There is no such thing like "minimal sample size for analysis of a kind". Analysis can be performed on sample of any size, but the sensitivity (or precision) of the results depends on the sample size severely. Hence, the "minimal sample size" depends upon what precision is enough for your particular problem, i.e. the magnitude of differences that you want to prove to be statistically significant.

So, being in your boots, I'd calculate confidence intervals of the estimated regression coefficients (or, preferably, confidence set) and look what coefficients are statistically different from the neutral/"does-not-matter" value. If a coefficient turn out to be statistically indistinguishable from neutral, it would likely mean that sample size is too small to capture the effect of the respective parameter on the outcome.

On the other hand, one should check the predictive power of the model: if the predictions are good enough (the outcome is correctly predicted in most cases) but some regression coefficients are still "statistically neutral" then it means that respective predictors likely have no or almost no effect on the outcome (and, thus, should be thrown out of the model).

Just wanted to add: I am aware of power calculations or sample size calculations...just wondered whether there is conceptual work which makes statements about required number of cases etc.

There is no such thing like "minimal sample size for analysis of a kind". Analysis can be performed on sample of any size, but the sensitivity (or precision) of the results depends on the sample size severely. Hence, the "minimal sample size" depends upon what precision is enough for your particular problem, i.e. the magnitude of differences that you want to prove to be statistically significant.

So, being in your boots, I'd calculate confidence intervals of the estimated regression coefficients (or, preferably, confidence set) and look what coefficients are statistically different from the neutral/"does-not-matter" value. If a coefficient turn out to be statistically indistinguishable from neutral, it would likely mean that sample size is too small to capture the effect of the respective parameter on the outcome.

On the other hand, one should check the predictive power of the model: if the predictions are good enough (the outcome is correctly predicted in most cases) but some regression coefficients are still "statistically neutral" then it means that respective predictors likely have no or almost no effect on the outcome (and, thus, should be thrown out of the model).

There is also the type of software used to consider. For instance, 200 is the minimum sample size for SPSS. You can also use 5 or 10 samples per measurement. But the best way, in my opinion, consider margin of error and boundaries. I have attached my sample size calc with the formula excerpt from my dissertation to give you something tangible to associate with Konstantin's comments.

Dear Konstantin: thanks for your suggestion. It is indeed a good idea in such a small study like mine to reduce variables that do not add to the prediction: maybe that is a way to reduce the set of potential confounder to actual empirical confounders. I know there are various confounder selection strategies, but a more pragmatic approach could indeed increase the precision in my limited sample.

Dear Beth: thanks a alot for sharing your calculation. That is a very useful resource!

Dear Rohit:

@ 1) multivariate vs multivariable: thanks for this crucial clarification. I wasn't aware of this issue....though this is quite crucial.

@ 2) yes, the model is logistic. Having searched some more after I had posted the question, I also came across Peduzzis paper on "10 events per predictor"...only to find later that there quite some occassions when this "rule" can be handled less strictly (http://www.ncbi.nlm.nih.gov/pubmed/17182981). Fortunately, I am a SAS user myself and will look up Firth's penalized likelihood. Thanks for this great advice!

best

Adrian

In fact some statisticians recommend sample size that is 10 times the number of independent variables. Therefore, 1,500 is more than enough.

In fact, it is a complicating question. I don't think there is a simple answer to your question. In terms of your primary objective 'prediction', two issues need to be considered.

First, you have to assess  or assume the fit of goodness of your forecasting model. If one or a few predictors (e.g. =80%), it is fine. In this case, you may not need a large sample size. 

Secondly, if the predictive mdoel highly relies on the combination of mutiple variables (e.g. >10 predictors) and most of their effects are slight or moderate, you may need to collect a large sample to gurantee they are statistically significant in final predictive model. In this case, you need to assume the regression coefficient and calculate the minimum sample size. As I know, there is no simple programes in statistical softwares like SAS, SPSS. You need to consult statisticians.

In an ideal world you would have specified your analysis a priori and would live with the results, but it's not an ideal world.  Having done logistic with continuous IV (which, knowing nothing else, would be more powerful than median split or tertiles), my question is: did you get a statistically significant result from the logistic with continuous IV? If so, you're done.  If neither it nor the median split was significant, you might be accused of 'torturing the data' if you now move to tertiles, and I'd be surprised if it would reveal anything.

The number of cases we need in anthropology are directly link:  first to the type of questions or objectives you mark and second to the human and economic resources you count with. The principal methodology in anthropology  is ethnography and we use quantitative methods to complement it.

I agree that the sample size for multivariat analyais should be at least  = 10 times the number of independent variables.

Take a look at paper by Cohen 1992 showing relation between sample size, effect size and power