Family.Rmd##
+## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
+##
+## filter, lag## The following objects are masked from 'package:base':
+##
+## intersect, setdiff, setequal, union
+if (!require("remotes")) {
+ install.packages("remotes")
+}## Loading required package: remotes
+remotes::install_github(
+ "openpharma/RobinCar2"
+)## Using GitHub PAT from the git credential store.## Skipping install of 'RobinCar2' from a github remote, the SHA1 (4f016471) has not changed since last install.
+## Use `force = TRUE` to force installation##
+## Attaching package: 'RobinCar2'## The following object is masked from 'package:base':
+##
+## tableThis vignette is to accompany the Results section of the RobinCar +Family paper.
+Data Manipulation
+Creates continuous and binary outcomes, and does simple data +manipulations.
+
+# Data are from the speff2trial package
+data <- tibble(speff2trial::ACTG175)
+
+data <- data %>% mutate(
+ # Create continuous and binary outcomes
+ y_cont = cd420 - cd40,
+ y_bin = as.numeric((y_cont / cd40) > 0.5)
+) %>% filter(
+ # Focus on two treatment arms
+ arms %in% c("0", "1")
+) %>% mutate(
+ # Factor variables for treatment
+ # and stratification variable
+ arms = factor(arms),
+ strat = factor(strat)
+)Linear Adjustment
+The following shows a linear model with treatment-by-covariate +interactions, including strata as covariates, and using the four +covariates of weight, hemophilia status, and prior use of non-zidovudine +antiretroviral therapy. These specifications ensure that the covariate +adjustment has guaranteed efficiency gain (asymptotically).
+
+robin_lm(
+ y_cont ~ arms * (strat + wtkg + hemo + oprior),
+ treatment = arms ~ pb(strat),
+ data=data)## Model : y_cont ~ arms * (strat + wtkg + hemo + oprior)
+## Randomization: arms ~ pb(strat) ( Permuted-Block )
+## Variance Type: vcovG
+## Marginal Mean:
+## Estimate Std.Err 2.5 % 97.5 %
+## 0 -16.9304 4.4915 -25.7336 -8.1273
+## 1 54.0531 6.2848 41.7352 66.3710
+##
+## Contrast : h_diff
+## Estimate Std.Err Z Value Pr(>|z|)
+## 1 v.s. 0 70.984 7.673 9.2511 < 2.2e-16 ***
+## ---
+## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Generalized Linear Models
+For the binary outcome, we can use a logistic regression model +instead.
+
+robin_glm(
+ y_bin ~ arms * (wtkg + hemo + oprior),
+ treatment = arms ~ pb(strat),
+ family = binomial(link = "logit"),
+ contrast = "risk_ratio",
+ data = data
+)## Warning in robin_glm(y_bin ~ arms * (wtkg + hemo + oprior), treatment = arms ~
+## : Consider using the log transformation `log_odds_ratio` and `log_risk_ratio`
+## to replace `odds_ratio` and `risk_ratio` to improve the performance of normal
+## approximation.## Model : y_bin ~ arms * (wtkg + hemo + oprior)
+## Randomization: arms ~ pb(strat) ( Permuted-Block )
+## Variance Type: vcovG
+## Marginal Mean:
+## Estimate Std.Err 2.5 % 97.5 %
+## 0 0.0496651 0.0092998 0.0314378 0.0679
+## 1 0.1828118 0.0168988 0.1496908 0.2159
+##
+## Contrast : risk_ratio
+## Estimate Std.Err Z Value Pr(>|z|)
+## 1 v.s. 0 3.68089 0.76609 3.4994 0.0004662 ***
+## ---
+## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Rather than a linear contrast, we can instead estimate a risk ratio. +This does not change the marginal mean estimates, but it changes the +contrast estimates (and p-values).
+
+robin_glm(
+ y_bin ~ arms * (strat + wtkg + hemo + oprior),
+ treatment = arms ~ pb(strat),
+ family = binomial(link = "logit"),
+ contrast = "log_risk_ratio",
+ data=data
+)## Model : y_bin ~ arms * (strat + wtkg + hemo + oprior)
+## Randomization: arms ~ pb(strat) ( Permuted-Block )
+## Variance Type: vcovG
+## Marginal Mean:
+## Estimate Std.Err 2.5 % 97.5 %
+## 0 0.0493622 0.0093041 0.0311264 0.0676
+## 1 0.1835664 0.0168944 0.1504539 0.2167
+##
+## Contrast : log_risk_ratio
+## Estimate Std.Err Z Value Pr(>|z|)
+## 1 v.s. 0 1.31339 0.20904 6.2831 3.318e-10 ***
+## ---
+## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Mantel-Haenszel
+RobinCar includes functions for robust Mantel-Haenszel estimation. +Here we create a new variable that is the interaction of prior use of +non-zidovudine antiretroviral therapy and hemophilia status, and use +that as the stratification variable.
+By default, the function uses the average treatment effect as the +estimand of interest. Specifying the estimand argument as “MH” does not +change the estimate, but it does change the standard error +calculation.
+The MH function in RobinCar is only valid for simple +randomization.
+
+data <- data %>% mutate(
+ X=interaction(oprior, hemo)
+)
+
+robincar_mh(
+ data, "arms", "y_bin",
+ strata_cols=c("oprior", "hemo")
+)## Treatment group contrasts based on ATE
+## Estimand: ATE
+## Stratified by oprior, hemo
+## SE calculated via modified Greenland's estimator
+##
+## Contrasts:
+## # A tibble: 1 × 4
+## contrast estimate se `pval (2-sided)`
+## <chr[1d]> <dbl> <dbl> <dbl>
+## 1 treat 1 - 0 0.134 0.0193 3.83e-12Survival Analysis
+For a survival outcome with right-censoring, we can use the RobinCar2
+function robin_surv to do a covariate-adjusted, stratified
+log-rank test.
+surv <- robin_surv(
+ Surv(days, cens) ~ wtkg + oprior + hemo + strata(strat),
+ treatment = arms ~ pb(strat),
+ data = data
+)
+surv## Model : Surv(days, cens) ~ wtkg + oprior + hemo + strata(strat)
+## Randomization: arms ~ pb(strat) (Permuted-Block)
+## Stratification variables: strat
+## Covariates adjusted for: wtkg, oprior, hemo (including interactions with arms)
+##
+## Contrast : Covariate-adjusted Stratified Log Hazard Ratio
+##
+## Estimate Std.Err Z Value Pr(>|z|)
+## 1 v.s. 0 -0.69673 0.12323 -5.6539 1.569e-08 ***
+## ---
+## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+##
+## Test : Covariate-adjusted Stratified Log-Rank
+##
+## Test Stat. Pr(>|z|)
+## 1 v.s. 0 -5.7736 7.757e-09 ***
+## ---
+## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1You can use the table function to see the number of
+events and number at-risk
+table(surv)## Number of patients and events per stratum and treatment arm:
+## strat arms Patients Events
+## 1 1 0 223 59
+## 2 1 1 213 34
+## 3 2 0 96 30
+## 4 2 1 106 20
+## 5 3 0 213 92
+## 6 3 1 203 49