Williams Deisgn 6*3 model, sample size calculation

[Laiju]

Hi Everyone,

How can we calculate the sample size for a 6*3 Williams model in non central t-distribution. The equation I have is below code. But I am stuck and is not able to go ahead. Any help would be of great use.

Thanks in advance.

3. Algorithm for Sample Size Calculation

Let σˆ2eσˆe2 denote the residual intrasubject MSE from a historical study; with Method 1, the sample size can be calculated with the following algorithm:

1. Set values for α, φ, and µT/µR (default α = 0.05, φ = 0.80, and µT/µR = 1);

2. Select a range of sample size (N1,N2), for each N ∊ [N1,N2], and do the following:

   1. V1=1.5σˆ2e/NV1=1.5σˆe2/N

   2. τ1 = [log(µT/µR) – log(▵L) ] / V1

   3. τ2 = [log(µT/µR) – log(▵U) ] / V1

   4. Calculate PRNT(–tν,α,ν6×3,τ2) – PRNT(–tν,α,ν6×3,τ1), where PRNT(·) is the probability from a noncentral t distribution, and ν6×3 = 2N – 4

[Rick_SAS]

You can use the CDF function to compute the probability of a noncentral t distribution.  I am not an expert in this area, but I know that PROC POWER also has support for noncentral t as part of its CUSTOM statement. An expert like @IanWakeling might be able to give more explicit advice.

[FreelanceReinh]

Just in case somebody is going to proceed with this thread: The article from which @Laiju apparently copied the algorithm can be found here (with much better readable formulas).

In principle, a SAS program implementing the algorithm would consist of only a few lines of code. Most of the terms in the formulas seem to be clearly defined. Moreover, the article contains a table of calculated values (Table 2, p. 245) for comparison. However, I was unable to replicate these values. I even tried to solve the equation for unclear parameters numerically (given a few values from Table 2; without sophisticated tools such as SAS/OR, though), but didn't obtain satisfactory results.