Sunday, January 25, 2015

Solving the Mystery of the Swedish Mammography Trial cont.

Ja. Jeg fandt det!  

Dicte would be proud. I had been looking for causality to the mammography trial in the two Swedish counties of Dalarna and Ostergotland, but the culprit turned out to be Malmo, across the way from Denmak.  Ironically, Malmo was fingered by lead author of the Two-County trial, Laszlo Tabar.  

Tabar argued in the BMJ that the Malmo trial shouldn't be used to determine the value of mammography screening because between 70% and 74% of women invited to the trial actually had a mammogram and some 24% of women who were not invited had a mammogram.

Fik dig!

The researchers who conducted the Malmo trial actually determined both the compliance rate for the women who were invited to the trial and separately for the women who were not invited.  For the second group the researchers surveyed 500 women and determine the number of mammograms that they had.

The Malmo study, randomized women between 45 and 69 living in the city of Malmo between an invitation to have a mammogram and a control group.  The study found that after about 9 years of follow up 63 of 21,088 in the invitation group and 66 of 21,195 in the control group passed away from breast cancer.  Again, these are very small differences and we have the issue that it is an intent-to-treat analysis. But now have estimates of the mammography rates in the two groups.

If we assume that the take up rate of mammography of those receive the letter is 70% and the take up rate for those who didn’t is 24% and we also make the "exclusion restriction" that the letter has no impact on the probability of dying from breast cancer, we can calculate the average effect of mammography on survival from breast cancer for women in Malmo. 

We can write down the following system of equations, where A is the probability of dying from breast cancer conditional on getting mammography screening and B is the probability of dying from breast cancer without mammography screening. 

0.7*A + 0.3*B = 63/21088
0.24*A + 0.74*B = 66/21195

Plugging these equations into Mathematica we get.

A = 0.00291
B = 0.00317

While the intent-to-treat analysis suggest a 4% reduction in death from breast cancer associated with mammographic screening.  Accounting for the actual take up rate suggests an 8% reduction. Note that none of this accounts for sampling variation and is only presented for illustrative purposes.

Now this analysis also assumes that everyone who took up mammography screening is the same as those that didn't take up the screening, excepting for the fact that they took up mammography screening.  This is plainly not true. 

To be continued....

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