rm(list=ls())
## load dataset
data(breslow.dat, package = "robust")
names(breslow.dat)
[1] "ID" "Y1" "Y2" "Y3" "Y4" "Base" "Age" "Trt"
[9] "Ysum" "sumY" "Age10" "Base4"
summary(breslow.dat[c(6,7,8,10)])
Base Age Trt sumY
Min. : 6.00 Min. :18.00 placebo :28 Min. : 0.00
1st Qu.: 12.00 1st Qu.:23.00 progabide:31 1st Qu.: 11.50
Median : 22.00 Median :28.00 Median : 16.00
Mean : 31.22 Mean :28.34 Mean : 33.05
3rd Qu.: 41.00 3rd Qu.:32.00 3rd Qu.: 36.00
Max. :151.00 Max. :42.00 Max. :302.00
## look at the response variable in more detail
opar <- par(no.readonly = TRUE)
par(mfrow = c(1,2))
attach(breslow.dat)
The following objects are masked from breslow.dat (pos = 3):
Age, Age10, Base, Base4, ID, sumY, Trt, Y1, Y2, Y3, Y4,
Ysum
The following objects are masked from breslow.dat (pos = 4):
Age, Age10, Base, Base4, ID, sumY, Trt, Y1, Y2, Y3, Y4,
Ysum
hist(sumY, breaks = 20, xlab = "Seizure Count", main = "Distribution of Seizures")
boxplot(sumY ~ Trt, xlab = "Treatment", main = "Group Comparisons")
par(opar)
## from above figure, we can see the skewed nature of the dependent variable and the possible presence of outliers.
## fit the poisson regression
fit <- glm(sumY ~ Base + Age + Trt, data = breslow.dat, family = poisson())
summary(fit)
Call:
glm(formula = sumY ~ Base + Age + Trt, family = poisson(), data = breslow.dat)
Deviance Residuals:
Min 1Q Median 3Q Max
-6.0569 -2.0433 -0.9397 0.7929 11.0061
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.9488259 0.1356191 14.370 < 2e-16 ***
Base 0.0226517 0.0005093 44.476 < 2e-16 ***
Age 0.0227401 0.0040240 5.651 1.59e-08 ***
Trtprogabide -0.1527009 0.0478051 -3.194 0.0014 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 2122.73 on 58 degrees of freedom
Residual deviance: 559.44 on 55 degrees of freedom
AIC: 850.71
Number of Fisher Scoring iterations: 5
detach(breslow.dat)
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