Lets say I am analyzing a genetic polymorphism data where I have genotyped 120 cases and 50 controls. I guess it is not statistically right to compare a larger number of cases to fewer controls as it may cause some false results. I thought of comparing the 50 controls with a randomly chosen group of 50 cases. Then I could repeat my analysis with other 50 cases and same controls, and check if I could reproduce the significance? This is just a thought. Anyone has any suggestions about dealing with such situation?
If Your data are normally distributed I would try so-called "power t-test".
Unequal sample sizes between the experimental group and the control group are not uncommon in true experiments. For this situation you employ t-test of mean difference between two independent samples (small) or z-test of mean difference between two independent samples (large).
Here the data is categorical (genotypes). I need to do chi-squared test and logistic regression. Can you comment on using those tests for this data. @Eddie Seva See @ Albert Batushansky
I am not sure that can help without details of Your experiment...
As far as I understood, first, the question was: how to compare two groups with unequal sizes. It can be done with t-test in case of normal distribution with calculation of power to eliminate false results.
Now Your are asking about logistic regression which is a probabilistic statistics. It can be done. But again, the first step should be to understand what do You need to test and compare.
Hello,
As far as i know, logistic regression doe not rely on equal group size (from : http://www.uk.sagepub.com/burns/website%20material/Chapter%2024%20-%20Logistic%20regression.pdf)
But given such a difference with your sample sizes, bootstrap as you mentionned could be a solution (resampling equal size sample).
I hope this could help.
Alan
Assumptions for Logistic regression are :
Logistic regression does not assume a linear relationship between the dependent and independent variables.
The dependent variable must be a dichotomy (2 categories).
The independent variables need not be interval, nor normally distributed, nor linearly
related, nor of equal variance within each group.
The categories (groups) must be mutually exclusive and exhaustive; a case can only be
in one group and every case must be a member of one of the groups.
My understanding is that there is no problem here. It is common in case comparison studies where you sample on the cases and the comparisons to have more of the comparisons as they are easier/ cheaper to collect information on. Eg there may be only 95 cases of the rare outcome (the case) but getting a thousand comparison from the general population is easy.
However, there is little gain in efficiency once you have 5 times as many controls/comparisons as cases; so it is not worth going beyond that number when designing your study. So with 95 cases it is worth having 5*95 comparisons if they are easy to recruit/collect and up to that point they will increase the power of the study to detect effects.
See p168 of Clayton and Hills Statistical models in epidemiology for the theory behind this advice.
THis paper show how to analyse case - comparison responses in a logit model
http://www.oxfordjournals.org/our_journals/tropej/online/ma_chap11.pdf
Dear Veera;
Wacholder et al have reported that the best way to increase precision in a case-control study is to increase the number of cases by widening the base geographically or temporally rather than by increasing the number of controls, because the marginal increase in precision from an additional case is greater than from an additional control.
Fore more detail please see the following link:
http://www.ncbi.nlm.nih.gov/pubmed/1595688
Best.
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