CAS Exam MAS-II Spring 2019, Question 1
Study guide: Exam MAS-II
In the supplemental material, you have been given a case study, "Systolic Blood Pressure Case Study", showing the results of different treatment options and the description of how that study was set up. You have also been asked to evaluate three statements regarding the results of the study.
The relevant output from the case study is reproduced below. Change in systolic blood pressure is measured over one year for 2,099 patients across 21 hospitals; hospital enters as a random effect and the three treatments are coded 0 (reference), 1 and 2.
Box plot of change in systolic by treatment
Model 1 — main effects of treatment and age, hospital as a random effect, constant variance:
## Linear mixed-effects model fit by REML
## Data: systolic_g
## AIC BIC logLik
## 7327.429 7361.313 -3657.715
##
## Random effects:
## Formula: ~1 | hospital
## (Intercept) Residual
## StdDev: 0.4262212 1.361067
##
## Fixed effects: change_systolic ~ Treatment + Age
## Value Std.Error DF t-value p-value
## (Intercept) -12.487130 0.3181821 2075 -39.24523 0
## Treatment1 0.654929 0.0709604 2075 9.22950 0
## Treatment2 5.024052 0.0784480 2075 64.04309 0
## Age 0.165733 0.0049154 2075 33.71726 0
##
## numDF denDF F-value p-value
## (Intercept) 1 2075 55.3061 <.0001
## Treatment 2 2075 2521.6816 <.0001
## Age 1 2075 1136.8534 <.0001
Model 3 — same main effects plus a treatment-by-age interaction:
## Fixed effects: change_systolic ~ Treatment + Age + Treatment * Age
## Value Std.Error DF t-value p-value
## (Intercept) -12.383800 0.5482496 2073 -22.587888 0.0000
## Treatment1 0.638400 0.7128276 2073 0.895588 0.3706
## Treatment2 4.672223 0.7881578 2073 5.928030 0.0000
## Age 0.164038 0.0088235 2073 18.591054 0.0000
## Treatment1:Age 0.000267 0.0116514 2073 0.022920 0.9817
## Treatment2:Age 0.005757 0.0128419 2073 0.448268 0.6540
##
## numDF denDF F-value p-value
## (Intercept) 1 2073 55.3245 <.0001
## Treatment 2 2073 2519.5614 <.0001
## Age 1 2073 1135.9036 <.0001
## Treatment:Age 2 2073 0.1305 0.8777
I. None of the treatments significantly reduce systolic blood pressure. II. The age of the patient has a significant effect on the change in blood pressure expected over a one-year time period. III. The age of the patient interacts significantly with the treatment.
Determine which of the above statements are true.
- A) I only
- B) II only
- C) III only
- D) I, II and III
- E) The answer is not given by (A), (B), (C), or (D)
Answer this question and see the worked solution