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I am trying to do a multiple logistic regression for 2 similar groups. I have a few questions:

  1. In doing a univariate analysis, do I enter each independent variable, one at a time, first into the binary regression, before going on to do the multivariate analysis? Or is the significance values from Chi-square or t-test enough to go on with?

  2. I have a test group and a control group and I want to determine the effect of independent variables (e.g HIV status, maternal weight etc) on a particular dependent variable (low birth weight). Should I perform the regression on a dataset with both the test and the control cases or should I split the file? In this case I want to see the effect of HIV on birthweight and I am having a hard time knowing how to move on.

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I would start with estimating a (simple) bivariate correlation matrix which includes your outcome variable as well as all predictors. This will give you very first insights into the dependency structure of all your variables. Especially correlation coefficients of $|r| > 0.4$ (between your predictor variables) can indicate later multicollinearity problems.

Next, I would continue with a series of bivariate regressions. That is, for each predictor ('independent variable') run one logistic regression. One of these regressions will focus on your control-/treatment-group variable. This will inform you about the 'gross' effects, that is the unadjusted effects. Please, do not think that statistically non-significant effects could be excluded from later analysis.

Do you assume an interaction effect between HIV and your treatment-variable (1=treatment, 0=control)? Then you could run two separate models with HIV as predictor variable, i.e. one model for control- and one model for treatment-group. Given that you observe different coefficients for HIV, you will need to run another model which includes an interaction effect $HIV \times treatment$ (and the two main effects). This second model will allow you to test for statistically significant differences between the groups. You also might include your other predictor variables.

Please be aware that interaction effects in logistic regression models are more complicated than in the case of a simple linear regression model. Edward Norton has published several papers which discuss that topic.

You also did not tell us what software you are using to estimate the models. However, most software packages are able to test for multicollinearity (VIF or tolerance).

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  • $\begingroup$ Thanks a lot for the answer. It was really helpful. Indeed HIV had an effect on the treatment group as well as some other predictors and so i am running separate models for the two groups which includes these other predictors too.However, in discussing my findings,do i concentrate more on the model with the treatment group as my aim is to evaluate the effect of HIV on birthweight of infants? I am using SPSS 19. $\endgroup$ – user3355 Feb 22 '11 at 18:47
  • $\begingroup$ I wrote: "Given that you observe different coefficients for HIV, you will need to run another model which includes an interaction effect...". I would report the findings of the interaction model. However, reporting the findings of two separate models (control and treatment), can be more instructive, esp. for an audience with less statistical background. $\endgroup$ – Bernd Weiss Feb 22 '11 at 18:50
  • $\begingroup$ You generate a new variable which is the product of HIV and treatment ($x_1 \times x_2$). Then, include your new variable as well as HIV ($x_1$) and treatment ($x_2$) in your model: $... = ... + b_1x_1 + b_2x_2 + b_3x_1x_2$. However, you seem to have less experience with this kind of analysis. Don't get me wrong but may I suggest that you contact a local statistician or other person who can help you. $\endgroup$ – Bernd Weiss Feb 22 '11 at 19:39

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