Sample size calculations for co-primary endpoints

[#1]

Is it possible to calculate sample size in JMP when we have co-primary endpoints? (Co-primary endpoints are more than one primary endpoint and the study success can be declared only if both primary endpoints are statistically significant in favor of the experimental treatment.)

[#2]

HI @billi ,

That is an interesting statistical problem. I'm not sure if there might be some clever workaround to enable you to use the standard power calculation based on a single hypothesis test.

As an alternative, I am fairly sure that simulation would be a solution and there are good tools for this in JMP Pro.

Hopefully some other people can chime in with some more concrete advice but I hope this helps a little at least.

Phil

[#3]

Hello @Phil_Kay

Thank you very much for the suggestion. Do you mind guiding me little bit about the simulations option that you mention or if you can please share any documentation that will be helpful in finding this capability and trying it out.

Thank you.

[#4]

Clearly @Thierry_S knows much more about this type of problem.

For a general procedure for using power simulation in JMP Pro you should find this thread useful:
https://community.jmp.com/t5/Discussions/Testing-Sample-sizes-for-a-full-factorial/td-p/52709

[#5]

Hi,

Based on my experience, the simplest approach to calculating the power for co-primary endpoints is to determine the split in Alpha for each primary endpoint. In most cases, it will be an equal split (i.e., significance reached at 0.025 for a total Alpha of 0.05). Next, calculate the power for each endpoint at the split Alpha. Finally, the total power for the study is calculated as the product of the individual powers. (i.e., each primary endpoint power = 90%, then total power = 81%).

I am sure there are more sophisticated approaches, but that should give you a base for designing your experiment.

Best,

TS

[#6]

Hello @Thierry_S 

In my situation the endpoints are correlated (i.e. not fully independent). So how do you take that into account with the above mentioned approach?

Appreciate your help.

[#7]

Hi,

Before addressing your question, it is essential to note that the process described above is more a design than a statistical approach. Hence, my suggestion is not based on defined rules; it is meant to reach an agreement on the prespecified criteria for "success."

In clinical research, it is not uncommon to have a certain degree of correlation between co-primary endpoints. For example, if you want to assess the improvement upon treating a patient, most improvement measures will correlate. In that case, your question becomes a design issue. You will need to evaluate carefully the value of selecting two co-primary endpoints rather than declaring the most meaningful one as primary and the other as key secondary.  Still, if the co-primary endpoints approach makes sense, you may want to split your alpha unequally (e.g., alpha1 = 0.01 and alpha2 = 0.04) depending on the relative importance of each of the co-primary endpoint.

Ultimately, as @Phil_Kay proposed, exploring simulations may inform your final design by letting you set different alphas and different population sizes.

Best,

TS

[#8]

@Thierry_S Thank you very much for the information. I agree with this approach and planning on using the simulations platform that @Phil_Kay suggested  (once I get more information on it).

Thank you again.

[#9]

@Thierry_S Really appreciate your help on this. Although, I am curious how sample size calculation is different when we have composite endpoint instead of co-primary. I am assuming, the sample size required for composite endpoint will be less than co-primary endpoint.

[#10]

Hi @billi,

That is an interesting and challenging question. If you were to take two co-primary endpoints and create a composite endpoint, it would intuitively lead to a smaller population. However, the variance of your new composite endpoint may increase substantially, leading to a reduction in relative effect size and a corresponding larger population required to achieve the same power. Traditionally, the primary motivation for using co-primary endpoints is based on the known validity of each endpoint as an instrument and their relevance in capturing meaningful effects. Combining two validated endpoints into a new composite measure can take a long time because one needs to determine the combination's mathematical formula and the composite measure's performance.

Best,

TS