Tony H.

# p values differing amongst two groups in comparison

this is a board exam practice question, so I apologize in advance for leaving out all the details. I don't even know if this is a legitimate study.

this was a study based on serum glucose levels and the association with developing dementia, comparing those WITH diabetes and those WITHOUT Diabetes. The results appear to be counterintuitive. I noticed both p-values are not equivalent, though both less than the arbitrary 0.05. My overall question is one trying to develop a larger understanding of potential loop hole data biases. Is having two VERY different p levels (though both less than 0.05) justifiable when comparing between two groups? see below to make sense of what I am saying.

sugars

Average glucose level (left);Hazard ratio for dementia (95% confidence interval) (Right)

Participants without diabetes

95 mg/dL 0.85( 0.77-0.96)

100 mg/dL . 1.00

105 mg/dL 1.11 (1.03-1.18)

110 mg/dL 1.14 (1.03-1.27)

115 mg/dL 1.12 (1.04-1.31)

p-value 0.02

Participants with diabetes

150 mg/dL 1.10 (0.92-1.30)

160 mg/dL 1.00

170 mg/dL 1.01 (0.92-1.12)

180 mg/dL 1.16 (0.98-1.29)

190 mg/dL 1.38 (1.12-1.68)

p-value 0.003

According to these results, those WITHOUT diabetes have an association with dementia at glucose levels lower than those WITH diabetes.... so its like saying: "at a certain point, both groups have a greater risk of dementia when average glucose levels reach a certain point, but those WITH Diabetes can tolerate higher levels before becoming at risk"

Im curious too see someone's thoughts on this result and whether not each group having different p values would cause those in "statistics-world" to be squeamish.

Yves S.

tutor
Tony, not sure how to answer this one. If you were to make a study on the continuous dependent variable Y (hazard ratio for dementia) against the independent variables X, "with or without diabetes" being categorical variable 1, and "glucose level" being continuous independent variable 2, a multiple linear regression would be appropriate and would show you a p-value for each coefficient and an overall significance for that regression. It would allow you to test the significance of "with or without diabetes". It appears the tests above are looking at the effect of one single variable (glucose level) on the dependent variable (hazard of dementia risk) studying two different groups so the p-values cannot be compared; they have to be analyzed in the context of their individual test. Anyone else has an opinion?
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11/09/19

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