R Notebook

Analysis of “birthwt” dataset

This birthwt dataset contains 10 variables. The data were collected at the Baystate Medical Center, Springfield, Mass during the year of 1986. The data contains risk factors associated with low infant birth weight. I will look at birth weight and which indicators in particular how a mothers actions and health during pregnancy affects the birth weight of a baby.

Four variables were selected from the data set to conduct this analysis. The dependent variable, “low” is an indicator of birth weight less than 2.5 kg (5 lbs 8 ounces) in which “1” an unhealthy birth weight less than 2.5 kg and “0” represented a healthy birth weight above 2.5 kg. The independent variables used in this study are “smoke”, “race” and “ht”. Smoke measured whether the mother smoked during pregnancy, race was recoded for “1” to represent white and “0” to represent all other variables and “ht” measures whether the mother had a history of hypertension or not.

library(tidyverse)
library(magrittr)
library(dplyr)
library(Zelig)
library(pander)
library(texreg)
library(visreg)
library(lmtest)
library(visreg)
library(sjmisc)
library(MASS)

data("birthwt")
head(birthwt)

summary(birthwt)

      low              age             lwt             race           smoke             ptl        
 Min.   :0.0000   Min.   :14.00   Min.   : 80.0   Min.   :1.000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:19.00   1st Qu.:110.0   1st Qu.:1.000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.0000   Median :23.00   Median :121.0   Median :1.000   Median :0.0000   Median :0.0000  
 Mean   :0.3122   Mean   :23.24   Mean   :129.8   Mean   :1.847   Mean   :0.3915   Mean   :0.1958  
 3rd Qu.:1.0000   3rd Qu.:26.00   3rd Qu.:140.0   3rd Qu.:3.000   3rd Qu.:1.0000   3rd Qu.:0.0000  
 Max.   :1.0000   Max.   :45.00   Max.   :250.0   Max.   :3.000   Max.   :1.0000   Max.   :3.0000  
       ht                ui              ftv              bwt      
 Min.   :0.00000   Min.   :0.0000   Min.   :0.0000   Min.   : 709  
 1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:2414  
 Median :0.00000   Median :0.0000   Median :0.0000   Median :2977  
 Mean   :0.06349   Mean   :0.1481   Mean   :0.7937   Mean   :2945  
 3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:3487  
 Max.   :1.00000   Max.   :1.0000   Max.   :6.0000   Max.   :4990  

dim(birthwt)

[1] 189  10

birthwt2 <- birthwt%>%
  rename(hypertension = ht)%>%
  mutate(race = ifelse(race == 1, "white", "non-white"))
head(birthwt2)

Logistic Regression Models

In this first model i looked at whether a child is born with a below normal birthweight is affected by race. Looking at the results from this first model we can see that being white had a negative affect on whether a child is born below normal birth weight (-0.6954) as opposed to other races. Depending on race one may get better care than other races because of income, health, etc. Based on the p value we can see the results are statistically significant.

m0 <- glm(low ~ race, family = binomial, data = birthwt2)
summary(m0)

Call:
glm(formula = low ~ race, family = binomial, data = birthwt2)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.9895  -0.9895  -0.7401   1.3777   1.6905  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)  
(Intercept)  -0.4595     0.2129  -2.159   0.0309 *
racewhite    -0.6954     0.3202  -2.172   0.0298 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 234.67  on 188  degrees of freedom
Residual deviance: 229.86  on 187  degrees of freedom
AIC: 233.86

Number of Fisher Scoring iterations: 4

Model 2

In this second model i added the variable smoke which indicated whether the mother smoked during pregnancy or not. In this model we can see that mothers who smoked during pregnancy had a higher chance (1.1130) of giving birth to a baby that would be below normal birth weight of 2.5 kg. This relationship is significant at a .01 confidence level.

m1 <- glm(low ~ race + smoke, family = binomial, data = birthwt2)
summary(m1)

Call:
glm(formula = low ~ race + smoke, family = binomial, data = birthwt2)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.3402  -0.8840  -0.5433   1.4968   1.9930  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)   
(Intercept)  -0.7382     0.2379  -3.103  0.00191 **
racewhite    -1.1003     0.3645  -3.019  0.00254 **
smoke         1.1130     0.3643   3.056  0.00225 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 234.67  on 188  degrees of freedom
Residual deviance: 219.98  on 186  degrees of freedom
AIC: 225.98

Number of Fisher Scoring iterations: 4

Model 3

In this third model we added another variable called hypertension which recorded whether the mother had a history of high blood pressure. Having a history of smoking and high blood pressure can add to the chances of a child birth weight being below normal. In this model we see that hypertension does increase the likelihood that a childs birth weight will be below 2.5 kg (1.1725). However, this indicator is not statistically significant with a p-value of >.05.

