extrapolation and selection bias I have a cohort of patient data.
I have 100 Affected and 900 UnAffected
I am reassessing one of the variables for each of the patients, however I can only do so for 90 Affected and 200 UnAffected.
It's obvious that the proportions of Affected/UnAffected in my new subset is different from the original cohort. As such, if I wanted to extrapolate the subset to the same size as my original cohort of 1000 patients, what would be the best method to do so?
 A: If you had take a random sample of unaffected subjects, it would have been possible to estimate the cohort characteristics of the  new-technique distribution (e.g. mean, median, quartiles) and, therefore similar characteristics of the new-old differences. This would have "extrapolated" to the original cohort and perhaps is what you were thinking about. 
Unfortunately, your decision to implement a matching design means that the reassessed unaffected subjects are not a random sample of all unaffected. 
You have quite a bit of covariate information on all subjects. There you could reweight unaffected subjects so that the reweighted distributions match those of the original 900. The techniques for doing this are known as post-stratification, raking, and calibration. For these, see Lohr, 2009.
You can also go some way to compensate for the missing reassessments with multiple imputation (MI) and reweighting techniques. See, e.g. White et al., 2012.
References:
Lohr, Sharon L. 2009. Sampling: Design and Analysis. Boston, MA: Cengage Brooks/Cole.
Seaman, Shaun R, Ian R White, Andrew J Copas, and Leah Li. 2012. Combining Multiple Imputation and Inverse-Probability Weighting. Biometrics 68, no. 1: 129-137.
