diff --git a/R/Data.R b/R/Data.R
index 8094c96..1874600 100644
--- a/R/Data.R
+++ b/R/Data.R
@@ -176,6 +176,11 @@ validate.RoboDataTTE <- function(data, ref_arm){
   if(!is.null(data$event)){
     data$event <- as.vector(data$event[[1]])
   }
+  if(ncol(data$exposure) == 0){
+    data$exposure <- NULL
+  } else {
+    data$exposure <- as.vector(data$exposure[[1]])
+  }
   if(ncol(data$strata) == 0){
     data$strata <- NULL
   }
diff --git a/R/adjust-glm.R b/R/adjust-glm.R
index ae7dffb..add9571 100644
--- a/R/adjust-glm.R
+++ b/R/adjust-glm.R
@@ -12,6 +12,9 @@ predictions.GLMModel <- function(model, data, mod){
   if(!is.null(dmat)){
     df <- cbind(df, dmat)
   }
+  if(!is.null(data$exposure)){
+    df <- cbind(df, exposure=data$exposure)
+  }
   preds <- stats::predict(mod, newdata=df, type="response")
   return(preds)
 }
diff --git a/R/adjust-linear.R b/R/adjust-linear.R
index ce160d8..e4991ea 100644
--- a/R/adjust-linear.R
+++ b/R/adjust-linear.R
@@ -35,7 +35,12 @@ linmod.ANOVA <- function(model, data, family=stats::gaussian, center=TRUE){
     treat=data$treat,
     response=data$response
   )
-  mod <- fitmod(family=family, formula=response ~ 0 + treat, data=df)
+  if(is.null(data$exposure)){
+    mod <- fitmod(family=family, formula=response ~ 0 + treat, data=df)
+  } else {
+    df <- cbind(df, exposure=data$exposure)
+    mod <- fitmod(family=family, formula=response ~ 0 + treat + offset(exposure), data=df)
+  }
   return(mod)
 }
 
@@ -48,10 +53,21 @@ linmod.ANCOVA <- function(model, data, family=stats::gaussian, center=TRUE){
   dmat <- get.dmat(data, model$adj_vars)
   if(center) dmat <- .center.dmat(dmat)
   df <- cbind(df, dmat)
+  if(!is.null(data$exposure)){
+    df <- cbind(df, exposure=data$exposure)
+  }
   if(center){
-    mod <- fitmod(family=family, formula=response ~ 0 + treat + ., data=df)
+    if(is.null(data$exposure)){
+      mod <- fitmod(family=family, formula=response ~ 0 + treat + ., data=df)
+    } else {
+      mod <- fitmod(family=family, formula=response ~ 0 + treat + . - exposure + offset(exposure), data=df)
+    }
   } else {
-    mod <- fitmod(family=family, formula=response ~ 1 + treat + ., data=df)
+    if(is.null(data$exposure)){
+      mod <- fitmod(family=family, formula=response ~ 1 + treat + ., data=df)
+    } else {
+      mod <- fitmod(family=family, formula=response ~ 1 + treat + . - exposure + offset(exposure), data=df)
+    }
   }
   return(mod)
 }
@@ -65,10 +81,21 @@ linmod.ANHECOVA <- function(model, data, family=stats::gaussian, center=TRUE){
   if(center) dmat <- .center.dmat(dmat)
   df <- cbind(df, dmat)
 
+  if(!is.null(data$exposure)){
+    df <- cbind(df, exposure=data$exposure)
+  }
   if(center){
-    mod <- fitmod(family=family, response ~ 0 + treat:., data=df)
+    if(is.null(data$exposure)){
+      mod <- fitmod(family=family, response ~ 0 + treat:., data=df)
+    } else {
+      mod <- fitmod(family=family, response ~ 0 + treat:(. - exposure) + offset(exposure), data=df)
+    }
   } else {
-    mod <- fitmod(family=family, response ~ 1 + treat:., data=df)
+    if(is.null(data$exposure)){
+      mod <- fitmod(family=family, response ~ 1 + treat:., data=df)
+    } else {
+      mod <- fitmod(family=family, response ~ 1 + treat:(. - exposure) + offset(exposure), data=df)
+    }
   }
   return(mod)
 }
diff --git a/R/robincar-SL.R b/R/robincar-SL.R
index f072031..03a8a7e 100644
--- a/R/robincar-SL.R
+++ b/R/robincar-SL.R
@@ -92,7 +92,8 @@ robincar_SL <- function(df,
     treat_col=treat_col,
     response_col=response_col,
     strata_cols=strata_cols,
-    covariate_cols=covariate_cols
+    covariate_cols=covariate_cols,
+    exposure_col=NULL
   )
   validate(data)
 
