# Sample size needed?

I need some help calculating the minimum sample size needed for my upcoming trial. I’m doing higher degree research on eHealth, so I have little knowledge about statistics and sample size calculation. Was doing loads of research online and trying out online calculators but I’m still not too sure.

So basically I’ve done an initial trial on a small sample of 24 participants, randomly allocated to two groups (13 in control group and 11 in intervention group), the aim is to see whether the use of an IT based intervention can improve health supplement adherence rate when compared to a control group using a pillbox. Below is the result from the initial trial:

Control group- average baseline adherence rate before trial was 86%, and after trial the average adherence rate increased to 95% Intervention group- average baseline adherence rate before trial was 81%, and after trial the average adherence rate increased to 98%

So what I would like to know is: what is the minimum number of participants I will need for each group (I want a 2:1 ratio, so more people in the intervention group). I need to know the very minimum number as I was having problem recruiting enough participants in the initial trial, and I’m currently starting the recruitment process for the upcoming full trial.

Power=at least 80%, and alpha=0.05

I’ve tried this online calculator, but unsure what to put in the anticipated incidence sections, or if it is the right calculator to use in my case: https://clincalc.com/stats/samplesize.aspx

Any help will be appreciated.

Time will severely affect adherence - as you saw you got really high adherence even in the control group, but one would not expect that to last for months (I assume your pilot was just a few weeks). Thus, it really matters how long your trial is. Additionally, calculating adherence over a longer time period will also reduce day-to-day variability (while at the same time potentially increasing variability as people may start to behave differently).

If you perform a long enough trial you may be able to treat the proportion of days adherent as approximately normal* (a lot of hand-waving involved), so you'd primarily need to know what difference between groups you would expect and how much residual variability in the outcome (after adjusting for baseline and the treatment group) you would have. The first you would really need to guess, because your pilot likely won't help you there (your sample size is very small leading to noisy estimates and importantly the difference would likely be different over a longer trial). The second you can get a guess from your pilot (with all the difficulties of extrapolating to a longer trial). You may also wish to see whether the published literature can give you a good idea.

* This is assuming a linear regression (ANCOVA) adjusted for baseline to estimate a treatment difference, which may well be good enough. For the actual analysis you might wish to consider a random effects model for binomial data, but you would have to simulate to get a sample size for that.

If you can get a consultation with the statistics group in your institution that would be very helpful, because this is not a straightforward problem.

• Thanks. So basically what I need to be able to get an estimate sample size is the difference between control and intervention group, but in a larger scale? So if I can find some existing research that has results from a larger study participants then I can use that? Commented Feb 14, 2019 at 5:17
• That would be a plausible approach, particularly if your intervention is similar / should in your judgement should likely have a similar effect. You also need the variability if the outcome, which can also be back calculated from the type of data people tend to publish. Commented Feb 14, 2019 at 6:31
• Sorry but have another question, once I’ve found the larger data from existing similar literatures, with the data on adherence rates, what kind of calculation should I use to calculate the sample size? Sorry I’m a complete beginner in statistics Commented Feb 14, 2019 at 8:57
• A sample size calculation for a two sample t-test may give you a reasonable answer, but consulting a statistician at your institution in depth would be a good idea. Commented Feb 14, 2019 at 17:51
• Yeah I’ve sent email to my uni’s statistician, but still awaiting response. So I thought I might come online and ask around first. Thanks for your help Commented Feb 15, 2019 at 14:54