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I'm reading a study about a certain drug and how it might cause some kidney issues as a longterm side effect. To be more precise the study is about PPIs (proton pump inhibitors).

I don't know why but the guys working on it did not present the intersection (which is really important I believe) of data sets.

Here is the picture:

enter image description here

I know that this is quite impossible what I would like, but is there at least some kind of approximation formula on how I could get:

How many people have diabetes and chronic lung disease

or as another example:

diabetes and lung disease and hyperlipidemia.

Unfortunately no other relevant parameters are present.

N is the number of people in the study, the number in the parenthesis is the percentage based on the big N for every disease separately calculated .

Explaining intersection: By intersection I mean, for example, How would I get the number of people based on this data set who have diabetes, chronic lung disease and peripheral artery disease OR maybe: Dementia and Hep C. etc. Something like a VENN diagram intersection circle between two or multiple data sets

Here is the whole picture, Is it possible to make the intersection out of this data on the image? enter image description here

Here is the entire study in PDF 12 pages. https://www.filedog.io/StarTurtle

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    $\begingroup$ You are showing marginal descriptive statistics, namely, frequency of positive value, for each of 9 binary variables. Of course it would be possible to obtain frequencies for any combination among the variables - if you have the original dataset. Do you have it? Alternatively, you could estimate the co-occurence frequencies from the literature or official health care documents, if you dig and find enough info. $\endgroup$
    – ttnphns
    Oct 21, 2017 at 10:30
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    $\begingroup$ In their research they used the algorithm of Schneeweiss ncbi.nlm.nih.gov/pubmed/28237709 to select covariates. They speak of top 500 covariates plus demographic data, it is unclear whether they also did the subanalysis in which they use the interaction terms of the top 20 covariates plus demographic variables and a group of pre-selected covariates. So they may have used intersections like you suspect can be important. It is not so nice that they have not been very clear about the used covariates in the models. However imho it is not neccesary to publish these as descriptive data. $\endgroup$ Oct 21, 2017 at 11:20
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    $\begingroup$ If you really like to know the intersections. Then you can go look into the used database yourself (or maybe just email/call the authors), $\endgroup$ Oct 21, 2017 at 11:22
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    $\begingroup$ eugen, my personal recommendation would be to get the raw data from the authors, otherwise it is difficult to accomplish what you want. Meanwile, you may just delete your question (I doubt it can be answered positively/helpfully). $\endgroup$
    – ttnphns
    Oct 21, 2017 at 13:20
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    $\begingroup$ You could change the question (which has a simple negative answer, and might be why not so many people care to post the answer, and first you get lots of comments that investigate the question). Based on your comments it seems you want to show something else/more than just getting the value of the intersection. The intersection actually seems irrelevant for your goal if you just want to point out that the effect is not something to worry (much) about. $\endgroup$ Oct 21, 2017 at 14:26

1 Answer 1

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I know this information is contained in the comments above, but a concrete answer can't hurt.

The answer is no, because there are multiple solutions which result in the same total disease counts.

Imagine that we represent each individual in the study with a $1$-by-$p$ vector $x$ (where $p$ is the number of diseases). Each element of $x$ is then $0$ or $1$, where $0$ indicates the absence of the disease and $1$ indicates its presence. Then we have $n$ of these $1$-by-$p$ vectors, and we build an $n$-by-$p$ array $X$ by appending them sequentially row-wise. The sums of each column must add up to the total number of instances of each of the $p$ diseases, but that is the only constraint we have, and it is satisfied for a great many unique instances of $X$. Since there are obviously multiple solutions satisfying the only constraint provided, there is no way to achieve your goal with only the information provided.

Edit: My answer is a slight oversimplification of this problem because the individuals don't have specific identities, i.e., rearranging the rows of $X$ is not a different instance of $X$ for this application, so it's not quite as simple as saying that we only have $p$ equations (disease instance sums) and $np$ variables (elements of $X$). It still isn't possible to find these "intersections," though.

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