Using oalasso with psAve

Two packages, two kinds of propensity score model uncertainty

oalasso and psAve are companion packages that address different sources of uncertainty in a propensity score (PS) analysis:

Which covariates? The outcome-adaptive lasso (Shortreed & Ertefaie 2017) selects the covariates that belong in the PS model — confounders and outcome predictors — and excludes instruments and noise variables, whose inclusion inflates variance and can amplify unmeasured-confounding bias (Brookhart et al. 2006; Myers et al. 2011).
Which model form? psAve::psave() (Kabata, Stuart & Shintani 2024) averages candidate PS models of different functional forms (logistic regression, CART, random forest, gradient boosting, …), with convex mixing weights selected by balance on the prognostic score.

The two compose cleanly because both packages speak the same minimal contract: a propensity score is a plain numeric vector of length $n$, named by rownames(data), strictly inside (0, 1). psave() accepts such a vector as an extra candidate via its ps.append argument, so the OAL score can compete with — and be averaged with — the flexible learners:

fit <- oal(treat ~ x1 + x2 + ..., data = dat, outcome = ~ y, estimand = "ATT")
ma  <- psAve::psave(treat ~ x1 + x2 + ..., data = dat, outcome = ~ y,
                    ps.append = cbind(oal = fit$ps))

Contract compliance is by construction: oal() errors on missing data rather than dropping rows (so no reordering or shrinking can misalign rows), its default clip = c(0.01, 0.99) equals psave()’s default clip (so psave’s re-clipping of the appended column is a no-op), and fit$ps carries the rownames of data, which psave() checks. Passing the bare vector (ps.append = fit$ps) also works; the candidate is then labeled "append" in psave’s output. Wrapping it as a one-column matrix, cbind(oal = fit$ps), keeps the rownames for psave’s alignment check and gives the candidate a readable label.

When this composition helps

Use it when both kinds of uncertainty are live at once:

Suspected instruments. Some covariates plausibly predict treatment assignment but not the outcome (e.g., prescriber preference, calendar or access variables). None of psave’s default candidate learners performs variable selection against instruments; the OAL candidate contributes exactly that.
Model-form uncertainty. The covariate–treatment relationship may be nonlinear or involve interactions that OAL’s logistic-linear PS model misses; the flexible candidates contribute that. (OAL’s selection is also linear-in-covariates on the outcome side — see the method-details vignette for honest notes on this limitation.)

The averaging step then adjudicates empirically: if the instrument-free linear score balances the prognostic score better, it earns weight; if the flexible learners capture something the linear model misses, they do.

A worked example

We use the lalonde data. Two alignment choices deserve a comment. First, oal()’s default estimand is ATE (Shortreed & Ertefaie’s wAMD convention) while psave()’s is ATT, so for a coherent pipeline set them explicitly to the same estimand — here ATT. Second, give both functions the same outcome variable: OAL uses it to build its penalty weights, psave to build the prognostic score its criterion balances.

library(oalasso)
data("lalonde", package = "MatchIt")

fit <- oal(treat ~ age + educ + race + married + nodegree + re74 + re75,
           data = lalonde, outcome = ~ re78, estimand = "ATT")
fit$lambda            # the selected (delta, gamma) tuning point
#>         delta      lambda.n         gamma       lambda2 
#> -1.000000e+01  1.313156e-28  2.600000e+01            NA

oal() is deterministic; the seed below is for psave(), whose default learner menu includes stochastic learners. To keep this vignette light we restrict psave to its two deterministic learners — with the full default menu (ranger, xgboost) the call is the same:

