Question

Suppose that in a particular year in your county, there were 1000 births. In reviewing their birth certificates, you found that 72 had low birthweights (<2500 grams), and 158 had mothers who smoked during the pregnancy. Of the mothers who smoked during the pregnancy, you found that 19 had low birth weight babies. In order to explore the relationship between maternal smoking and low birth weight outcomes, you would construct the following table

		Low Birth Weight
		Yes (Disease)	No (Not Diseased)	Total
Smoked During Pregnancy	Yes (Exposed)	19	139	158
	No (Unexposed	53	789	842
	Total	72	928	1000

a) Calculate AND interpret the relative and absolute measures of association.

b) In your interpretation, explain which of the measures is a measure of public health impact.

c) Finally, calculate the proportion of disease among the exposed that would be eliminated if the exposure were eliminated (assuming a causal relationship between maternal smoking and low birth weight).

Answer 1

Given that there were 1000 births in a country.

Out of those, 72 infants had low birth weights (< 2500 grams). And 158 mothers smoked during pregnancy and out of those 158, 19 mothers had low birth weight babies.

(a). So, the formula of relative risk is:

RR = (a/a +b) / (c/c + d)

As we are calculating the relative risk to check the relationship between maternal smoking and infant has low birth weight.

Here a = 19, b = 139, c = 53, d = 789.

RR = (a/a +b) / (c/c + d)

RR = (19/19 +139) / (53/ 53 +789) = 1.9.

From the above calculations, 12% risk that the smoking mothers have low birth weights.

Whereas, this risk is 6% for non-smoking mothers. And relative risk of low infant birth weight in relation to smoking during the pregnancy is 1.9.

Absolute risk is similar to odds ratio. So, the formula of absolute risk is:

AR = (a/b) / (c/d) = (19/139) / (53/789) = 2.03.

If the difference between incidence rate or prevalence rate of any outcome is very less, then relative risk and absolute risk give similar results.

(b). For regular public health impact, we use, the relative risk as it is more preferred over the absolute risk (or odds ratio) as they are directly related to the probability of developing or having a health outcome.

(c). We need to calculate that the proportion of disease in the exposed infants that would be eliminated if the exposure were also will be eliminated.

For this, we need to subtract the risk of the non-exposed group of infants from the risk for the exposed group infants. Also, this risk is known as Attributable risk.

p₁  = proportion of smoking mothers during pregnancy with Low birth weights infants (a/a + b)

p₂ = proportion of non-smoking mothers during pregnancy with Low birth weights infants (c/c +d)

p₁  = a / a +b = 19 / 19 + 139 = 0.120.

p₂= c / c + d = 53 / 53 + 789 = 0.063.

Attributable risk.= p₁ - p_{2 =} 0.120 - 0.063 = 0.057.