# type of study and sample size

I'm a medical student and for my thesis I'll study some features of the retina in patients in neurodegenerative disorders (Parkinson, Alzheimer) compared with controls. We are not going to make a follow up so it's not a prospective study but I've read that cross sectional studies are observational by definition. it's an experimental study because patients will undergo instrumental exams but I can't find the right definition of the study.

The second problem is that I can't calculate sample sizes for patients and controls since I don't know how to define this study.

• I don't think there is enough information here to give specific advice, but @Chris C has given solid general advice on how to proceed. In particular step 1 seems relevant. Unclear that you've defined your specific aim (hypothesis). – charles Nov 1 '14 at 15:34

fellow student here, so I hope a real professional can come in and give his advice. This advice is just from experience, and I would love to be corrected.

Step 1: Decide what you are looking for.

I assume you have already done this and not specified it in your question. For example, are you going to look at the density of cone cells, or maybe the optic nerve / retinal surface ratio. Whatever the biology of the study is.

Step 2: Decide what difference of effect size would be biologically significant.

You have to decide what kind of increase in effect size would be of biological significance. For example, would a 2% increase in cone cells have significant ramifications, or are you looking more around the range of a 30% increase? This is up to you and your supervisor.

Step 3: Calculate statistical power

There are tons of tools that you can use to do this, but my personal preference is either R or a program called G*Power. Power is a crucial part of study design from a statistical point of view. In a nutshell (to my understanding), power is the chance that you correctly reject the null (say there is an effect) when in fact there is an effect. Power is influenced by your sample size, variance of population, your difference in effect size, and a few other things depending on what specific test you're doing. The larger the biological effect you're looking for, the lower sample size you will need to detect it. Decide if you want 70% power, 80% power, etc. This will change the group sizes that you will need.

Step 4: Decide exclusion criteria

Are there any other conditions that are known to influence the thing you're looking for? For example, is cardiovascular disease known to affect this? In that case, you will need to exclude patients with cvd prior to the collection of specimens. You do not have the complications of follow ups, so that's good.

Step 5: Collect samples

You will want your specimens to be well matched for most criteria, as you are not selecting them from the whole population. I assume this because a very small amount of people will want to go undergo eye surgery (as you have suggested) to measure what you are looking for. Ergo, it would be best (in my opinion, and I hope that more people chime in to maybe tell me that I'm wrong) to match patients for age, sex ratio, weight, and other potentially confounding factors. These things can be adjusted for statistically, but it is never as good as having a well matched population (or so I've been told).

Step 6: Analyze Samples

You are looking for a difference in one feature among 3, or possibly more, groups. You will want to look into ANOVA or multi-way ANOVA depending on how you're performing it. Following up on the ANOVA, you could do pairwise T tests with multiple testing correction to see which groups in particular differ, since the null of a single way ANOVA is that none of the groups are different. You must check to make sure that all of the assumptions of ANOVA (normality of observations, homoscedasticity, independence of observations) has been met. A Welch T-Test can avoid the problem of homoscedasticity. If you do not meet the assumptions you will need to do non-parametric analysis (Kruskal Wallis perhaps). If you are feeling confident you can also do permutation testing or bootstrapping, but I'm not sure how much statistical background you have, so I will not get into the details. Be aware of interaction effects, as these will give you important information as well.

General notes

As you have presented it, I see your study as a cross-sectional study. Though you are using a surgical approach to get your data, you are not really looking at a treatment, as you are more observing how your brain disorder changes things. See here,here, and many others for more information on details. The sample size that you will need will be decided by your power analysis in step 3. If you find that the effect you want is small, then the population might be too large, and you may decide not to do the study. This is up to you and your sup.

Again, just a student, and I would love to be corrected. Best of luck!