Thalidomide and TB Status in Weight Gains in HIV+ Patients
2-Way ANOVA Using Regression with Dummy Variables

All patients are HIV+

16 also have Tuberculosis (TB+), 16 do not have Tuberculosis (TB-)

Half of TB+ patients received Thalidomide, half received placebo

Half of TB- patients received Thalidomide, half received placebo

Y = weight gain (kg) in 21 day period
Define dummy variables:
TB=1 if patient is TB+, 0 if patient is TBThal=1 if patient was assigned Thalidomide, 0 if placebo
TB_Thal=TB*Thal
Model: E(Y) = TB + Thal + TB_Thal
Group Means:
Group
TB
+
TB /Thal
1

TB Placebo
1
TB /Thal
0
TB-/Placebo
0
Thal
1
0
1
0
TB_Thal
1
0
0
0
E(Y)




Conditional on TB+, Thalidomide (vs Placebo) Effect:
(

Conditional on TB-, Thalidomide (vs Placebo) Effect:
(

So, the thalidomide effect is the same in the two patient populations (TB+/TB-) if 






Results fitting model in SPSS, with wt_gain as dependent variable, tb and thal in block
1 for independent variables, and tb_thal in block 2. Note that with either variable
having more than 2 levels, there would be more than 2 variables in block 1, and more
than one variable in block 2.
Variables Entered/Removedb
Model
1
2
Variables
Entered
THAL, TBa
TB_THALa
Variables
Removed
Method
Enter
Enter
.
.
a. All requested variables entered.
b. Dependent Variable: WTGAIN
Model Summary
Model
1
2
R
.649a
.723b
R Square
.422
.522
Adjusted
R Square
.382
.471
Std. Error of
the Estimate
2.0463
1.8928
a. Predictors: (Constant), THAL, TB
b. Predictors: (Constant), THAL, TB, TB_THAL
ANOVAc
Model
1
2
Regres sion
Residual
Total
Regres sion
Residual
Total
Sum of
Squares
88.563
121.438
210.000
109.687
100.313
210.000
df
2
29
31
3
28
31
Mean Square
44.281
4.188
F
10.575
Sig.
.000a
36.562
3.583
10.206
.000b
a. Predic tors: (Constant), THAL, TB
b. Predic tors: (Constant), THAL, TB, TB_THAL
c. Dependent Variable: W TGAIN
Model 1 is Reduced Model
Model 2 is Full (Complete) Model
Coeffi cientsa
Model
1
2
(Const ant)
TB
THAL
(Const ant)
TB
THAL
TB_THAL
Unstandardized
Coeffic ients
B
St d. Error
-.125
.627
-.313
.723
3.313
.723
.687
.669
-1. 937
.946
1.688
.946
3.250
1.338
St andardiz ed
Coeffic ients
Beta
-.061
.647
-.378
.329
.549
t
-.200
-.432
4.579
1.027
-2. 047
1.783
2.428
Sig.
.843
.669
.000
.313
.050
.085
.022
a. Dependent Variable: W TGAIN
Test for interaction
H0: No interaction between TB status and drug (thalidomide/placebo) on weight gains in
HIV+ patients ()
HA: Interaction exists ( Not equal to 0)
t-test (This can only be used because there is only one interaction term in model)
TS: tobs = 3.250 / 1.338 = 2.428
p-value=.022 (see above table for variable TB_THAL)
F-test (This can me used when there are any number of interaction terms being
simultaneously tested equal to 0).
SSE(REDUCED) = 121.438 (See ANOVA table above)
SSE(FULL) = 100.313 (See ANOVA table above)
MSE(FULL) = 3.583 (See ANOVA table above)
# of Parameters being tested = 0 in H0 = 1
dfError(Full) = 28
TS: Fobs = [ (SSE(REDUCED) – SSE(FULL))/#Parms in H0 ] / MSE(FULL)
= [ (121.438 – 100.313) /1 ] / 3.583 = 5.90
RR: Fobs > F.05,1,28 = 4.20
Reject H0, conclude there is a significant interaction.
Estimated group means (Parameter values in previous tables replaced by estimates
from full model):
Group
TB+/Thal
TBPlacebo
TB-/Thal
TB-/Placebo
TB
1
1
0
0
Thal
1
0
1
0
TB_Thal
1
0
0
0
Estimated mean
0.687-1.937+1.688+3.250 = 3.688
0.687-1.937 = -1.250
0.687 + 1.688 = 2.375
0.687
Plot these means with TB status (+/-) on the horizontal axis to observe the interaction
(separate lines for each treatment group: thalidomide and placebo).
4
3
2
1
0
WTGAIN
THA L
-1
Thalidomide
-2
Placebo
-.2
0.0
.2
.4
.6
.8
1.0
1.2
TB
Source: J.D. Klausner, S. Makonkawkeyoon, P. Akarrasewi, et al. (1996). “The Effect of
Thalidomide on The Pathogenesis of HIV-1 in M. Tuberculosis Infection”, Journal of
Acquired Immune Deficiency Syndromes and Hunan Retrovirology. Vol. 11, pp 247-257.