set.seed(1234)
ma <- psAve::psave(treat ~ age + educ + race + married + nodegree + re74 + re75,
                   data = lalonde, outcome = ~ re78,
                   ps.methods   = c("glm", "rpart"),
                   prog.methods = c("glm", "rpart"),
                   ps.append    = cbind(oal = fit$ps))
ma
#> A psave object (model-averaged propensity score)
#>  - estimand:  ATT
#>  - criterion: prog (weighted ASMD of the model-averaged prognostic score)
#>  - sample:    614 units (185 treated, 429 control)
#> 
#> lambda (PS mixing weights):
#>   glm    0.000  |                    |
#>   rpart  0.000  |                    |
#>   oal    1.000  |====================|
#> 
#> gamma (prognostic mixing weights):
#>   glm    0.050  |=                   |
#>   rpart  0.950  |=================== |
#> 
#> Criterion value at selected lambda: 0.0387
#> 
#> Balance preview (worst covariates + prognostic score):
#>          smd.un smd.wt ks.un ks.wt
#> age       0.309  0.119 0.158 0.308
#> married   0.826  0.047 0.324 0.019
#> nodegree  0.245  0.041 0.111 0.018
#> prog      0.426  0.039 0.395 0.088
#> 
#> Next:
#>   MatchIt::matchit(treat ~ age + educ + race + married + nodegree + re74 + re75, data = lalonde, distance = x$ps)
#>     or: psave_match(x)
#>   WeightIt::weightit(treat ~ age + educ + race + married + nodegree + re74 + re75, data = lalonde, ps = x$ps, estimand = "ATT")
#>     or: psave_weight(x)

The printed mixing weights $\lambda$ now include an oal column: the share of the averaged score contributed by the outcome-adaptive lasso candidate. A weight of 0 means the criterion preferred the base learners (appended candidates are placed last on psave’s grid, so exact ties favor the base candidates — a documented psAve rule); a large weight means instrument exclusion paid off in prognostic-score balance. Everything downstream is unchanged psAve usage: psave_match(ma), psave_weight(ma), cobalt::bal.tab(ma).

The criterion-interaction caveat

One honest paragraph before you interpret the mixing weights. An OAL candidate pairs naturally with psave’s default criterion = "prog": both are outcome-oriented — OAL leaves instruments unbalanced on purpose because they cannot cause confounding, and the prognostic-score criterion does not charge it for that, because instruments contribute nothing to the prognostic score. The other criteria can mis-rank an instrument-free candidate for reasons that have nothing to do with bias. Covariate-balance criteria ("smd", "ks") treat every covariate equally, so they penalize the OAL candidate for residual imbalance on the very instruments it deliberately declined to balance — imbalance that is harmless (instruments do not confound) and whose “repair” is what Myers et al. (2011) warn amplifies unmeasured-confounding bias. The prediction criterion ("logloss") is worse still: instruments are, by definition, strong treatment predictors, so a score that excludes them must predict treatment less accurately — log loss systematically rewards exactly the covariates OAL exists to remove. If you append an OAL candidate, keep criterion = "prog" (the default); with "smd", "ks", or "logloss", a low weight on the oal column is not evidence against instrument exclusion.

Validation status

Label this composition honestly in your reporting: it is an extension beyond both packages’ validated sets. The simulations of Kabata, Stuart & Shintani (2024) did not include an outcome-adaptive-lasso candidate among the averaged models, and Shortreed & Ertefaie (2017) did not study model averaging over their score. Each component is implemented exactly as published (each package’s provenance labels say precisely what is validated and what is not), but the combination has no dedicated published evaluation — treat it as a principled sensitivity analysis rather than a validated named method, and cite it as such (e.g., “an OAL propensity score (Shortreed & Ertefaie 2017), included as a candidate in prognostic-score-based model averaging (Kabata et al. 2024)”).

References

Brookhart, M. A., Schneeweiss, S., Rothman, K. J., Glynn, R. J., Avorn, J., & Stürmer, T. (2006). Variable selection for propensity score models. American Journal of Epidemiology, 163(12), 1149–1156. doi:10.1093/aje/kwj149

Kabata, D., Stuart, E. A., & Shintani, A. (2024). Prognostic score-based model averaging approach for propensity score estimation. BMC Medical Research Methodology, 24, 228. doi:10.1186/s12874-024-02350-y

Myers, J. A., Rassen, J. A., Gagne, J. J., Huybrechts, K. F., Schneeweiss, S., Rothman, K. J., Joffe, M. M., & Glynn, R. J. (2011). Effects of adjusting for instrumental variables on bias and precision of effect estimates. American Journal of Epidemiology, 174(11), 1213–1222. doi:10.1093/aje/kwr364

Shortreed, S. M., & Ertefaie, A. (2017). Outcome-adaptive lasso: Variable selection for causal inference. Biometrics, 73(4), 1111–1122. doi:10.1111/biom.12679