Why is it important to have a large cohort or sample size in epidemiological studies?
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3$\begingroup$ It's not. Many important studies are conducted with small $n$. Studies can also be invasive or costly: if anything it's important to have a small enough sample size to answer a question. $\endgroup$– AdamOCommented Feb 13, 2018 at 19:23
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3$\begingroup$ What kind of epidemiological studies are you referring to? Epidemiologists conduct many kinds! $\endgroup$– whuber ♦Commented Feb 13, 2018 at 19:28
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$\begingroup$ I guess I'm referring to cohort studies. $\endgroup$– JackJackAttack0214Commented Feb 13, 2018 at 23:35
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2 Answers
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Epidemiological cohort studies select subjects based on their exposure (to disease) status (or outcome) as expressed in the simplest case as $2\times2$ tables. How much confidence one has in the resulting odds ratio point estimate of a randomized controlled trial depends on the confidence interval of that estimate. For example, if one has an odds ratio of 2 with a 95% confidence interval of odds ratios of 0.5 to 8 then one has little confidence in a result significantly different from no effect (i.e., odds ratio of 1).
A simple indication of the confidence ($\leftarrow$ read this link for much more information) one has in a given point estimate was estimated as
$$\text{Confidence}=\dfrac{Signal}{Noise}\sqrt{sample\,size}$$
Note, "confidence" is inversely (reciprocally) related to confidence interval width. This equation shows that for low signal, high noise or small sample size, our confidence is small (and our odds ratio confidence interval is correspondingly large.) This, in effect, means that if, for example, we are looking at a factor suspected to be causal of breast cancer in women, where the incidence of breast cancer is larger than that caused by the factor being considered alone, that we will need a very large sample size to detect that particular effect. This can be thought of as "reliable finding one needle per haystack requires examining a lot of hay." The alternative to this is to design our experiment to remove the tedium by various methods...modify the question$-$for example by increasing the number of longitudinal time-samples...take shortcuts$-$for example the precision/granularity of exposure and outcome measures—e.g., dichotomous vs. continuous—will likewise affect statistical power/sample size concerns. The nature of cohort definition w/r/t exposure and/or outcome status likewise affects statistical power/sample size/concerns since these affect the precision of change in those measures....and for needles in haystacks, use one heck of a big magnet.
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2$\begingroup$ This answer frames too narrow a view on what constitutes cohort studies, which can produce measures at more than two points in time per subject, can accommodate continuous (ordinal, multidimensional, etc.) measures of either outcome or exposure or both, and the assertion about defined cohort can also apply to outcome, to both outcome and exposure, and to neither outcome nor exposure. $\endgroup$– AlexisCommented Feb 15, 2018 at 0:10
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$\begingroup$ @Alexis Your comment is disassembling, i.e., not constructive. Consider adding, for example, to the Wikipedia entry. But, while you are at it, consider that, for example, Newtonian physics is not "wrong," it is just incomplete without relativity. What I wrote is not "wrong." It is a solid basis that can be expanded upon. $\endgroup$– CarlCommented Feb 15, 2018 at 9:48
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$\begingroup$ @Alexis I edited to account for your criticism. It doesn't change much, and, you could have done the edit yourself, and, if you have any outstanding complaints, do that, edit it yourself. $\endgroup$– CarlCommented Feb 15, 2018 at 12:32
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1$\begingroup$ @alexis We both know how "cost ineffective" or downright ineffectual the average medical study is. I put your examples in bold. Slide me a break here, I am not writing book, or even a set of recommendations, just a few words to the wise. $\endgroup$– CarlCommented Feb 15, 2018 at 20:42
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The exact reason will depend on what you are trying to study. In some epidemiological studies, you don't even need large samples (of course, one person's large is another person's small; it would be better to state a sample size).
However, in general, the precision of the estimate of whatever it is you are estimating goes up as sample size increases.
If you are studying something unusual then you will need a large sample size in order to have any cases. E.g. if you are estimating the incidence or prevalence of a rare disease in the general population, then a small sample will probably not have any cases at all.
answered Feb 14, 2018 at 13:27
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$\begingroup$ I said that. If the frequency of disease is rare, the signal to noise ratio is small and the confidence is low for the same sample size. $\endgroup$– CarlCommented Feb 14, 2018 at 13:43