Question

In a study investigating maternal risk factors for congenital syphilis, syphilis is treated as a dichotomous response variable, where 1 represents the presence of disease in a newborn and 0 its absence. The estimated coefficients from a logistic regression model containing the explanatory variables cocaine or crack use, marital status, number of prenatal visits to a doctor, alcohol use, and level of education are listed below [4]. The estimated intercept = 0: is not given. Variable Coefficient Cocaine/Crack Use 1.354 Marital Status 0.779 Number of Prenatal Visits -0.098 Alcohol Use 0.723 Level of Education 0.298

Marital status is a dichotomous random variable, where the value 1 indicates that a woman is unmarried and 0 that she is married. What are the relative odds, aka the odds ratio, that a newborn will suffer from syphilis for unmarried versus married mothers?

Answer 1

The odds ratio for newborns suffering from syphilis for unmarried versus married mothers is approximately 2.179, indicating higher odds for unmarried mothers.

The odds ratio for marital status in the context of the logistic regression model can be calculated by exponentiating the coefficient associated with marital status. In this case, the coefficient for marital status is 0.779. The odds ratio (OR) is calculated as:

`\[ \text{Odds Ratio (OR)} = e^{\text{Coefficient}} \]`

Substituting the given coefficient:

`\[ \text{OR} = e^(0.779) \]`

Calculating this, the odds ratio for syphilis in newborns for unmarried versus married mothers is approximately 2.179. This means that, holding other variables constant, the odds of a newborn suffering from syphilis are about 2.179 times higher for unmarried mothers compared to married mothers, according to the logistic regression model used in the study.