m2 <- glm(low ~ race + smoke + hypertension, family = binomial, data = birthwt2)
summary(m2)

Call:
glm(formula = low ~ race + smoke + hypertension, family = binomial, 
    data = birthwt2)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.3371  -0.8496  -0.5222   1.0587   2.0297  

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)   -0.8331     0.2460  -3.386 0.000708 ***
racewhite     -1.0904     0.3686  -2.958 0.003095 ** 
smoke          1.1190     0.3681   3.040 0.002367 ** 
hypertension   1.1725     0.6225   1.883 0.059633 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 234.67  on 188  degrees of freedom
Residual deviance: 216.38  on 185  degrees of freedom
AIC: 224.38

Number of Fisher Scoring iterations: 4

Model 4

In this final model we examine race and the interaction between smoking and hypertension to analyze the impact it has on the likelihood a child being born below normal child birth of 2.5 kg. The model shows that people of white race are still more likely to have a child that is of normal birth weight or higher also that smoking negatively affect that but there is no relationship between hypertension and having a child of lower birth weight.

m3 <- glm(low ~ race + smoke * hypertension, family = binomial, data = birthwt2)
summary(m3)

Call:
glm(formula = low ~ race + smoke * hypertension, family = binomial, 
    data = birthwt2)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.3706  -0.8456  -0.5213   1.0561   2.0314  

Coefficients:
                   Estimate Std. Error z value Pr(>|z|)    
(Intercept)         -0.8446     0.2518  -3.354 0.000797 ***
racewhite           -1.0828     0.3700  -2.926 0.003431 ** 
smoke                1.1367     0.3766   3.018 0.002544 ** 
hypertension         1.2881     0.8128   1.585 0.113016    
smoke:hypertension  -0.2821     1.2652  -0.223 0.823550    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 234.67  on 188  degrees of freedom
Residual deviance: 216.33  on 184  degrees of freedom
AIC: 226.33

Number of Fisher Scoring iterations: 4

Likelihood Ratio Test

The likelihood ratio test illustrates that Model 4 is the best fit because it has the smallest deviance. Lower deviance in Model 4 means that it is a better fit for the data.

anova(m0, m1, m2, m3, test = "Chisq")

Analysis of Deviance Table

Model 1: low ~ race
Model 2: low ~ race + smoke
Model 3: low ~ race + smoke + hypertension
Model 4: low ~ race + smoke * hypertension
  Resid. Df Resid. Dev Df Deviance Pr(>Chi)   
1       187     229.86                        
2       186     219.98  1   9.8802 0.001671 **
3       185     216.38  1   3.5949 0.057956 . 
4       184     216.33  1   0.0495 0.823892   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Comparing models

From this test we see that model 2 is the best fit because it contained the lowest AIC(225.98) and lowest BIC(235.70) this may be due to the fact that we found hypertension was not a serious indicator of whether a child was born with a normal birth weight above 2.5 kg.

screenreg(list(m0, m1, m2, m3))

===================================================================
                    Model 1    Model 2     Model 3      Model 4    
-------------------------------------------------------------------
(Intercept)           -0.46 *    -0.74 **    -0.83 ***    -0.84 ***
                      (0.21)     (0.24)      (0.25)       (0.25)   
racewhite             -0.70 *    -1.10 **    -1.09 **     -1.08 ** 
                      (0.32)     (0.36)      (0.37)       (0.37)   
smoke                             1.11 **     1.12 **      1.14 ** 
                                 (0.36)      (0.37)       (0.38)   
hypertension                                  1.17         1.29    
                                             (0.62)       (0.81)   
smoke:hypertension                                        -0.28    
                                                          (1.27)   
-------------------------------------------------------------------
AIC                  233.86     225.98      224.38       226.33    
BIC                  240.34     235.70      237.35       242.54    
Log Likelihood      -114.93    -109.99     -108.19      -108.17    
Deviance             229.86     219.98      216.38       216.33    
Num. obs.            189        189         189          189       
===================================================================
*** p < 0.001, ** p < 0.01, * p < 0.05

graphs using visreg package

Likelihood of child being born below normal birth weight by race. The graph shows us that whites have a lower chance of their child being born with low normal birth weight than non-whites.

library(visreg)
visreg(m1, "race", scale = "response")

Likelihood of child being born with below normal birth weight by whether mother smoked during pregnancy

The graphs clearly shows the relationship by which if mothers who responded yes to smoking during pregnancy had a higher chance of being born with a child that was below normal birth weight.

library(visreg)
visreg(m1, "smoke", scale = "response")