Sample size calculation for survival proportion at fixed time point

[Shola Adeyemi]

Dear Expert Statisticians,

In some survival studies, survival rate (percent) are reported as primary end point at fixed time point. E.g 9 or 12 months. I want to know how the sample size is calculated that reflects the element of time, hazards and censoring.

I hope I'm asking a relevant question.

Kind regards,

Shola

--

Quote:

Things may come to those who wait, but only the things
left by those who hustle."
-- Abraham Lincoln, Sixteenth president of the United States

[Marc Schwartz]

> On Feb 18, 2015, at 12:23 PM, Shola Adeyemi <shola....@gmail.com> wrote:
>
> Dear Expert Statisticians,
>
> In some survival studies, survival rate (percent) are reported as primary end point at fixed time point. E.g 9 or 12 months. I want to know how the sample size is calculated that reflects the element of time, hazards and censoring.
>
> I hope I'm asking a relevant question.
>
> Kind regards,
> Shola

Hi,

When calculating sample sizes for freedom from event analyses (eg. Kaplan-Meier), you base the calculation on a hypothesized hazard ratio (if, for example, a two arm comparison) or perhaps the median time to event or event probability at Time T (if, for example, a one arm analysis versus a historical control). That leads you to the number of events required to be observed at a given power and alpha level.

Then you extend that to account for how long it will take to observe that number of events, which can include considerations for dropouts/LTFU and so forth. So you need to have some a priori assumptions regarding accrual and minimum follow up times.

There are various programs that can assist with this. If you are using R, Frank has the cpower() and spower() functions in his Hmisc CRAN package:

http://cran.r-project.org/web/packages/Hmisc/

There are also online calculators, such as the SWOG group:

http://www.swogstat.org/statoolsout.html

and Jeff Horner has an online implementation of Frank's spower() from Hmisc:

http://glimmer.rstudio.com/jeffreyhorner/PowerSample/


There can be differences in some of the underlying methods used, which can then of course, lead to some differences in the sample size estimations.

Another option is directly via Monte Carlo simulation using exponential family (eg. Weibull) event distributions and making some assumptions about censoring times. Frank's spower() function uses this approach internally.

Regards,

Marc Schwartz

[Marc Schwartz]

> On Feb 18, 2015, at 1:09 PM, Marc Schwartz <marc_s...@me.com> wrote:
>
>
>> On Feb 18, 2015, at 12:23 PM, Shola Adeyemi <shola....@gmail.com> wrote:
>>
>> Dear Expert Statisticians,
>>
>> In some survival studies, survival rate (percent) are reported as primary end point at fixed time point. E.g 9 or 12 months. I want to know how the sample size is calculated that reflects the element of time, hazards and censoring.
>>
>> I hope I'm asking a relevant question.
>>
>> Kind regards,
>> Shola
>
>
>
> Hi,
>
> When calculating sample sizes for freedom from event analyses (eg. Kaplan-Meier), you base the calculation on a hypothesized hazard ratio (if, for example, a two arm comparison) or perhaps the median time to event or event probability at Time T (if, for example, a one arm analysis versus a historical control). That leads you to the number of events required to be observed at a given power and alpha level.
>
> Then you extend that to account for how long it will take to observe that number of events,

Correction on the wording above. It should be:

...how many patients it will take to observe that number of events, ...


Marc