I would suggest using all the data from both years to create 1 logistic regression model that includes all the risk factors *and year*, and then create year by risk factor interactions. Any year * risk factor interactions that are significant will indicate that the risk factors varied by year.

Significance be determined by a Wald test or change in deviance when terms are dropped, etc. All the typical model building comments/advice/restrictions still apply.

I would suggest using all the data from both years to create 1 logistic regression model that includes all the risk factors *and year*, and then create year by risk factor interactions. Any year * risk factor interactions that are significant will indicate that the risk factors varied by year.

Significance be determined by a Wald test or change in deviance when terms are dropped, etc. All the typical model building comments/advice/restrictions still apply.

1. Including a multiplicative interactions between Year and risk factors, and statistical significance can be ascertained. When the risk factors are highly correlated with each other these interactions become less interpretable.

2. It sounds like you have committed to a stratified approach, having run two separate regressions, one for each year. This results in some loss of statistical power relative to the interaction approach. If you have information on time, on a continuous scale, doing so has also resulted in a loss of power. To ascertain the significance of the difference between the odds ratios (OR) for each year, you could look to see whether the confidence intervals overlap.

3. You could bootstrap. Resample with replacement many times and run the regressions over and over again until you get a distribution of differences between ORs. You could look at the 2.5th and 97.5th centiles of this distribution and ascertain whether the associated interval contains

There are other approaches. I think these are the simplest. Best of luck with it.

Hi Mahmoud, I agree with the previous comments. Normally all our tests are for within a model because the assumption is that the data are in some way "dependent." Thus, there was a long standing problem when questionnaires were administered to husbands and wives and then analyzed in separate regressions. There was no appropriate test to say something was different for the two groups because the samples were dependent. Even the most obvious thing, a predictor being "significant" for husbands, but "not significant" for wives was relatively meaningless and there was certainly no test for "larger than," for example. So the answers above assume that your models are from the same population or in some other way dependent. If they are not, there must be some test for the different in the coefficient from two logistic regressions just as there is for two independent linear regressions. Since this has never come up for me, I don't have a reference, but I wanted to make the point that the answer to this is dependent on whether the samples for these two models are related or unrelated. This shouldn't be exotic. I'd start by searching for "difference between regression coefficients" and read up on that, and then look for the special case of logistic regression. Bob

I should add a little to my answer. To expand my example, if you had men and women from separate samples you could test that difference in regression coefficients, but then you would have to question what does it mean? Is the difference because on the one hand you have women and the other men or because they came from two different samples? So the same would be true in your case, if you have both two different years and two truly independent samples, what would you be testing? So if your coefficients are from one sample, you need to combine them in one model add "year" to the model and interact with the effect you want to test, as above. Bob

Hello Mahmoud. You say you have two models using data from the same population, but in two different years. That could mean any of the following:

1. Two independent samples from the same population (i.e., different individuals sampled in the two years);

2. Exactly the same individuals examined both times (i.e., paired data);

3. Some individuals appearing in only one of the samples, others appearing in both samples.

Which of these is it? If it is number 1, then I agree with previous posters who said you can include an indicator for year and its product with the risk factor(s) of interest. The null hypothesis for those interaction terms is that the effect of the risk factor is independent of year.

If it is number 2 (or 3), you'll have to take into account the correlated nature of the paired observations. There are at least a couple of ways to do that: generalized estimating equations (GEE) is one; a multilevel model (with occasions clustered within ID) is another.

I hope this helps.

Hello William, Gavin, Robert, Bruce and colleagues,

Thank you very much for your valuable responses. In fact, the data came from two official surveys on domestic violence in the same population in 2005 and 2011. Dramatic political, social and economic changes happed in the region between those two years. The variable of interest is whether a woman has been exposed to violence of any sort. Two logistic models were fitted from the two independent samples to study the effect of possible political, social and economic risk factors on violence against women in each year. Interesting results were obtained along two different types of localities in the country but I am interested to conduct some comparisons between different risk factors or model coefficients in order to identify the most important risk factors on violence against women in the society. Your feedback would be highly appreciated.

Hello

You can enjoy two options

Combine the two populations into a new data set; as such you'll need to create a new variable (say “population”) defining whether or not an observation belongs to population "0" or population “1”. That is, each observation will be assigned to either “0” for one population or “1” for the other. Introduce the interaction term for the Var_population *Var_i , where Var_i represents the predictors of which you are examining the effect on the outcome of interest. Testing the significance of interaction between the population and each predictor is corresponding to testing the hypothesis that the risk ratios (in this case OR) of the two populations are equal.

Separately estimate OR for each predictor in each population and use the following formula to test the significance of difference between ORs.

z=((β_([F])- β_([T])))/√(〖〖SE〗_F〗^2+〖〖SE〗_T〗^2 )

Mo matter which pathway you’ll take, the point to be born in mind is that the two models components MUST have same components. That is the level of adjustments needs to be the same. Otherwise any comparisons will be meaningless.

good luck

Replace F and T with "population 0" and "population 1", respectively.

Thank you very much Mohammadreza for your interesting answer..