1. 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

2. 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)

3. 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 ( IU/mL) –C-reactive protein (mg/L) –Whether or not stayed on diet

4. 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)

5. 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 H 0 : = 0 vs H A : 0 with the t-test:

6. Comparison of Weight Loss @ 12 Months Note that authors report P-value of.40 (round-off differences)

7. 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 H A. Consider a more general alternative (the means are simply not all equal). H 0 : A = Z = W = O H A : Means not all equal Conduct the F-test based on Completely Randomized Design

8. 1-Way ANOVA Note still no evidence of diet differences.

9. 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 Test Statistic: X obs 2 =3.158 P-value=P(X 3 2 3.158) = 0.3679

10. Other Possible Analysis Repeated Measures ANOVA –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)