diff --git a/R/robincar-covhr.R b/R/robincar-covhr.R
index 40fdee6..9b9bd64 100644
--- a/R/robincar-covhr.R
+++ b/R/robincar-covhr.R
@@ -36,7 +36,8 @@ robincar_covhr <- function(df,
     response_col=response_col,
     event_col=event_col,
     strata_cols=strata_cols,
-    covariate_cols=covariate_cols
+    covariate_cols=covariate_cols,
+    exposure_col=NULL
   )
   validate(data, ref_arm)
 
diff --git a/R/robincar-glm.R b/R/robincar-glm.R
index fb8874a..c3fc5fd 100644
--- a/R/robincar-glm.R
+++ b/R/robincar-glm.R
@@ -20,13 +20,14 @@
 #'                 If you wish to use a negative binomial working model with an unknown dispersion parameter, then use `g_family="nb"`.
 #' @param g_accuracy Level of accuracy to check prediction un-biasedness.
 #' @param formula An optional formula to use for adjustment specified using as.formula("..."). This overrides strata_cols and covariate_cols.
+#' @param exposure_col An offset variable to use for Poisson or negative binomial working models
 #'
 #' @export
 robincar_glm <- function(df,
                          treat_col, response_col, strata_cols=NULL, covariate_cols=NULL,
                          car_scheme="simple", adj_method="heterogeneous", # vcovHC="HC0",
                          covariate_to_include_strata=NULL,
-                         g_family=stats::gaussian, g_accuracy=7, formula=NULL,
+                         g_family=stats::gaussian, g_accuracy=7, formula=NULL, exposure_col=NULL,
                          contrast_h=NULL, contrast_dh=NULL){
 
   .check.car_scheme(car_scheme)
@@ -42,7 +43,8 @@ robincar_glm <- function(df,
     response_col=response_col,
     strata_cols=strata_cols,
     covariate_cols=covariate_cols,
-    formula=formula
+    formula=formula,
+    exposure_col=exposure_col
   )
   validate(data)
 
diff --git a/R/robincar-tte.R b/R/robincar-tte.R
index b5178d6..966be85 100644
--- a/R/robincar-tte.R
+++ b/R/robincar-tte.R
@@ -38,7 +38,8 @@ robincar_tte <- function(df,
     response_col=response_col,
     event_col=event_col,
     strata_cols=strata_cols,
-    covariate_cols=covariate_cols
+    covariate_cols=covariate_cols,
+    exposure_col=NULL
   )
   validate(data, ref_arm)
 
diff --git a/man/robincar_glm.Rd b/man/robincar_glm.Rd
index 0b79714..586eef2 100644
--- a/man/robincar_glm.Rd
+++ b/man/robincar_glm.Rd
@@ -16,6 +16,7 @@ robincar_glm(
   g_family = stats::gaussian,
   g_accuracy = 7,
   formula = NULL,
+  exposure_col = NULL,
   contrast_h = NULL,
   contrast_dh = NULL
 )
@@ -44,6 +45,8 @@ If you wish to use a negative binomial working model with an unknown dispersion
 
 \item{formula}{An optional formula to use for adjustment specified using as.formula("..."). This overrides strata_cols and covariate_cols.}
 
+\item{exposure_col}{An offset variable to use for Poisson or negative binomial working models}
+
 \item{contrast_h}{An optional function to specify a desired contrast}
 
 \item{contrast_dh}{An optional jacobian function for the contrast (otherwise use numerical derivative)}
diff --git a/tests/testthat/test-glm.R b/tests/testthat/test-glm.R
index fd6339d..715b556 100644
--- a/tests/testthat/test-glm.R
+++ b/tests/testthat/test-glm.R
@@ -159,6 +159,41 @@ test_that("GLM full function -- NEGATIVE binomial, permuted block", {
 
 })
 
+test_that("GLM full function -- NEGATIVE binomial, permuted block w offset", {
+
+  DATA2$offset1 <- DATA2$y + rbinom(n=nrow(DATA2), size=10, prob=0.5)
+
+  # Known dispersion parameter
+  non <- robincar_glm(
+    df=DATA2,
+    response_col="y",
+    treat_col="A",
+    strata_cols=c("z1"),
+    covariate_cols=c("x1"),
+    car_scheme="permuted-block",
+    g_family=negative.binomial(1),
+    g_accuracy=7,
+    adj_method="heterogeneous",
+    covariate_to_include_strata=TRUE,
+    exposure_col="offset1")
+  expect_equal(class(non), "GLMModelResult")
+
+  # Known dispersion parameter
+  non <- robincar_glm(
+    df=DATA2,
+    response_col="y",
+    treat_col="A",
+    strata_cols=c("z1"),
+    covariate_cols=c("x1"),
+    car_scheme="permuted-block",
+    g_family="nb",
+    g_accuracy=7,
+    adj_method="heterogeneous",
+    covariate_to_include_strata=TRUE)
+  expect_equal(class(non), "GLMModelResult")
+
+})
+
 test_that("GLM Settings", {
   non <- robincar_glm(
     df=DATA2,