## Welch’s t-test [Regulatives / Guidelines]

Hi Imph,

» I would like to know if in the parallel design, we should not assume the equality of the variances.

Correct. Specifically stated by the FDA

For parallel designs […] equal variances should not be assumed.

and in between the lines by the EMA

The precise model to be used for the analysis should be pre-specified in the protocol. The statistical analysis should take into account sources of variation that can be reasonably assumed to have an effect on the response variable.

» […] how do the statistical model, the statistical analysis and the formula for the confidence interval become?

Perform Welch’s t-test, i.e., with Satterthwaite’s approximation of the degrees of freedom. $$\nu=\frac{\big{(}\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}\big{)}^2}{\frac{s_1^4}{n_1^2(n_1-1)}+\frac{s_2^4}{n_2^2(n_2-1)}}$$where $$\small{n_1,n_2}$$ are the number of subjects under treatments T and R, respectively. $$\small{s_1,s_2}$$ are the standard deviations of treatment arms. Not by any chance it is the default in and SAS, whereas SPSS calculates always the conventional t-test (assuming equal variances) and the Welch-test. In the output table, use the second row.
Calculate the confidence interval as usual with the t-value for given $$\small{\alpha,\,\nu}$$.

It’s also easy in Phoenix WinNonlin and PKanalix. Consult the respective manual. You should check whether your setup is correct.*

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