I assume that your response is positively valued except for the zeros. If that is correct, and if the values are all integers (like a count: 0, 1, 2, 3, ...), then you can fit a zero-inflated Poisson or negative binomial model using PROC GENMOD. See the GENMOD documentation. If the response is positive and continuous, then you could try fitting a zero-inflated gamma model using PROC FMM - for example:
data a;
call streaminit(2342);
do i=1 to 100;
y=rand("gamma",2);
output;
end;
do i=1 to 10; y=0; output; end;
run;
/* histogram of data */
proc sgplot data=a;
histogram y / showbins nbins=9;
run;
/* zero-inflated gamma model */
proc fmm data=a plots=density(nbins=9);
model y= / dist=gamma;
model + / dist=constant;
run;
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