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I have problems with choosing which model / link function should I use for my analysis.

My response: numbers from -100% to +500% (increase of tumor after therapy, may switch to ratios or log-ratios, so -50% will become 1/2 or -1)

My predictors: numbers N from 0% to 100% which denote "mutation of gene X happened in N% of tumor". The problem is - major part of patients do not have mutations in any particular gene, so for most samples it will be 0%. Data matrix look like: a looot of 0s (more than 95%) and sometimes a number from 0% to 100%. So none of "classic" models (I denote "classic model" as "model that I know") can be applied due to violated assumptions and really not clear distribution of residuals. So it is like "zero inflation in predictors".

I have tried random forest...negative R^2 XD

I have approx 100 genes to investigate and approx 100 samples, if it matters. Could you give any direction on where to look?

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    $\begingroup$ Random forest may require a sample size of perhaps 200 * 100 = 20000 to be reliable in your situation as described here. Strange distributions of predictor values are not of major concern. If you were doing regression this particular situation can be handled by having for each predictor x an indicator variable for x > 0 and also putting x and x$^2$ in the model. $\endgroup$ – Frank Harrell May 11 at 12:20
  • $\begingroup$ @FrankHarrell I clearly understand why we need indicator variable, thanks a lot, but why do we need to put x^2? $\endgroup$ – German Demidov May 11 at 12:32
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    $\begingroup$ Inlcude $x^2$ if you do not know that the effect of the predictor is linear when it is greater than zero. Better would be cubic spline functions but quadratic effects may be adequate approximators here. $\endgroup$ – Frank Harrell May 11 at 13:35
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    $\begingroup$ Hard to say from information given. Only suggestion is to use penalized regression and compare effective AIC of 3 models: fully linear, indicator variable + linear, indicator + linear + square. $\endgroup$ – Frank Harrell May 11 at 17:04
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    $\begingroup$ Just make sure that the cross-validation repeats afresh all supervised learning steps for each inner loop. $\endgroup$ – Frank Harrell May 12 at 13:38

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