Two one sided test (TOST) for equivalence

Statistical test for equivalence within effect bounds

Statistical test for equivalence within effect bounds as described in:

Schuirmann, D. J. (1987). A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. Journal of pharmacokinetics and biopharmaceutics, 15, 657-680.

Example Code:

%%Example with x1~N(1,1) and x2~N(1.1, 1)
NoRange = [10^3, 10^4, 10^5, 10^6];
ColorInd = 0;
Colors{1} = [1 0 0];Colors{2} = [0 1 0];Colors{3} = [0 0 1] ;Colors{4} = [1 1 0] ;
figure
for No =NoRange
    ColorInd = ColorInd +1;
    mu1 = 1;
    mu2 = 1.1;
    sigma1 = 1;
    sigma2 = 1; %for simplicity
    x1 = normrnd(mu1,sigma1, 1,No);
    x2 = normrnd(mu2,sigma2, 1,No);
    alpha = 0.03;
    range = 0.01:0.001:0.2;
    AllP = zeros(1,length(range));
    ind = 0;
    for min_effectsize = range
        ind = ind +1;
        [TestResult, p] = TOST(x1, x2, min_effectsize);
        AllP(ind) =  max(p);
    end
    hold on
    plot(range, AllP, '*', 'Color', Colors{ColorInd})
end
hold on
line([abs(mu1-mu2)/((sigma1 + sigma2)/2) abs(mu1-mu2)/((sigma1 + sigma2)/2)], [0 1])
ylabel('p-Value')
xlabel('Minimal Effect Size')
legend('Sample: 10^3', 'Sample: 10^4', 'Sample: 10^5', 'Sample: 10^6', '(\mu_1-\mu_2)/\sigma')
ax = gca;
ax.FontSize = 16;