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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?

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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.

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  • $\begingroup$ Thank you so much. I was drowning in statistical tests when I didn't even need them due to the nature of the research. The confusing thing (to me) was that some variables like birth weight can be turned into a nominal variable (low birth weight, normal birth weight). Is it better to keep these variables as values on continuous ranges or as nominal variables? Sorry if its a dumb question, I'm quite new to PCA. $\endgroup$ – induvidyul May 11 '11 at 16:11
  • $\begingroup$ @JMS - I liked your 1st paragraph. The 2nd: PCA with 27 cases and 6 variables? Better to simply look at scatterplots, as you said earlier. (Even correlations can hardly be trusted because with this small sample outliers can have a dramatic distorting effect.) $\endgroup$ – rolando2 May 11 '11 at 16:34
  • $\begingroup$ @rolando2, what number of variables is more sensible to use for PCA with 27 cases? It may be possible to leave some variables out or combine them into a ratio. $\endgroup$ – induvidyul May 11 '11 at 16:50
  • $\begingroup$ @rolando2 I agree to a point. But though it'll be noisy I still think that one PC will probably be a reasonable composite of area/perimeter/number of vessels and might be useful. I wouldn't include the "responses" in the PCA. $\endgroup$ – JMS May 11 '11 at 19:47
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    $\begingroup$ But I should also mention that your responses should be transformed to look roughly normally distributed in PCA, so you wouldn't want to discretize any continuous variables in general. Anyway, the takehome is to plot your data every which way and see what you find and whether it is interesting - it sounds like this isn't the phase of your research where you need to start plowing through models and tests, and your dataset is small enough that you can basically do the exploration by hand. $\endgroup$ – JMS May 11 '11 at 19:55
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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,

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  • $\begingroup$ Well that is the thing, the placenta is not clearly the cause or effect of any one thing, it is the middle-man between mother and baby. So I am searching for hypotheses to potentially investigate in the future using more samples. $\endgroup$ – induvidyul May 11 '11 at 19:27
  • $\begingroup$ Hi Sarah,If I were you I will try to do "data mining", which means, I will do the cluster analysis using all possible continuous variables. Then you might find the (dis)similar characteristic (between)within clusters. After that, you might have better idea what you want to do for the next step. Good Luck $\endgroup$ – Tu.2 May 11 '11 at 19:43
  • $\begingroup$ do you have any suggestion on what kind of clustering (hierarchical, partitional, density, subspace), and what distance metric (Euclidean, mahalanobis, k-means, etc) to use? I am not familiar with cluster analysis. Mahalanobis seems appealing since it corrects for scale in data but I'm not sure if that is important. $\endgroup$ – induvidyul May 13 '11 at 5:09
  • $\begingroup$ You might want to try "Model-based clustering". If you use R, you could install this package by install.packages("mclust"). This method will provide the best cluster numbers, which are determined by BIC value. Of course, you could use other clustering methods but I believe this model-based clustering method is the best. $\endgroup$ – Tu.2 May 13 '11 at 20:59
  • $\begingroup$ Thank you for your insight, I will try cluster analysis :] $\endgroup$ – induvidyul May 14 '11 at 6:16

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