Simulations in SAS

Gompertz

data IB;
do sim=1;
	do dose=0,20,40,60,80,100,160 ;
		do pen=1 to 100;
		if dose=0 	then Y=200	+ rand("Normal", 0, sqrt(480.779));
		if dose=20 	then Y=304 	+ rand("Normal", 0, sqrt(480.779));
		if dose=40 	then Y=317 	+ rand("Normal", 0, sqrt(480.779));
		if dose=60 	then Y=321 	+ rand("Normal", 0, sqrt(480.779));
		if dose=80 	then Y=326 	+ rand("Normal", 0, sqrt(480.779));
		if dose=100 then Y=332 	+ rand("Normal", 0, sqrt(480.779));
		if dose=160 then Y=332 	+ rand("Normal", 0, sqrt(480.779)); /* 332 is assumption */ 
		output;
		end;
	end;
end;
run;
proc nlin data=IB plots=all maxiter=20 hougaard nlinmeasures bias;
where sim=1;
parms a=314 k=0.06 T=-15;
model Y=a*exp(-exp(-k*(Dose-T)));
output out=IBpred p=yhat r=resid student=stresid lcl=lpl lclm=lcl ucl=upl uclm=ucl parms=a k T;
run; /* a=347 / k=0.00975 / T=-205.4 */
proc sgplot data=IBpred;
scatter y=Y         x=dose;
series  y=yhat   	x=dose / name="fit" lineattrs=(color=red pattern=2) LegendLabel="Predicted";
series  y=lpl 		x=dose / lineattrs=GraphConfidence name="lpl" legendlabel="95% Prediction limits";
series  y=upl 		x=dose / lineattrs=GraphConfidence;
band  	x=dose lower=lcl upper=ucl / fillattrs=(color=red) name="lcl" legendlabel="95% Confidence limits" transparency=0.75;
refline k / axis=x lineattrs=(color=orange pattern=2) label="Inflection Point" labelpos=max labelloc=outside labelattrs=(color=orange) ;
refline a / axis=y lineattrs=(color=green pattern=2) label="Asymptot" labelpos=max labelloc=inside labelattrs=(color=green);
keylegend "fit" "lpl" "lcl";
yaxis label="Y  ";
xaxis label="Day  ";
Title "Gompertz to describe Y  ";
run;