13 Pure ML

Tip

We show an example using LASSO aproach

14 Pure ML approach (LASSO)

Start with all recurrence variables (EC in the following equation)

(Karim, Pang, and Platt 2018; Franklin et al. 2015)

Say, 100 proxies (associated with outcome) were selected by LASSO approach (ML-hdPS)

14.1 Choose variables associated with outcome

proxy.dim <- out2 # from step 3
dim(proxy.dim) 
#> [1] 7585  143
proxy.dim$id <- proxy.dim$idx
proxy.dim$idx <- NULL
fullcovproxy.data <- merge(data.complete[,c("id",
                                    outcome, 
                                    exposure, 
                                    investigator.specified.covariates)], 
                       proxy.dim, by = "id")
dim(fullcovproxy.data)
#> [1] 3839  170
fullcovproxy.data$outcome <- as.numeric(I(fullcovproxy.data$diabetes=='Yes'))
fullcovproxy.data$exposure <- as.numeric(I(fullcovproxy.data$obese=='Yes'))

proxy.list <- names(out2[-1])
# out3$autoselected_covariate_df[,-1] for hybrid 
# out2 is from step2$recurrence_data
covarsTfull <- c(investigator.specified.covariates, proxy.list)
Y.form <- as.formula(paste0(c("outcome~ exposure", 
                              covarsTfull), collapse = "+") )
covar.mat <- model.matrix(Y.form, data = fullcovproxy.data)[,-1]
lasso.fit<-glmnet::cv.glmnet(y = fullcovproxy.data$outcome, 
                             x = covar.mat, 
                             type.measure='mse',
                             family="binomial",
                             alpha = 1, 
                             nfolds = 5)
coef.fit<-coef(lasso.fit,s='lambda.min',exact=TRUE)
sel.variables<-row.names(coef.fit)[which(as.numeric(coef.fit)!=0)]
proxy.list.sel.ml <- proxy.list[proxy.list %in% sel.variables]
length(proxy.list.sel.ml)
#> [1] 54

From all proxies, we try to identify proxies that are empirically associated with the outcome based on a multivariate LASSO (outcome with all proxies in one model).
Note that LASSO model is choosing variables based on association with the outcome conditional on the ’exposure`.
Variable selection is only happening for proxy variables.
Investigator specified variables are not being subject to variable selection.

14.2 Build model formula based on selected variables

covform <- paste0(investigator.specified.covariates, collapse = "+")
proxyform <- paste0(proxy.list.sel.ml, collapse = "+")
rhsformula <- paste0(c(covform, proxyform), collapse = "+")
ps.formula <- as.formula(paste0("exposure", "~", rhsformula))

Build propensity score model based on selected variables based on LASSO.

14.3 Fit the PS model

hdps.data <- fullcovproxy.data
require(WeightIt)
W.out <- weightit(ps.formula, 
                    data = hdps.data, 
                    estimand = "ATE",
                    method = "ps")

Propensity score model fit to be able to calculate the inverse probability weights.

14.4 Obtain log-OR from unadjusted outcome model

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 <- c(fit.summary, conf.int)
knitr::kable(t(round(fit.summary_with_ci,2)))

Estimate	Std. Error	Pr(>\|z\|)	2.5 %	97.5 %
0.29	0.13	0	0.19	0.39

Summary of results (log-OR).