p values differing amongst two groups in comparison

Question

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.

Answer 1

When I saw that people WITHOUT diabetes developed dementia at lower glucose levels than people WITH diabetes, I was surprised too. But I read the study and it was a different

implication.

This is how the authors conducted the study:

The authors selected a baseline dementia risk for each of the 2 groups: With diabetes and Without diabetes.

The authors chose the projected Dementia Risk at 100 mg/dl as the BASELINE DEMENTIA RISK for the "Without Diabetes" group. So the "adjusted hazard ratio" is NOT THE RAW DEMENTIA RISK. It is the dementia risk relative to the BASELINE DEMENTIA RISK OF THE WITHOUT DIABETES GROUP. The With Diabetes group has its own baseline dementia risk.

So when you see that a "without diabetes" person has a 1.12 dementia risk at ONLY 115 mg/dl glucose while a "with diabetes" person has a 1.10 dementia risk at 150 mg/dl glucose ...........it doesn't mean that a diabetes patient with HUGE glucose levels has a LESS dementia risk than a non-diabetes with tiny glucose levels. It means that the without diabetes person has 12% more dementia risk than the baseline without diabetes person's dementia risk and the with diabetes person has 10% more dementia risk than the baseline with diabetes person's dementia risk.

"Is having two VERY DIFFERENT p-values justifiable when comparing the two groups?"

Yes it is justifiable. The p-value only helps us to determine whether the correlation is zero or not. The fact that both the without and with diabetes groups had significant correlations means that the glucose-dementia correlation is not zero for both populations (diabetes and no-diabetes). Just because the with diabetes group had a smaller p-value doesn't mean that it has a stronger correlation than the without diabetes group, it just means we are more confident that the glucose dementia correlation is not zero.

Also, I don't believe the study was comparing the two groups. It was showing that even if

someone does not have diabetes, just having increased blood glucose is associated with increased risk of dementia.

Here's the study: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3955123/

Crane PK, Walker R, Hubbard RA, et al. Glucose levels and risk of dementia [published correction appears in N Engl J Med. 2013 Oct 10;369(15):1476]. N Engl J Med. 2013;369(6):540–548. doi:10.1056/NEJMoa1215740