Main causal contrast of the theory The frequency of Alzheimer’s disease in persons exposed to high sugar consumption is greater than frequency of Alzheimer’ disease in persons exposed to high sugar consumption if they had not been exposed. b. Hypotheses in operationalized form HYPOTHESIS 1: High sugar intake (E) causes Alzheimer’s disease (D) beyond chance. (Main Effect and its magnitude) HYPOTHESIS 2: Chronic stress is an alternative explanation for the association between high sugar intake and Alzheimer’s disease. Confounding) HYPOTHESIS 3: High sugar intake leads to diabetes, a major contributor to Alzheimer’s disease. (Mediation) HYPOTHESIS 4: The relationship between high sugar intake and Alzheimer’s disease is particularly apparent among those with a family history of Alzheimer’s disease. (Effect Modification) c. DAG d. Causal pies for main effect: Where X is unknown. e. Response types for main effect Type 1 – Doomed; Type 2 – Causal f. Results that would be consistent with each hypothesis HYPOTHESIS 1: HYPOTHESIS 2: HYPOTHESIS 3:
HYPOTHESIS 4: 2. TRUTH (DR. MEDITATIVE’S “STUDY”) DATA IN TABLE 1 a. Test of each hypothesis: ANALYSIS FOR HYPOTHESIS 1: Testing for Association | Alzheimer’s disease (D+)| No Alzheimer’s disease (D-)| High Sugar Intake (E+)| 56,312 + 33,456 =89,768| 428,431 + 80,249 =508,680| No High Sugar Intake (E-)| 9,355 + 13,386 =22741| 124,298 + 251,926 =376,224| OR = [(PrD+|E+)/(PrD-|E+)]/[(PrD+|E-)/(PrD-|E-)] = (ad)/(bc) = [(89,768)(376,224)]/[508,680)(22,741)] ? 2. 92 Find the Confidence Interval:
Step 1. Variance for the natural log of the OR: 1/a + 1/b + 1/c + 1/d = (1/89,768) + (1/508,680) + (1/22,741) + (1/376,224) = 0. 0000597371305904 Step 2. Standard error for lnOR: (1/a + 1/b + 1/c + 1/d)1/2 = (0. 0000597371305904)1/2 = 0. 0077289799191355129 ? 0. 008 Step 3. Upper limit for the Log Odds Ratio: ln OR + [(za * (1/a + 1/b + 1/c + 1/d)1/2] = ln(2. 92) + (1. 96 * 0. 008) ? 1. 09 Step 4. Lower limit for the Log Odds Ratio: ln OR – [(za * (1/a + 1/b + 1/c + 1/d)1/2] = ln(2. 92) – (1. 96 * 0. 008) ? 1. 06 Step 5.
Confidence Interval around OR: e(lower limit log OR) to e(upper limit log OR) e1. 06 to e1. 09 = (2. 88 to 2. 97) ANALYSIS FOR HYPOTHESIS 2: Testing for Confounding | Alzheimer’s disease (D+)| No Alzheimer’s disease (D-)| TOTAL| Chronic Stress (CS+)| 42,974 + 22,410 + 6451 + 10,193 =81758| 183,947 + 8272 + 53,651 + 101,257 = 347,130| 428,888| No Chronic Stress (CS-)| 13,338 + 11,316 + 2904 + 3193 =30751| 244,484 + 71,977 + 70,644 + 150,669 = 537,774| 568,525| RR (CS & D) = (a/a+b)/(c/c+d) = (81,758/428,888)/(30,751/568,525) ? 3. 52
OR (CS & D) = (ad/bc) = (81,758*537,774)/(347,130*30,751) ? 4. 12 | High Sugar Intake (E+)| No High Sugar Intake (E-)| TOTAL| Chronic Stress (CS+)| 42,794 + 22,140 + 183,947 + 8272 = 257,333| 6451 + 10,193 + 53,654 + 101,257 = 171,555| 428,888| No Chronic Stress (CS-)| 13,338 + 11,316 + 244,484 + 71,977 = 341,115| 2904 + 3193 + 70,644 + 150,669 = 227,410| 568,525| RR (CS & E) = (a/a+b)/(c/c+d) = (257,333/428,888)/(341,115/568,525) ? 1. 00 OR (CS & E) = (ad/bc) = (257,333*227,410)/(171,555*341,115) ? 1. 00 ANALYSIS FOR HYPOTHESIS 3: Testing for Mediation
ANALYSIS FOR HYPOTHESIS 4: Testing for Effect Modification | Family History of Alzheimer’s (FH+)| No Family History of Alzheimer’s (FH-)| | Alzheimer’s disease (D+)| No Alzheimer’s disease (D-)| Alzheimer’s disease (D+)| No Alzheimer’s disease (D-)| High Sugar Intake (E+)| 33,456| 80,249| 56,312| 428,431| No High Sugar Intake (E-)| 13,386| 251,926| 9355| 124,298| Stratum RR (FH+) = [(33,456/(33456+80,249)]/[13,386/(13,386+251,926)] ? 5. 83 Stratum RR (FH-) = [56,312/(56,312 + 428,431)]/[9355/(9355+124298)] ? 1. 66
