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# Exponential Model

Let $$\lambda_1$$ be the hazard ratio of a treatment applied to arm 1 of a trial and $$\lambda_2$$ be the hazard ratio of a treatment applied to arm 2. The exponential model compares the difference of these two values, $$\lambda_2 - \lambda_1$$.

## 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 (Arm $$i$$)
The sample size, for arm $$i$$, used to test the hypothesis.
Ratio
The ratio of the sample size in arm 1 to arm 2. The total sample size is minimized for a given power when the ratio is 1 (i.e. the design is balanced).
Alpha
The $$\alpha$$ (Type I error rate) level of the hypothesis test.
Power
The power (1 - Type II error rate) of the hypothesis test.
$$\lambda_1$$
The hazard ratio of group 1
$$\lambda_2$$
The hazard ratio of group 2
$$\gamma$$
The patient entry paramemter. If $$\gamma = 0$$, patient entry is uniform. If $$\gamma > 0$$, patient entry is faster at the beginning of the trial. If $$\gamma < 0$$, patient entry is faster towards the end of the trial.
Trial Time
The length of time the trial runs
Accrual Time
The length of time the trial accures patients. This should be in the same units at trial time.
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.

N (Arm 1) N (Arm 2) Alpha Power Hazard Ratio (Control) Hazard Ratio (Treatment) Gamma Trial Time Accrual Time Margin
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