Number of bootstrap runs needed for confidence intervals

Dear nmusers, I have a question about bootstrap techniques. I have developed a 2-compartment PK model and I wanted to evaluate the model with the bootstrap technique. After 200 successful bootstrap runs obtained with Wings for Nonmem I calculated the parameter means of the 200 runs. Am I correct that at least 1000 bootstrap runs are needed to get correct confidence intervals? (But due to long run times and access to only 2 CPUs 1000 runs can’t be performed unfortunately.) If I calculate confidence intervals from the 200 runs, how well is the quality of them? Can I use them at all? Also I’m interested in your opinion about the following method: A prerequisite for this nethod has to be that the 200 bootstrap runs and by this the parameter values are a representing distribution of the true parameter population. Is it possible to perform a bootstrap from the bootstrap results? Is it possible to get 1000 new bootstrap parameter results by bootstrapping from the 200 old bootstrap values. And finally could I calculate from these 1000 parameter values the confidence intervals and compare them with my original model parameter values. >From my point of view this procedure can only be possible if we have the >representing distribution of the 200 runs. But how could we be sure, that this >is true? Any help or opinion is appreciated! Thanks in advance, Kati ________________________________ Katharina Kuester Pharmacist PhD student Freie Universitaet Berlin Institute of Pharmacy Dept. Clinical Pharmacy Kelchstr. 31 D-12169 Berlin Phone: +49-30-838 506 27 Fax: +49-30-838 507 11 e-mail: [EMAIL PROTECTED]

Hi Kati, It is better to use parameter medians (not the means) of the bootstrap runs as estimates. If you have just 200 runs, use those for CI, it is not as precise as with 1000 runs but you will not gain anything by "bootstrap from bootstrap". Below is the R code that demonstrates the differences in the estimates and precision of the lower 95%CI bound for 200 samples, 1000 samples drawn from 200 samples, 1000 samples and 100000 samples. Standard normal was used to draw random sets. Leonid temp200 <- double(1000) temp200v2 <- double(1000) temp1000 <- double(1000) temp100000 <- double(1000) for(i in 1:1000) { temp200[i] <- sort(rnorm(200))[5] temp200v2[i] <- sort(sample(rnorm(200),1000,replace=T))[25] temp1000[i] <- sort(rnorm(1000))[25] temp100000[i] <- sort(rnorm(100000))[2500] } median(temp200) # -1.982658 median(temp200v2) # -1.956067 median(temp1000) # -1.966652 median(temp100000) # -1.959679 sd(temp200) # 0.1984375 sd(temp200v2) # 0.2052445 sd(temp1000) # 0.08406183 sd(temp100000) # 0.008499137 -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 Katharina Küster wrote: > Dear nmusers, > > I have a question about bootstrap techniques. > > I have developed a 2-compartment PK model and I wanted to evaluate the model with the bootstrap technique. After 200 successful bootstrap runs obtained with Wings for Nonmem I calculated the parameter means of the 200 runs. > > Am I correct that at least 1000 bootstrap runs are needed to get correct confidence intervals? > > (But due to long run times and access to only 2 CPUs 1000 runs can’t be performed unfortunately.) > > If I calculate confidence intervals from the 200 runs, how well is the quality of them? Can I use them at all? > > Also I’m interested in your opinion about the following method: > > A prerequisite for this nethod has to be that the 200 bootstrap runs and by this the parameter values are a representing distribution of the true parameter population. Is it possible to perform a bootstrap from the bootstrap results? Is it possible to get 1000 new bootstrap parameter results by bootstrapping from the 200 old bootstrap values. And finally could I calculate from these 1000 parameter values the confidence intervals and compare them with my original model parameter values. > > From my point of view this procedure can only be possible if we have the representing distribution of the 200 runs. But how could we be sure, that this is true? > > Any help or opinion is appreciated! > > Thanks in advance, Kati > > ________________________________ > > Katharina Kuester > Pharmacist > PhD student > Freie Universitaet Berlin > Institute of Pharmacy > Dept. Clinical Pharmacy > Kelchstr. 31 > D-12169 Berlin > > Phone: +49-30-838 506 27 > > Fax: +49-30-838 507 11 > e-mail: [EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]>