# Data Analysis

The data collected yield the following counts:

Total number of Cases: 112
Total number of Controls: 224
Number of Cases who ingested Endurobrick: 28
Number of Controls who ingested Endurobrick: 56
Number of Cases who consumed Quench-it: 50
Number of Controls who consumed Quench-it: 56

8. How would you set up the classic 2x2 table using the above information to test the hypothesis that cases are more likely to have ingested EnduroBrick than controls?

none:
Case Control Total
Exposed (Endurobrick) 28 56 84
Unexposed (No Endurobrick) 84 168 252
Total 112 224 336
none:

Odds of exposure among cases (# of Cases exposed) / (# of Cases unexposed)

28 / 84 = 0.333

none:

Odds of exposure among controls (# of Controls exposed) / (# of Controls unexposed)

56 / 168 = 0.333

none:

OR = (Odds of Exposure among Cases) / (Odds of Exposure among Controls)

(28/84) / (56/168) = 1.0 or 0.33 / 0.33 = 1.0

none:

Odds of disease among exposed (# of Cases Exposed) / (# of Controls Exposed)

28 / 56 = 0.50

none:

Odds of disease among unexposed (# of Cases Unexposed) / (# of Controls Unexposed)

84 / 168 = 0.50

none:

OR = Odds of disease among Exposed / Odds of disease among Unexposed

(28/56) / (84/168) = 1.0 or 0.50 / 0.50 = 1.0

none:

Individuals with Susser Syndrome (cases) have the same odds of having ingested EnduroBrick as those without Susser Syndrome (controls). Conversely, individuals who ate EnduroBrick have the same odds of developing Susser Syndrome as those who did not eat EnduroBrick. An Odds Ratio = 1.0 suggests that there is no association between Susser Syndrome and EnduroBrick ingestion.

9. How would you set up the classic 2x2 table using the above information to test the hypothesis that cases are more likely to have consumed Quench-It than controls?

none:
Case Control Total
Exposed (Quench-it) 50 56 106
Unexposed (No Quench-it) 62 168 230
Total 112 224 336
none:

Odds of exposure among cases (# of Cases exposed) / (# of Cases unexposed)

50 / 62 = 0.806

none:

Odds of exposure among controls (# of Controls exposed) / (# of Controls unexposed)

56 / 168 = 0.333

none:

OR = (Odds of Exposure among Cases) / (Odds of Exposure among Controls)

OR = (50/62) / (56/168) = 2.4 or 0.806 / 0.333 = 2.4

none:

Odds of disease among exposed (# of Cases Exposed) / (# of Controls Exposed)

50 / 56 = 0.893

none:

Odds of disease among unexposed (# of Cases Unexposed) / (# of Controls Unexposed)

62 / 168 = 0.369

none:

OR = Odds of disease among Exposed / Odds of disease among Unexposed

OR = (50/56) / (62/168) = 2.4 or 0.893/0.369 = 2.4

none:

Individuals with Susser Syndrome (cases) have 2.4 times higher odds of having consumed Quench-It than those without Susser Syndrome (controls). Conversely, individuals who drank Quench-It have a 2.4 times higher odds of developing Susser Syndrome than those who did not drink Quench-It. The OR = 2.4 supports a positive association between Susser Syndrome and Quench-It consumption.

Answer (a) — incorrect: The OR of 2.4 supports an association between Susser Syndrome and Quench-It consumption. The OR of 1.0 suggests no association between Susser Syndrome and EnduroBrick ingestion.
Answer (b) — incorrect: You must not confuse association with causation. The data suggest that Quench-It is associated with Susser Syndrome development whereas EnduroBrick is not. However, as detailed in Aschengrau & Seage (pp. 383-405), to move from association to causation requires a substantial amount of epidemiological evidence as well as biological plausibility. At this stage in the investigation, we are far from having enough data to conclude that Quench-It is the cause of Susser Syndrome.
Answer (c) — correct: The data do suggest that Quench-It is associated with the development of Susser Syndrome while EnduroBrick is not. However, we need to check the statistical significance of these findings as they may be due to chance. Furthermore, it is important to rule out alternate explanations for the association (such as bias and confounding) before we make a causal claim.

After reporting your results, you decide to do a little bit more detective work. You head over to the Public Health Laboratory records department and check the log file on Quench-It. Since its production, the Health and Food Safety Inspector has taken random samplings of Quench-It back to the lab to analyze for any possible contamination. This is a routine surveillance procedure. Looking over the file you notice something interesting . Since 2002, a substantial amount of SUPERCLEAN has been found in Quench-It, probably a result of the bottle sterilization process. Following the Department of Health's repeated and stern demands, Glop Industries has recently changed its production techniques, and now Quench-It is now completely free of SUPERCLEAN. Those who consumed Quench-It prior to these changes, however, might have been exposed to trace amounts of SUPERCLEAN