Post-baseline Prognostic Factor Adjusted Per Protocol Estimation

Post-baseline prognostic factor adjusted PP estimates use the subset of patient observations where treatments adhered to their randomly assigned treatments to calculate the effect estimate in the following form:

\[logit(Y) = \gamma_{0} + \gamma_{A} A + \gamma_{L} L + \gamma_{t} t\]

Using the artificially censored dataset of adherent patient observations, we fit the pooled logistic regression:

LAdjPPFit <- glm(Y ~ t0 + A + L1 + L2, data = 
                   simulated.data.combined, 
                 family = binomial(link="logit"))
LAdjPPFit

## 
## Call:  glm(formula = Y ~ t0 + A + L1 + L2, family = binomial(link = "logit"), 
##     data = simulated.data.combined)
## 
## Coefficients:
## (Intercept)           t0            A           L1           L2  
##   -13.30911      0.09248      1.78801      0.22582      1.55136  
## 
## Degrees of Freedom: 99371 Total (i.e. Null);  99367 Residual
## Null Deviance:       2365 
## Residual Deviance: 1921  AIC: 1931

Then similar to our previous models we calculate the clustered standard errors:

cov.m1 <- vcovCL(LAdjPPFit, type = "HC0", 
                 cluster = simulated.data.combined$id) 
co.test <- coeftest(LAdjPPFit, vcov = cov.m1)
co.CI <- coefci(LAdjPPFit, vcov = cov.m1, level = 0.95)

cat("Post-baseline prognostic factor adjusted PP effect estimate:", "\n",
        "log(OR)", round(coefficients(LAdjPPFit)[["A"]],3), "\n",
      "95% CI:", round(co.CI["A","2.5 %"],3), ",",round(co.CI["A","97.5 %"],3), "\n",
      "p-value", round(co.test["A","Pr(>|z|)"],3), "\n",
      "robust standard error", round(sqrt(diag(cov.m1))[["A"]],3))

## Post-baseline prognostic factor adjusted PP effect estimate: 
##  log(OR) 1.788 
##  95% CI: 1.429 , 2.147 
##  p-value 0 
##  robust standard error 0.183

Alternatively, we can again use the summ() function to obtain the same estimates:

summ(LAdjPPFit, robust = "HC0", 
     confint = TRUE, digits = 3, cluster="id", 
     model.info = FALSE, model.fit = FALSE)

	Est.	2.5%	97.5%	z val.	p
(Intercept)	-13.309	-14.289	-12.329	-26.610	0.000
t0	0.092	0.078	0.107	12.238	0.000
A	1.788	1.405	2.171	9.141	0.000
L1	0.226	0.158	0.294	6.521	0.000
L2	1.551	0.961	2.142	5.152	0.000
Standard errors: Cluster-robust, type = HC0