Bioequivalence and Bioavailability Forum • The n ext crackpot iteration

The n ext crackpot iteration [Two-Stage / GS Designs]

posted by Helmut – Vienna, Austria, 2017-08-20 04:20 (2440 d 18:15 ago) – Posting: # 17717
Views: 27,564

Capt’n,

some remarks. More maybe tomorrow.

❝ The polynomial provides a fantastic approximation within our entire interval of interest.

Played around a little. Based on the AIC the 4^th degree is the winner indeed.

❝ ##note: We might not want to write blah^3 etc if we optimize for speed, not sure.

Old wisdom. Here with my coefficients (total sample sizes [not N/seq], exact method for GRM 0.95, 80% power, CV 0.1–1.0).

library(microbenchmark) a <- c(5.897943, -40.988390, 603.109578, -338.281351, 70.43138) old.school <- function(a, CV) { x <- a[1] + a[2]*CV + a[3]*CV*CV + a[4]*CV*CV*CV + a[5]*CV*CV*CV*CV x + (2 - x %% 2) } lazy <- function(a, CV) { x <- a[1] + a[2]*CV + a[3]*CV^2 + a[4]*CV^3 + a[5]*CV^4 x + (2 - x %% 2) } res <- microbenchmark(old.school(a, CV), lazy(a, CV), times=500L, control=list("random", warmup=10)) boxplot(res, boxwex=0.25, las=1) options(microbenchmark.unit="us") print(res)

❝ ## perhaps ceil would be better?

I would round up to the next even (as above).

❝ You see, the sample size estimates are sort of almost perfect already. If you want to remove the very few 1's and -1's then just increase the polynomial degree above.

That doesn’t help. With CV <- seq(0.1, 1, 0.01) I got a match in 46/91 and +2 in 45/91. OK, conservative.

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Complete thread:

Initial sample size guess for the Potvin methods ElMaestro 2017-08-19 15:04 [Two-Stage / GS Designs]
- Initial sample size guess for the Potvin methods Helmut 2017-08-19 16:06
  - Initial sample size guess for the Potvin methods ElMaestro 2017-08-19 16:14
    - Initial sample size guess for the Potvin methods Helmut 2017-08-19 17:12
      - Initial sample size guess for the Potvin methods ElMaestro 2017-08-19 17:17
        
        Confuse-a-Cat Helmut 2017-08-19 17:33
        
        Confuse-a-Cat ElMaestro 2017-08-19 17:56
    - loop ↔ vectorized ↔ direct Helmut 2017-08-20 14:40
      - loop ↔ vectorized ↔ direct ElMaestro 2017-08-20 15:22
        
        loop ↔ vectorized ↔ direct Helmut 2017-08-20 16:23
        
        loop ↔ vectorized ↔ direct ElMaestro 2017-08-20 17:22
- The n ext crackpot iteration ElMaestro 2017-08-19 20:04
  - The n ext crackpot iterationHelmut 2017-08-20 02:20
- The ultimate crackpot iteration! ElMaestro 2017-08-20 14:35
  - The ultimate crackpot iteration! Helmut 2017-08-20 15:11
    - The ultimate crackpot iteration! ElMaestro 2017-08-20 15:28
      - The ultimate crackpot iteration! Helmut 2017-08-20 16:06
        
        The ultimate crackpot iteration! ElMaestro 2017-08-20 16:15
        
        The ultimate crackpot iteration! Helmut 2017-08-20 18:58
        
        The ultimate crackpot iteration! ElMaestro 2017-08-20 19:32
        
        Suggested code ElMaestro 2017-08-21 18:13
        
        Nitpicker! Helmut 2017-08-22 13:33
        
        Nitpicker! ElMaestro 2017-08-22 17:27
        
        Nitpicker! Helmut 2017-08-22 17:49
        
        Nitpicker! ElMaestro 2017-08-22 17:59
        
        Nitpicker! Helmut 2017-08-22 19:15
        
        Benchmark code ElMaestro 2017-08-22 22:29
        
        Benchmark code Helmut 2017-08-23 01:48