I have very little background in statistics, so I need some advice. I know that Jaccard is used to compare the similarity (elements in data sets). But can I use the Jaccard coefficient (or something similar – any suggestions?) also to compare the overlapping of for example two symptoms (binary data, asymmetric) in a large sample? Should I then treat the patients as elements in the datasets of symptoms (so I count the yes/yes, yes/no, no/yes, while no/no is considered irrelevant)? For example I have 801 patients, and I want to know the overlapping of two (or more) symptoms (for example those who have nausea and also have vomiting). How would I calculate it? I took the phi coefficient (would it be better in this case to stick to it?) but I doubted – the symptoms are not necessarily correlated, but may simply co-exist. So I though that I just want to show the co-existence of symptoms. Should I simply show the percentages? Gratefully,
Liidia
The phi statistic would include the no/no in the calculation. I imagine this is not desirable here. What you are describing is used in a different situation than the Jaccard index is usually used, but the idea is the same. Really, you are just describing the proportion of cases where the two symptoms occur together out of all cases where at least one symptom occurs. It might be fine to describe it this way. Below is some R code. You can run it at http://rdrr.io/snippets . You might want to play with the numbers a bit just to get a handle on what the output means. In the example given, Nausea and Vomiting occur together in 50% of cases where at least one symptom occurs.
Input =("
Nausea VomitYes VomitNo
Yes 100 50
No 50 NA
")
Matrix = as.matrix(read.table(textConnection(Input), header=TRUE, row.names=1))
Proportion = Matrix[1,1] / ( Matrix[1,1] + Matrix[1,2] + Matrix[2,1] )
Proportion
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