What to do with a small (27) medical dataset? I'm working with a lot of data that was collected by obstetricians regarding the health of infants (birth weight, gestational age at delivery, mother's BMI), and I am trying to connect this data with geometric measurements performed on microscopic slide scans for each associated placenta (area, perimeter, number of blood vessels). Each mother-infant-placenta trio is identified with a lab ID so it is possible to know which is which, but there are only 27 sets of mother-infant-placenta.
All the clinical data were taken before I arrived on the scene. I was pretty much given the placenta slide images, and an excel sheet of the clinical data. Then I performed the geometric measurements of the placentas. So the data was not taken with my purpose in mind.
My question is, what can I do with this data? I collected measurements with some clinical knowledge that the condition of a placenta is both an influence on and reflection of the infant health outcome. But I desperately need advice on which statistical/data mining techniques I can use to see how my measurements affect/are an indicator of infant health. 
Is there any hope for ad-hoc analysis on a small sample size?
 A: If you're looking for statistical significance I wouldn't hold out hope unless you have a very targeted hypothesis and/or there is a very strong effect. But certainly you could generate some new hypotheses with this data via some exploratory analysis. With 6 variables overall I'm not sure I'd start with any sophisticated modeling. Never underestimate the power of scatterplots and histograms :)
One really simple thing to do would be to run PCA and see if the scores on any of the components have an apparent relationship with the response(s) you're interested in. It's probably a good<\strike> reasonable idea anyhow since your measurements are certainly correlated.
Edit: My thought on using PCA was basically to reduce the area/perimeter/number variables to a single dimension. Not strictly necessary but it might make visualizing the relationships easier.
A: I agree with JMS, you will need to plot each of your variable first because PCA requires the normality assumption. If your variables are not normally distributed then it is not appropriate to use PCA before transforming the variables. I think you will need to ask yourself, what you really want to know from this data set (set up your hypothesis) then you will be able to pick the right statistical tests.
It is not good to dichotomize continuous variables into categorical variables because you will lose power to detect the difference. However, if this is the case, You could use "odds ratio", "risk difference" etc to interpret your data sets. 
Sincerely,
