XLSTAT: Calculate Sample size & Statistical Power for a Clinical Trial in Excel

 

Background

When testing a hypothesis using a statistical test, there are several decisions to take:

• The null hypothesis H0 and the alternative hypothesis Ha.

• The statistical test to use.

• The type I error also known as alpha. It occurs when one rejects the null hypothesis when it is true. It is set a priori for each test and is 5 %.

Type II error (beta) is the probability of failing to reject a false null hypothesis and is crucial yet less studied. The test's power (1-beta) is the chance of correctly rejecting a false null. XLSTAT calculates power and beta when parameters are known and determines the required sample size for a desired power. Power calculations are typically performed before experiments to estimate the necessary number of observations for valid results.

Dataset for Example

The attached example will be used to estimate the necessary sample size in classical clinical trials.

When planning the clinical trial, the key question is "How many patients are needed for valid results?".

Types of trials include:  
- Superiority trials: test if one treatment is better than another.  
- Equivalence trials: show the new treatment is neither better nor worse than the existing one.  
- Non-inferiority trials: demonstrate the new treatment is not worse than the current standard.Dataset for Example

These tests can be applied to a binary or a continuous outcome. 
We will give one example for each type.

 

Superiority Trial

A new treatment has been obtained and its expected results on patients should be better than the actual treatment. We wish to know the necessary sample size to reject the null hypothesis that both treatments have the same effect.
The outcome is the fact that a patient is cured or not. This is a binary outcome. We suppose that the control group (oldest treatment) has a recovery of 60% and the treatment group (new treatment) has a recovery rate of 70%.

We wish to estimate the necessary sample size for an alpha level of 5% and a power of 0.9.

 

Setting Up

• Open XLSTAT.

• Click on the Life Sciences/ Power analysis menu and select the Clinical trials feature.

• Once the button is clicked, the dialog box pops up.

In the General tab:

• Choose the Find the sample size goal.

• Select the superiority trial and the binary outcome.

• The alpha is 0.05. The desired power is 0.9.

• The % of success for the control group is 60% and the % of success for the treatment group is 70%. There is no cross-over.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The first table shows the main results followed by their interpretation.

 

We can see that 945 patients are required, which means two groups of at least 473 patients. 
The simulation plot gives you more information on the evolution of the sample size depending on power.

 

Equivalence trial

A new treatment has been obtained which has way fewer side effects than the classical treatment. We wish to be sure that both treatments are equivalent. To do so, we should test that both treatments are in the same range of results.
We use equivalence testing. An equivalence limit should be defined. Here, we define an equivalence limit of 10%.
The outcome is the fact that a patient is cured or not. This is a binary outcome. We suppose that the control group (with the oldest treatment) and the treatment group (with the new treatment) have a recovery rate of 60%.

We wish to estimate necessary sample size for a level of 5% and a power of 0.9. 

 

Setting Up

• Click on the Life Sciences/ Power analysis menu and select the Clinical trials feature.

• Once the button is clicked, the dialog box pops up.

In the General tab:

• Choose the Find the sample size goal.

• Select the equivalence trial and the binary outcome.

• The  alpha is 0.05. The desired power is 0.9.

• The  % of success for both groups is 60% and the equivalence limit is equal to 10%.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

 The first table shows the main results followed their interpretation.

We can see that 1038 patients are necessary, which means two groups of at least 519 patients. 
The simulation plot gives you more information on the evolution of the sample size depending on power.

 

Non-inferiority trial

A new treatment has been obtained; it is cheaper than the actual treatment. We wish to be sure that the new treatment has an at least equal or a little bit less efficient effect than the actual treatment. To do so, we should test that the new treatment is better or slightly worse than the original treatment.
We use non-inferiority testing. A non-inferiority limit should be defined. In our case we define a non-inferiority limit of 8%.
The outcome is the fact that a patient is cured or not. It is a binary outcome. We suppose that the control group (with the oldest treatment) has a recovery rate of 70% and the treatment group (with the new treatment) has a recovery rate of 75%.

We wish to estimate the needed sample size for a level of 5% and a power of 0.9. 

 

Setting Up

• Click on the Life Sciences/ Power analysis menu and select the Clinical trials feature.

• Once the button is clicked, the dialog box pops up.

In the General tab:

• Choose the Find the sample size goal.

• Select the non-inferiority trial and the binary outcome.

• The alpha is 0.05. The desired power is 0.9.

•  The % of success for the control group is 70% and the % of success for the treatment group is 75%.

• The non-inferiority limit is equal to 8%.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The first table shows the main results followed by their interpretation.

We can see that the analysis needs to be run on 302 patients to reach a power of 0.9. 
The simulation plot gives you more information on the evolution of the sample size depending on power.

 

Conclusion

By using XLSTAT Power features, you can obtain the necessary sample size for three types of trials. We have seen that non-inferiority trials are less restrictive but are also more controversial.
XLSTAT enables you to find the power and the sample size when the outcome variable is continuous and to represent many simulation plots.