# How to Calculate Sample Size for difference in Survival of 3 strata with varying proportions

Is there a way to calculate sample size for the following scenario:

3 strata:
Stratum (A) → 13% of total patient population → Survival (Overall 3-year) = 70%
Stratum (B) → 57% of total patient population → Survival (Overall 3-year) = 49%
Stratum (A) → 30% of total patient population → Survival (Overall 3-year) = 31%

In NCSS PASS, R, Medcalc, GPower, PSS and Openepi I can’t find more than 2 arms in sample size calculations for survival

So, I’d calculate for the smallest effect size (in this case 49% - 31%) it gives me total sample size of 216 (using PASS | Reference Machin, D., Campbell, M., Fayers, P., and Pinol, A. 1997. Sample Size Tables for Clinical Studies, 2nd Edition. Blackwell Science. Malden, MA). Should I report this result and divide this number over reported proportions, OR there is a way to calculate the sample size accounting for the three strata together?

1 Like

I have checked Stata as well. Weird.

This calculation doesn’t seem right either, may I propose using a chi-square test as an approximation for the log rank statistic? I haven’t tried this before and I am not sure if it is valid.

I guess the other alternative would be using univariable Cox regression.

1 Like

I tried using Cox regression, but one of the required parameters in R squared of the model, which is not reported in this case. Moreover, using the rule of thumb for sample size calculations depending on the EPP or EPV is now considered as inaccurate / non reliable solutions.

1 Like

You would need to specify the reason for the power calculation. If it is the classical reason (trying to detect a signal using a silly notion of “significance”) the R^2 should not come into the picture.

1 Like

but the power calculaiton should reflect the hypothesis, and you havent stated the hypothesis. This recent open access paper on comparing 3 groups might be useful: Comparing Three Groups eg declare one of the comparison as primary and power on that

1 Like

@f2harrell

We are trying to find the minimum number of cases needed per strata to find a significant difference in their survival, according to the these parameters (stated proportions and 3 years OS, at 5% alpha and 20% beta)… Do you know of any package that would support sample size calculations for three armed studies with time-to-event outcomes?

1 Like

Thanks a lot dear @pmbrown
we have a type of cells that is either absent or present, and when present it is categorized into high and low prevalence groups according to a specified cutoff

so we have patients with -ve cells, patients with low prevalence and patients with high prevalence

the hypothesis is: the high prevalence group is associated with poor prognosis (stratum C) compared to low prevalence group (Stratum B) and -ve group (stratum A, best prognosis)

1 Like

you could specify that contrast as primary ie C versus A and B combined. The above paper notes this when they say " The multcomp package can also be used if different contrasts are of interest, for example, μ1−(μ2+μ3)/2". But it depends on whether you expect a difference between A and B and whether A v B is of interest

edit: the reference given for the R package multcomp: “In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc.” Simultaneous Inference in General Parametric Models

1 Like