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# Test of Relative Risk (Crossover)

This calculator assumes a 2 by 1 crossover design to compare the log-odds ratio against 0. To perform the power and sample size calculations, we need to estimate $$\sigma_d = \text{Var}(d_j)$$ where

$d_j = \left( \frac{x_{1j}}{\hat{p}_1 (1 - \hat{p}_2)} - \frac{x_{2j}}{\hat{p}_2 (1 - \hat{p}_2)} \right)$

and $$x_ij$$ is the binary response for the $$j^{th}$$ subject under the $$i^{th}$$ treatment.

## Power Calculation Parameters

To input multiple values, seperate them by a comma.

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## Power Calculation Explanation

Solve For
The unknown you are interested in solving for.
N
The sample size used to test the hypothesis.
Alpha
The $$\alpha$$ (Type I error rate) level of the hypothesis test.
Power
The power (1 - Type II error rate) of the hypothesis test.
Odds Ratio
The odds ratio of the treatments.
$$\sigma_{d}$$
The standard deviation of the sample defined above.
Margin
The margin is a value the effect size needs to exceed to be meaningful. For hypotheses of equivalence, the margin must be greater than 0, or the calculation will not be solvable. For one sided tests, a margin is less than 0 implies a non-inferiority hypothesis. Otherwise, a superiority hypothesis is implied. Read More
Hypothesis
There are three types of hypotheses that can be tested: two-sided, one-sided and equivalence. Tests of equivalence must include a margin if the unknown and null means are equal. Read More

## Calculation Results

No calculation has been generated yet.

Hypothesis: {{ hypothesis }}

N Alpha Power Odds Ratio $$\sigma_{d}$$ Margin
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