Analysis of Low Birth Weight Rates by Smoking Status

Nov 22, 2025, 11:07 PM

lbw2.sav

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We will use the Hosmer & Lemeshow low birthweight data, which contains 189 birth records. Description identification code birthweight: 1 = birthweight<2500g, 0 = otherwise age of mother (years) weight at last menstrual period (Ibs.) race: 1 = White, 2 = Black, 3 = other smoked during pregnancy: 1 = yes, 0 = no history of premature labor: 1 = yes, 0 = no history of hypertension: 1 = yes, 0 = no presence, uterine irritability: 1 = yes, 0 = no number of prenatal visits during the 1st trimester birthweight (grams). Question 1

Q1. Obtain a 2x2 table between low birth weight and smoking. Report the low birth rate among smokers and non-smokers in % to the nearest tenth (e.g., 10.5, meaning 10.5 %).

a. Among non-smokers

Low birth-weight rate among non-smokers

From the 2×2 table we created, non-smokers had 29 low-birth-weight babies out of 115 total births, giving a rate of:

\text{Rate} = \frac{29}{115}\times 100 \approx 25.2\%

So, 25.2 % of babies born to mothers who did not smoke during pregnancy weighed less than 2 500 g.

Low-birth-weight rate among non-smokers

Using the Hosmer & Lemeshow data (N = 189) we built the 2 × 2 table between smoking and low birth weight and found:

Smoking status	Normal BW	Low BW	Low BW rate (%)
Non-smokers	86	29	25.2 %
Smokers	44	30	40.5 %

Therefore, the percentage of low-birth-weight babies among mothers who did not smoke during pregnancy is 25.2 % (to the nearest tenth).

A bar chart illustrating these rates has also been provided for visual comparison.

Question 2

b. Among smokers
Question 3

Q2. Calculate the odds of low birth weight among non-smokers and smokers. To avoid rounding errors, use the counts to calculate them instead of the answer you obtained in the previous question. Report them to the nearest hundredth. Include a leading zero if applicable (e.g., 0.70).

a. Among non-smokers
0.25 points

Question 4

b. Among smokers
0.25 points

Question 5

Q3. Calculate the odds ratio and log odds ratio of low birth weight comparing smokers with non-smokers. To avoid rounding errors, use the counts to calculate them instead of the answer you obtained in the previous question. Report them to the nearest hundredth. Include a leading zero if applicable (e.g., 0.70).

a. Odds ratio
Question 6

To avoid rounding errors, use the counts to calculate them instead of the answer you obtained in the previous question. Report them to the nearest hundredth. Include a leading zero if applicable (e.g., 0.70).

b. Log odds ratio

Answers to Questions 2 & 3

Quantity	Formula (based on counts)	Result
Low-birth-weight rate among smokers	$\dfrac{30}{30+44}\times100$	40.5 %
Odds of LBW (non-smokers)	$\dfrac{29}{86}$	0.34
Odds of LBW (smokers)	$\dfrac{30}{44}$	0.68
Odds ratio (smokers vs. non-smokers)	$\dfrac{30/44}{29/86}$	2.02
Log odds ratio	$\ln(2.02)$	0.70

Thus:

• Q2b. Among smokers, the low-birth-weight rate is 40.5 %.

• Q3a. Odds of low birth weight
• Non-smokers: 0.34
• Smokers: 0.68

• Q3b. Comparing smokers with non-smokers
• Odds ratio: 2.02
• Log odds ratio: 0.70

A bar plot of the odds for each group was also displayed above for visual reference.

Results using Hosmer & Lemeshow low-birth-weight data (N = 189)

Question	Quantity	Answer (rounded)
Q1b	Low-birth-weight rate among smokers	40.5 %
Q2a	Odds of LBW among non-smokers ((29 / 86))	0.34
Q2b	Odds of LBW among smokers ((30 / 44))	0.68
Q3a	Odds ratio (smokers vs. non-smokers)	2.02
Q3b	Log odds ratio (natural log of OR)	0.70

Interpretation: mothers who smoked during pregnancy had about twice the odds (OR ≈ 2.02) of delivering a low-birth-weight infant compared with non-smokers.

Feel free to ask for confidence intervals, hypothesis tests, or any further visualizations!

Question 7

Fit the unadjusted model

log odds of low birthweight = logfraction numerator P left parenthesis low space birth space weight right parenthesis over denominator 1 minus P left parenthesis low space birth space weight right parenthesis end fraction = β0 + β1(smoke)

Use the results to answer Questions 4 – 6.

Q4. What is the odds ratio of low birth weight compared to mothers who smoked to those who did not? Report to the nearest hundredth.

0.5 points

Question 8

Q5. Report estimated odds of low birth weight among smokers and non-smokers. Report to the nearest hundredth. Include a leading zero if applicable (e.g., 0.70).

a. Nonsmokers:
0.25 points

Question 9

b. Smokers:

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