15  Ensemble

Tip

We show an example using a super learner using 3 candidate learners.

If you want to know more about Super Learner, look at other tutorials.

flowchart LR
  S(Super Learner) --> l(Logistic regression)
  S --> g(LASSO)
  S --> m(Multivariate Adaptive Regression Splines MARS)
  style S fill:#90EE90;

The super learning approach is fundamentally different from the pure ML or LASSO approach discussed earlier. Here all of the candidate learners are using exposure as their outcome while running the model.

15.1 Build model formula based on all variables

proxy.list <- names(out2[-1])
# out3$autoselected_covariate_df[,-1] for hybrid 
# out2 is from step2$recurrence_data
length(proxy.list)
#> [1] 91
covform <- paste0(investigator.specified.covariates, collapse = "+")
proxyform <- paste0(proxy.list, collapse = "+")
rhsformula <- paste0(c(covform, proxyform), collapse = "+")
ps.formula <- as.formula(paste0("exposure", "~", rhsformula))

We work with all proxies

15.2 Fit the PS model with super learner

require(WeightIt)
W.out <- weightit(ps.formula, 
                  data = hdps.data, 
                  estimand = "ATE",
                  method = "super",
                  SL.library = c("SL.glm", 
                                 "SL.glmnet",
                                 "SL.earth"))
#> Loading required namespace: glmnet
#> Loading required namespace: earth
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Propensity score model fit based on super learning algorithm to be able to calculate the inverse probability weights.

15.3 Obtain log-OR from unadjusted outcome model

summary(W.out$ps)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#> 0.01919 0.22474 0.38968 0.42094 0.59528 0.99131
out.formula <- as.formula(paste0("outcome", "~", "exposure"))
fit <- glm(out.formula,
            data = hdps.data,
            weights = W.out$weights,
            family= binomial(link = "logit"))
fit.summary <- summary(fit)$coef["exposure",
                                 c("Estimate", 
                                   "Std. Error", 
                                   "Pr(>|z|)")]
fit.summary[2] <- sqrt(sandwich::sandwich(fit)[2,2])
require(lmtest)
conf.int <- confint(fit, "exposure", level = 0.95, method = "hc1")
fit.summary_with_ci.sl <- c(fit.summary, conf.int)
knitr::kable(t(round(fit.summary_with_ci.sl,2))) 

Estimate	Std. Error	Pr(>|z|)	2.5 %	97.5 %
0.43	0.09	0	0.32	0.54

Summary of results (log-OR).