Comparison of 4 Diets
Dansinger, et al (2005). “Comparison of
Atkins, Ornish, Weight Watchers and Zone
Diets for Weight Loss and Heart Disease Risk
Reduction,” JAMA. 293:43-53
Setting
• Started with 1010 Telephone Inquiries
• 763 Excluded (No interest, too busy, not in
range of BMI (27-42), insulin, unknown)
• 247 Screened in person-87 excluded for
various reasons
• 160 Randomized
–
–
–
–
40 Atkins
40 Zone
40 Weight Watchers
40 Ornish (Vegetarian)
Primary Measures
• Changes from baseline taken at 2, 6, 12 months:
–
–
–
–
–
–
–
–
–
–
–
Weight (kg)
BMI
Waist Circumference (cm)
Total, LDL, HDL Cholesterol (mg/dL)
Total/LDL and Total/HDL cholesterol ratios
Triglycerides (mg/dL)
Systolic and Diastolic BP (mm Hg)
Glucose (mg/dL)
Insulin (mIU/mL)
C-reactive protein (mg/L)
Whether or not stayed on diet
Miscellaneous Issues
• Diets were considered to be ordered in terms of
extremity: Atkins < Zone < Weight Watchers < Ornish
• Analyses were conducted at 3 points in time: 2 months,
6 months, 12 months
• Controlled for: dietary adherence, cardiac risk factors,
baseline characteristics, exercise changes, medication
• Analyzed two sets of individuals:
– All subjects randomized with baseline measure carried
forward if dropped out (intent-to-treat)
– Those subjects who were continuing in the study (completed
protocol aka study completers)
Tests Reported
• At each point in time for each measure, the
authors gave the diets levels of X=1, 2, 3, 4 based
on the ordering of their extremity
• They then fit a simple regression, relating the level
of the measure (change from baseline with
missing values being set at 0, no change) to the
diet level, and obtained the Pearson correlation
• They then tested H0: r = 0 vs HA: r  0 with the
t-test:
r
Test Statistic : tobs 
1  r / 158
2
P - value : P  2 P t158  tobs 
Comparison of Weight Loss @ 12 Months
Diet
Atkins
Zone
WW
Ornish
Sum
# in
21
26
26
20
SS_XX
SS_YY
SS_XY
r
t_obs
P-value
200
5320
71.25
0.069
0.87
0.385
Xbar
1
2
3
4
Ybar
3.9
4.9
4.6
6.6
S_y
6.0
6.9
5.4
9.3
SX
40
80
120
160
400
SY
81.9
127.4
119.6
132.0
460.9
S X^2
40
160
360
640
1200
S Y^2
1039.4
1814.5
1279.2
2514.5
6647.6
S XY
81.9
254.8
358.8
528.0
1223.5
Note that authors report P-value of .40 (round-off differences)
Alternative Tests
• The authors’ tests are very restrictive regarding the
diet means:
– The diets are “equally spaced” wrt extremity
– The means will vary in a linear fashion in HA.
• Consider a more general alternative (the means are
simply not all equal).
• H0: mA = mZ = mW = mO HA: Means not all equal
• Conduct the F-test based on Completely
Randomized Design
1-Way ANOVA
Diet
Atkins
Zone
WW
Ornish
Sum
n
40
40
40
40
160
Ybar
ANOVA
TRTS
ERROR
TOTAL
df
3
156
159
SY
81.9
127.4
119.6
132.0
460.9
S Y^2
1039.4
1814.5
1279.2
2514.5
6647.6
Ybar
2.05
3.19
2.99
3.30
S^2
22.35
36.12
23.63
53.31
MS
12.99
33.85
F
0.3839
P-value
0.7648
2.880625
SS
38.98
5280.94
5319.92
Note still no evidence of diet differences.
SSTrt
27.76
3.71
0.48
7.04
38.98
SSErr
871.71
1408.73
921.60
2078.90
5280.94
Test of Differences in Attrition (Chi-Square)
• Atkins: 21 of 40 still participating at 12 months
• Zone: 26 of 40 still participating at 12 months
• Weight Watchers: 26 of 40 still participating at 12 months
• Ornish: 21 of 40 still participating at 12 months
• Overall: 93 of 160 still participating at 12 months
Diet
Atkins
Zone
WW
Ornish
Total
Observed
Active
Dropout
21
19
26
14
26
14
20
20
93
67
Total
40
40
40
40
160
Expected
Active
Dropout
23.25
16.75
23.25
16.75
23.25
16.75
23.25
16.75
Chi-Square
Active
0.21774194
0.32526882
0.32526882
0.45430108
Dropout
0.302239
0.451493
0.451493
0.630597
Sum
0.519981
0.776761
0.776761
1.084898
3.158402
Test Statistic: Xobs2 =3.158 P-value=P(X32  3.158) = 0.3679
Other Possible Analysis
• Repeated Measures ANOVA
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–
–
–
–
Diet Effects (4-1=3 df)
Subject(Diet) Effects (4(40-1)=156 df)
Time Effects (3-1=2 df)
Diet x Time Interaction (3(2)=6 df)
Error (Time x Subject(Diet) Interaction) (2(156)=312 df)
H 0 : No Diet Effect
H 0 : No Time Effect
TS : FDiet 
MS Diet
MS Subj( Diet )
TS : FTime 
MSTime
MS Error
H 0 : No Diet x Time Interactio n TS : FDietTime 
MS DietTime
MS Error