You can merge their information with applying an analysis reducing the dimension such as PCA.

Another approach is to normalize each indicator to Normal (0,1), and then use the average of the six z variables. 

Dear Raid Amin

If I use this approach, can I implement the output as a variable in a Granger causality test? 

I am not knowledgeable on a Granger Causality Test, Elahe.  You would be using the average score pf six variables where each variable has equal weights. Using the PCA approach is reducing dimensionality based on the covariance matrix, resulting in a multivariate score of some sort.

Elahe, there are several approaches, but three are the most common for this situation. Which one you choose depends on your goal in the analysis, the nature of your data, and what you believe to be the relations among the variables.

Since you mention ICD-10, for indicators of a diagnosis, the simplest thing is to sum (or average) them and use that as your variable.

A somewhat more complex version of the same thing is principal component analysis, as has been suggested. Technically speaking, a PCA will give you the "first eigenvector" of the correlations among your variables. Practically speaking, it gives you a weighted sum that represents the greatest possible amount of information from your data that one score can. However, if your indicators are binary, like presence/absence, PCA doesn't always perform well. The other caution is that it optimizes for your dataset and won't necessarily generalize well.

The third is factor analysis, variations of which can accommodate binary indicators, but I think that's getting more complex than you want to.

Pat

Elahe I think what is more important here is the thing you asked in your second question.

Raid Amin and Patrick s Malone, thank you both. your answer was really helpful. 

Dear Mehmet, what I need to do, is to consider six variable (Y1,Y2,...,Y3) as one and test it as if cause for example X1,X2,...,X6 or not. If I want to test them separately, it would be so confusing, since all Ys represent one thing in general. 

My point was it would depend on the test (in your case, Granger causality test) you are going to perform.

The important thing is the answer to questions:  conceptually are you able to do is? Is your test meaningful when you do this? Or can Granger causality test be manipulated accordingly?

I suppose your aim is to use this composite variable in Granger causality test. Is that correct?

The valid way to measure six different indicators as one single variable is by using Factor analysis. If you are measuring one dimension then ask for computing the factor scores for that one dimension. I advise that you the criteria "Eigenvalue greater than 1.0"   and check if you are measuring one dimension and don't force the extraction to give you one dimension.

The golden rule in statistical analysis is to target the simplest methodology that can accomplish the main goals by valid ways. If an average does the job for you in a satisfactory way, go with it. If it is too basic, consider a principal components analysis if you have the right data structure for it and to get linear combinations of the X's. If a structure can be assumed, facyor analysis allows you to output the factor scores, which can be used in some analysis in the next stages. Note that using factor rotations is very important here. If you use orthogonal rotation, the resulting factor scores are independent of each other, and you can use some uinivariate methods. If the rotations are oblique, you must use some multivariate approaches on the correlated factor scores.

I agree with the previous colleagues on the use of PCA to achieve your goal. However it seems to me, from your own explanation, that you are looking for a dependence coefficient ("X1, X2, Xn strongly predicts or not Y"). As so you might also want to take a look into "Multiple Correlation" to see if it suits you.

"Here, we study the effects of all the independent variables simultaneously on a dependent variable. For example, the correlation co-efficient between the yield of paddy (X1) and the other variables, viz. type of seedlings (X2), manure (X3), rainfall (X4), humidity (X5) is the multiple correlation co-efficient R1.2345 . This co-efficient takes value between 0 and +1." in https://explorable.com/partial-correlation-analysis

Remember that a single point with multiple measures can be seen as a vector (with any number of dimensions). As so comparing vector properties such as orientation or norm might be a possibility for you depending on what you are trying to achieve. I'm speculating nonetheless but it seems a reasonable assumption.

 Dear Elahe Meydani,

I agree with all my colleagues on the possible techniques that can be applied to your problem. However, if all variables are continuous, I would like to suggest the construction of a graph not oriented using the inverse of the correlation matrix. Thus, it is possible to make inferences about conditional independence and determine which variables are directly related to your variable of interest. For a quick read on the potential use of graphs in statistics, I suggest

Wasserman, Larry. All of statistics: a concise course in statistical inference. Springer Science & Business Media, 2013.

and to use the inverse of the correlation matrix I suggest

Whittaker, Joe. Graphical models in applied multivariate statistics. Wiley Publishing, 2009.