Birth Weight and Maternal Smoking, Accounting for Gestation Length

1 Introduction

  Low birth weight has been associated with mortality for newborns. One important factor is maternal smoking during pregnancy. In this study, the relationship between birth weight and smoking during pregnancy was assessed, taking into account the length of gestation. Additionally, the association of birth weight to the length of gestation was examined when taking into account maternal smoking status. Further, a model was assessed for predicting mean birth weight with known values of gestation length and smoking status.

2 Method

2.1 Objective.

  This analysis was conducted to examine whether there was a significant association between average birth weight and smoking status, while taking gestation length into account. Additionally, this study intended to assess whether there was a significantly strong relationship between birth weight and gestation length, while taking smoking into account. Finally, it was hypothesized that mean birth weight can be predicted by the length of gestation and the maternal smoking status.

2.2 Data Collection.

  The data were collected and made available for Pennsylvania State University statistics projects. There were 32 observations collected. Birth weight was measured in grams. Gestation length was measured in weeks. Mothers were categorized based on self-report as smoking (YES) or non-smoking (NO).

2.3 Potential Confounding Variables.

  The potential confounding variables included: mother’s age, mother’s weight gain during pregnancy, and the number of cigarettes per day for smokers.

3 Statistical Analysis

  The associations of birth weight to maternal smoking and length of gestation were assessed using multiple linear regression (MLR). MLR was used to estimate the strength of the relationship between birth weight and smoking during pregnancy after taking into account the length of gestation. Additionally, the model was used to assess the strength of the association of birth weight to length of gestation after taking into account the mother’s smoking status. The prediction model was evaluated with a statistical threshold set at .05. The analysis was performed in R. It was hypothesized that:

\[H_0: \beta_1= \beta_2 = 0\] \[ H_{alt}: \mbox{at least one } \beta_i \neq 0, i=1,2 \]

\[ \hat{\mu}_{y|x1,x2} = (\beta_0 + \beta_{1}x_1 + \beta_{2}x_2 + \epsilon_i)\] The equation used for the prediction model is shown above, where \(\hat{\mu}_{y|x1,x2}\) is the mean birth weight given the gestation length and maternal smoking status. \(\beta_0\) represents the intercept. \(\beta_1\) is the coefficient for gestation length (\(x_1\)). \(\beta_2\) is the coefficient for the binary coded variable for smoking status (\(x_2\)), where smoking = 1 (YES) or 0 (NO). \(\epsilon_i\) represents the independent error term.

3.1 Descriptive Statistics.

  The summary table of the data shows quantiles, minimum, maximum, mean and medium for the two quantitative variables, birth weight (grams) and gestation length (weeks). The summary table shows category counts for smoking status. The summary specified no empty data cells.
weight gestation smoking_status
Min. :2420 Min. :34.00 no :16
1st Qu.:2737 1st Qu.:37.00 yes:16
Median :3068 Median :39.00 NA
Mean :3020 Mean :38.66 NA
3rd Qu.:3306 3rd Qu.:40.25 NA
Max. :3530 Max. :42.00 NA

3.1.1 Boxplots.

  Boxplots for quantitative variables weight and gestation showed no outliers.

3.1.2 Scatter Plot.

  A scatter plot of the data with birth weight in grams on the y-axis and gestation in weeks on the x-axis, grouped by smoking status showed no significant outliers or high leverage observations.

3.1.3 Scatter Plot Matrix.

  The scatter plot matrix showed a strong positive relationship for birth weight and gestation length. The relationship for smoking and birth weight was less easily discerned from the plot, as was the relationship between smoking and gestation length.

3.2 MLR Best Fit Line.

  The resulting fitted regression equation is shown below for mean birth weight in grams, gestation length in grams, and smoking status codes as smoking = 1 (YES) or 0 (NO).

\[\hat{y}_{bw|gest,smoke} = -2389.57 + (143.10*{Gestation Length}) - (244.54*{SmokingStatus})\] There was no significant interaction between gestation length and smoking status. Gestation length and smoking status acted independently on the mean birth weight.

3.2.1 MLR Model Assumptions.

  The residuals plots supported the assumption that a linear model was reasonable. They also showed that there were no significant outliers. The QQ plot was approximately linear, supporting the assumption that error terms were normally distributed.

4 Results

The analysis of variance showed that the multiple regression model was useful for prediction of birth weight, with \(R^2 = .8964\), \(F(2,29)=125.4, p<.001\). Both predictor variables (gestation length and smoking status) showed significant associations with the response variable (birth weight). Both predictor variables made significant contribution to the predictive model. There was a significant negative association between smoking and birth weight, accounting for gestation length \((\beta=-244.54, t=5.83, p<.001)\). The results also showed a significant positive association between gestation length and birth weight, accounting for smoking status, \((\beta=143.10, t=15.68, p<.001)\).

## 
## Call:
## lm(formula = weight ~ gestation + smoke)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -223.693  -92.063   -9.365   79.663  197.507 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2389.573    349.206  -6.843 1.63e-07 ***
## gestation     143.100      9.128  15.677 1.07e-15 ***
## smoke        -244.544     41.982  -5.825 2.58e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 115.5 on 29 degrees of freedom
## Multiple R-squared:  0.8964, Adjusted R-squared:  0.8892 
## F-statistic: 125.4 on 2 and 29 DF,  p-value: 5.289e-15
##                  2.5 %     97.5 %
## (Intercept) -3103.7795 -1675.3663
## gestation     124.4312   161.7694
## smoke        -330.4064  -158.6817

5 Discussion

The results showed that the model containing length of gestation and smoking status was useful in predicting mean birth weight, \(F(2,29)=125.4, p<.001\). The model showed that 89.6% of the variance in mean birth weight was accounted for using two predictors, gestation length and smoking status.

There was a significant negative association between smoking and birth weight \((\beta=-244.54, t=5.825, p<.001)\). The model showed a significant difference in mean birth weight between smokers and non-smokers when gestation length was held constant. With 95% confidence, we expect the mean birth weight of babies born to smoking mothers to be between 158.70 and 330.41 grams less than those born to non-smoking mothers, when gestation length is held constant.

The results showed a significant positive association between gestation length and birth weight, accounting for smoking status \((\beta=143.10, t=15.68, p<.001)\). With 95% confidence, we expect the mean birth weight to increase by between 124.43 and 161.77 grams for each additional week of gestation, when smoking status is held constant.

6 Conclusions

The addictive nature of cigarettes makes quitting extremely difficult. With a simple model to quantify the reduction in birth weight, while holding gestation length constant, mothers may recognize the significance of quitting. With 95% confidence, we expect the difference in mean birth weight for smoking mothers to be between 158.70 (5.60 ounces) and 330.41 grams (11.65 ounces) less than the mean birth weight for babies of non-smoking mothers. Knowledge may help motivate mothers as they work through nicotine addiction.

Data Source: From Penn State University.

02/2021