RMS General Regression

data analysis modeling strategy
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It’s hard to explain the interpretation of the estimate for the interaction term without first looking at the the other estimates. As the reference group for sex is set to “Male” and since you haven’t centered the lead exposure the interpretation of the coefficients are as follows:

  • Intercept: The estimated IQ-score for a male with a lead exposure of 0. I.e. the estimated IQ-score for such a man is 2012.1!! This is hardly realistic. If you want an estimate that makes more sense you could mean-center the lead exposure variable and re-run the analysis using this variable instead of the actual lead exposure. This will have the effect of changing the interpretation of the new intercept to be the estimated IQ-score for a man with an average/mean exposure to lead.

  • Sex(Female): The estimated difference in IQ-score between a male and a female that both have a lead exposure of zero. I.e., the estimated IQ-score is 31.0 points lower for the woman than the man. If, as suggested above, you mean-center the lead exposure and rerun the analysis, the interpretation of the new estimate becomes the difference between a man and a woman that both have an average/mean lead exposure.

  • Lead(Exposure): The slope of the regression line for men. I.e., it is the difference in IQ-score between two men where one has a lead exposure that is 1 unit higher than the other. The person with the higher lead exposure will have an estimated IQ-score that is 6.5 points lower than the person with the lower lead exposure.

  • Lead(Exposure)*Sex(Female): The difference in slopes between the regression line for men and women. I.e. the slope of the regression line for women is 21.1 higher than the slope for men, which means that the slope for women is 14.6 (= -6.5 + 21.1). An approximate 95% 2-sided CI for the difference in slopes is given by 21.1 +/- 1.96 x 4.3 = [12.6 ; 29.4].

For how to correctly interpret the p-value and 95% CI I suggest you take a look at this thread: https://discourse.datamethods.org/t/language-for-communicating-frequentist-results-about-treatment-effects/934

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