression adjustment AIPW: Augmented inverse probability weighting NNM: Nearest-neighbor matching PSM: Propensity-score matching REF: Introduction to treatment effects in Stata®: Part 1

Treatment-effects estimators: RA: Regression adjustment IPW: Inverse probability weighting IPWRA: Inverse probability weighting with regression adjustment AIPW: Augmented inverse probability weighting NNM: Nearest-neighbor matching PSM: Propensity-score matching estimators for the ATE that solve the missing-data problem by matching. REF: Introduction to treatment effects in Stata®: Part 1

REF: Introduction to treatment effects in Stata®: Part 1

The counterfactual outcomes are called unobserved potential outcomes. “How would the outcomes have changed had the mothers who smoked chosen not to smoke? “ The counterfactual outcomes are called unobserved potential outcomes. REF: Introduction to treatment effects in Stata®: Part 1

Prepare your dataset.

Var. Pregnancy (mbsmoke) Infant birthweight (bweight) Mother’s age (mage) Education level (medu) Marital status (mmarried) Whether the first prenatal exam occurred in the first trimester(prenatal1) Whether this baby was the mother’s first birth (fbaby) The father’s age (fage)

Matching Matching pairs the observed outcome of a person in one treatment group with the outcome of the “closest” person in the other treatment group. The outcome of the closest person is used as a prediction for the missing potential outcome.

Two points A cost to matching on continuous covariates We must specify a measure of similarity distance measures are used and the nearest neighbor selected. An alternative is to match on an estimated probability of treatment, known as the propensity score.

Nearest-neighbor matching imputes the missing potential outcome for each individual by using an average of the outcomes of similar subjects that receive the other treatment level. Similarity between subjects is based on a weighted function of the covariates for each observation. based on the inverse of the covariates’ variance–covariance matrix.

Nearest-neighbor matching ATE is the average of the difference between the observed and potential outcomes for each subject. NNM is nonparametric in that no explicit functional form needs more data to get to the true value than an estimator that imposes a functional form.

exact matching

biasadj() uses a linear model to remove the large-sample bias: more than one continuous covariate

Propensity-score matching matches on an estimated probability of treatment known as the propensity score. match on only one continuous covariate. Pro: no need for bias adjustment we can check the fit of binary regression models prior to matching

How to choose among the six estimators RA: Regression adjustment IPW: Inverse probability weighting IPWRA: Inverse probability weighting with regression adjustment AIPW: Augmented inverse probability weighting NNM: Nearest-neighbor matching PSM: Propensity-score matching RA: -277.06 IPW: -275.56 IPWRA: -229.97 AIPW: -230.99 NNM: -210.06 PSM: -229.45

Rules of thumb Under correct specification, all the estimators should produce similar results. (Similar estimates do not guarantee correct specification because all the specifications could be wrong.) When you know the determinants of treatment status, IPW is a natural base-case estimator. When you instead know the determinants of the outcome, RA is a natural base-case estimator. The doubly robust estimators, AIPW and IPWRA, give us an extra shot at correct specification.

Rules of thumb When you have lots of continuous covariates, NNM will crucially hinge on the bias adjustment, and the computation gets to be extremely difficult. When you know the determinants of treatment status, PSM is another base-case estimator. The IPW estimators are not reliable when the estimated treatment probabilities get too close to 0 or 1.