08LaPP.Rmd

# 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:

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

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

```{r, cache=TRUE}
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))

```

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

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