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john4525 · Wysłany: Śro 11:33, 09 Mar 2011 Temat postu: Table 12.11

90 = 1.060.50/0.05 = 10.0
TABLE 12.10
Estimating the Overall Reduction in Risk
SurviveDieTotalRisk of Death
Standard5055951100595/1100 = 0.54
New1959051100905/1100 = 0.82
Total70015002200
TABLE 12.11
The researchers would now like to estimate the overall reduction in risk for the
new treatmentso they combine all of the data (Table 12.11).
What has gone wrong? It now looks as though the standard treatment is supe-
rior to the new one. In factthe relative risktaken in the same direction as before
is 0.54/0.82 = 0.66. The death rate for the standard treatment is only 66% of
what it is for the new treatment.
The problem is that the more serious cases of the disease presumably were
treated by the famous research hospitalHospital A. Because they were more seri-
ous casesthey were more likely to die. But because they went to Hospital Athey
were also more likely to receive the new treatment. When the results from both
hospitals are combinedwe lose the information that the patients in Hospital A
12 / Relationships Bet [link widoczny dla zalogowanych][link widoczny dla zalogowanych]n Categorical Variables215
had both a higher overall death rate and a higher likelihood of receiving the new
treatment.
Simpson��s Paradox makes it clear that it is dangerous to summarize informa-
tion over groupyilai:
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