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;
引用格式
PabiG (2024). Two one sided test (TOST) for equivalence (https://www.mathworks.com/matlabcentral/fileexchange/124560-two-one-sided-test-tost-for-equivalence), MATLAB Central File Exchange. 检索来源 .
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