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October 29, 2010

What does the 95% confidence interval mean?

My take on interpreting the 95% CI:

Predictor: Riding a fixed gear bicycle
Outcome: Low-rise jeans
Result: Riding a fixie is associated with a 50% (95% CI: 25%-75%) higher probability of wearing low-rise jeans
Bias/confounding: None, of course

Here is a generally agreeable statement:
If the study were repeated again an infinite number of times, 95% of those studies would have the true risk difference in the 95% CI.

Here is what SOME call a crime against inference:
There is a 95% probability that the true risk difference is between 25% and 75%.

Image I flip a coin, it lands on the ground and I step on it before you can see how it landed.
Q: What is the probability that it is heads?
A1: 50% - Infidel, you have committed a crime against inference and are condemned to death*.
A2: 0% or 100%: Congratulations, you can join the League of Pedantic Professors

The source of confusion? The LPP uses a technical definition of probability that involves repeated observations. Meanwhile in the real world, 99% of us say that while the coin IS heads up (100%) or tails up (0%), because we don't know which we still say it has a 50% probability of being either. [Insert obligatory Schrodinger's cat here.]

Unless I am wrong, and I'm never wrong**, there is no problem with the stronger statement because the kind of people that interpret the CI that way are the kind of people that say 50%.

* At the age of 80 years, 95% CI: 50-120
** Inconceivable!

October 19, 2010

PubH8341 Wednesday evening study group

Please leave a comment with:

Your name
Best times to meet
Locations that would be good
Any thoughts on how you would like to structure the group (e.g. divide up readings, review basic concepts, etc.)

PubH8341 Monday study group

Please leave a comment with:

your name
Monday times you CANNOT meet at WBOB
A week 8 article you would like to present at the next meeting (including an author bio)

Poole - Nathan
Lecoutre - Meghan
Rothman - Nathan
Stang - Noel
Savitz - Noel?

October 5, 2010

Communicating BL-adjusted results

Table 3 had covariate-adjusted BL and FU means and baseline-adjusted intervention effects. The question was whether to baseline adjust the FU means or not, and if so how to center them. The way I see it is: You can put in incorrect numbers that add up, or incorrect numbers that don't add up. Or you can just present intervention effects!

Storing some comments from PH:

Section 1:

In Table 3, the Estimate of the intervention effect for MVPA (adults)
does not seem (to me) to fit the four means - recognizing that, in a
baseline adjusted analysis, one cannot simply take the NET difference -
instead it really is the difference in the FU adjusted means. For MVPA
(adults) I would have expected 145.5 - 103.6 = 41.9 not the 29.6 in the
Table. The footnote indicates that I am understanding the means as
presented correctly. It could be an issue with age which is not a fixed
covariate; in New Moves I incremented the age in my estimate statements
but I am not sure if that is the source of the mismatch. The MVPA
(adults) is the most obvious of the mismatches, but it applies to some
other outcomes as well.

Section 2:

Instead of generating the FU means separately from the estimation of the
intervention effect, I would estimate both FU means and Intervention
effect in the one analysis - in that way the results would be consistent.

Generation of the baseline is not a problem

Then have the data for FU with each observation also having the BL
value. (Is tt12 the followup, or the difference?)
proc mixed ;
class ...;
model &tt.22 = &tt.00 trt type ... smoker;
lsmeans trt/om ;
estimate 'Intervention effect' trt 1 -1;

Section 3:
If the FU means and the intervention effect are estimated
simultaneously, the difference between the FU means will equal the
intervention effect. However, one would need to take the mean of the
baseline values to subtract from the adjusted FU means and not simply
the separate BL means. That is because the FU means are ADJUSTED as if
they have the same baseline mean.