Dear Mohsen,

Please check these resources.

Regards

SM Najim

http://www.journalresearchijf.com/wp-content/uploads/P3-BES-V2-I1-C1-JN2016.pdf

https://www.degruyter.com/downloadpdf/j/amcs.2012.22.issue-4/v10006-012-0064-z/v10006-012-0064-z.xml

http://cowles.yale.edu/sites/default/files/files/pub/d20/d2032.pdf

One option is bootstrapping; see http://thepsychologist.bps.org.uk/volume-22/edition-5/methods-giving-your-data-bootstrap

Dear Stephen thanks in advance for your rapid and worthwhile answers, but I'm looking for a method of prediction instead of Multiple Regression which requires assumptions.

I want to predict and model the occurrence of a disease using 5 predictor variables.

Regression is indeed a method for prediction.

Also note that all methods have assumptions; regression is not unique in this respect. For example, both parametric and non-parametric regression techniques require that the measurement has validity (if you're not measuring what you think you're measuring, the results will be useless). See e.g. http://andrewgelman.com/2013/08/04/19470/. The "assumptions" you have in mind are probably the assumption of normally distributed residuals, and bootstrap regression does not require this assumption (see e.g. http://statweb.stanford.edu/~tibs/sta305files/FoxOnBootingRegInR.pdf, http://homepage.stat.uiowa.edu/~rdecook/stat3200/notes/bootstrap_4pp.pdf), which is why I suggested it.

You can try the non linear regression if you don't want to transform. Thank you

Dear Mohsen,

From my experience, the Generalized Additive Modeling (GAM) is a very good algorithm for modeling and it is better the linear regression models.

You can implement it in R through gam and mgcv packages.

Let me know if you need help about GAM coding in R.

Dear Mohsen,

Please check these resources.

Regards

SM Najim

http://www.journalresearchijf.com/wp-content/uploads/P3-BES-V2-I1-C1-JN2016.pdf

https://www.degruyter.com/downloadpdf/j/amcs.2012.22.issue-4/v10006-012-0064-z/v10006-012-0064-z.xml

http://cowles.yale.edu/sites/default/files/files/pub/d20/d2032.pdf

There is another option, you can use something like a CART model (regression tree) or similar method.  

I agree with Nirmala....