Use cases

Central use cases

0. Subgroup-specific effect estimation via difference of Hajek estimators
   1. no weights or clustering, but with differences in (stratumwise) assignment rates after subsetting down to the subgroup vs before. Weighting of types effect-of-treatment-on-treated, sample/population average treatment effects, harmonic/precision.
   2. As above, but with case weights (e.g. population size, w/ unit of analysis being a school, county or other aggregate). So that the ett, ..., precision weights become weighting factors. Subgroups still of intact cases (rather than fractional cases as below), with non-subgroup members potentially removed from the data prior to calculation of Hajek estimator difference.
   3. As above, except with the subgrouping "filter" potentially splitting some clusters (they contain subgroup members and subgroup non-members). Subgroup size is communicated via the case weight, which is potentially 0.
   4. As above, but with clusters. I.e., data/subgrouping category presented at level of elements rather than clusters. Hajek estimator difference also to be calculated off of a data set arranged in this way.
   5. As above, but with user-defined weighting factors (instead of our ett(), etc.)
1. Analysis of a binary outcome in a paired- or many-block design, combining (i) & (ii) or (i)-(iii) of:
   1. glm()-based binary regression for covariance adjustment, no fixed effect, study sample
   2. OLS for effect estimation, with fixed effects, same study sample as above
   3. As above, w/ clustering and clustered SE's for final-stage coefficients
2. Regression discontinuity analysis using same samples at each step, OLS at final step, but at preceding step:
   • robustbase::lmrob()
   • a quantile regression
3. Same as above, with clustering and clustered SE's for final-stage coefficients
4. "Covariance-assisted gain score analysis" involving a covariance model fit to broader sample, followed by OLS on a narrower sample for effect estimation
   • with ordinary lm() based modeling of covariance
   • with ordinary glm()-based modeling of covariance
   • with quantile regression modeling of covariance
   • with glmnet for modeling of covariance
5. "Covariance-assisted gain score analysis" with interaction of treatment and prognostic score
   • with glm-based covariance modeling
   • with lmrob() and/or quantile regression (relative priorities tbd) for covariance modeling
   • with same samples used for covariance and effect estimation
   • with overlapping but non-identical samples used for covariance and effect estimation (eg Peters-Belson, covariance model fit statewide but covariance fit to subset).

• (Others as described in proposal...)

Additional use cases

• Covariance assisted gain score analysis
  • with glmnet for modeling of covariance
  • with robustbase::glmrob() for covariance modeling (e.g. binary or outcomes)
  • with propensity score weighting as well as covariance adjustment
  • using robustbase::glmrob() for modeling a count outcome, but then don't use OLS for treatment effect term; instead use:
    • glm()
    • MASS::glm.nb() (or other negative binomial regression).