I have a potential problem that I may have to answer for within one of my working research projects. I have a variable that I am studying its effect on mortality of cancer patients. This variable was distributed over many groups with a wide range of group sizes. For example, Group A had 10,000 observations, Group B had 7,000, Group C had 4,000, Group D had 5,000, and Group E had just 100 observations. I am thinking of excluding Group E because of its extremely small sample size that might affect the statistical significance my results. Am I statistically allowed to do so? Is there a cut-off limit for group sizes, given the above example, that below which I can safely exclude the group with the smallest number of observations? What if the smallest group actually contained my "variable of interest" which I wanted to test its effect? Are there any statistically feasible solutions to the above problem?
You have several options to address this problem.
If you compare group E to others, you obviously have a relatively smaller group. However, 100 observations may be a good sample size to evidence associations, this will depend on the magnitude of the association.
You could exclude group E (the smallest) but this would imply that your study will no longer represent a population group and the conclusions would only be extrapolated to the other groups (A, B, C and D). This will affect the external validity of your results especially if, for example, group E contributes significantly to the burden of disease you are studying. In your case, if group E contributes significantly to cancer mortality, excluding it would be imprudent.
I understood you are evaluating a factor with 5 categories (A-E) and you are comparing cancer mortality among those categories.
In that case, I would advise you not to exclude group E, but be careful to use as a reference category for comparisons a group with big (or the biggest) sample size. For example, if you choice the group A as reference, then you can compare the group B vs A, C vs A, D vs A, etc. In that way, the small sample size of the group E will not affect the power of the associations evaluated for the other groups.
Analysed correctly, the data from the small group will always add information, so it is not advisable to remove it.
A suboptimal definition of groups and the use of inapropriate models or analysis tools is a different aspect. But given the definition of the groups is sensible and appropriate models and analysis tools are used, removing groups based on the group size is generally a bad thing to do.
It is not advisable to exclude any group even of small counts especially when our analysis is based on the health care system and otherwise too...
Sir, You may use the correct technique to analyse your data so that effect of every group can be seen on the mortality pattern which is the biggest problem in developing countries.
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