case1801: Obesity and Heart Disease

In Sleuth3: Data Sets from Ramsey and Schafer's "Statistical Sleuth (3rd Ed)"

Description

To better understand whether the relationship between heart disease and obesity could be due to the social stigma associated with obesity, researchers examined cardiovascular disease rates of obese and non-obese women in American Samoa, where obesity was considered socially desirable. 3,112 women were categorized according to whether they were obese or not and whether they died from cardiovascular disease (CVD).

Usage

case1801

Format

A data frame with 2 observations on the following 3 variables.

Obesity

a factor with levels "NotObese" and "obese"

Deaths

the number of women who died from CVD

NonDeaths

the number that died from other causes

Source

Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cenage Learning.

References

Crews, D.E. (1988). Cardiovascular Mortality in American Samoa, Human Biology 60: 417–433.

Examples

str(case1801)
attach(case1801)
   
## EXPLORATION
myTable             <- cbind(Deaths,NonDeaths)  # Form a 2 by 2 table of counts
row.names(myTable)  <- Obesity  # Assign the levels of Obesity as row names  
myTable   # Show the table

## INFERENCE (4 methods for getting p-values and confidence intervals)
prop.test(myTable, alternative="greater", correct=FALSE) # Compare 2 proportions
prop.test(myTable, alternative="greater", correct=TRUE) # ...with cont. corect.  
prop.test(myTable,correct=TRUE) # 2-sided alternative (default) to get CI
chisq.test(myTable) # Pearson's Chi-Squared Test
fisher.test(myTable, alternative="greater") # Fisher's exact test  
fisher.test(myTable) # 2-sided alternative to get CI for odds ratio
myGlm1  <- glm(myTable ~ Obesity, family=binomial)  # Logistic reg (CH 21)
summary(myGlm1)  # Get p-value-- 0.734
beta    <- myGlm1$coef
exp(beta[2])  #Odds of death are estimated to be 17% higher for  obese women 
exp(confint(myGlm1,2)) # 95% confidence interval  


## GRAPHICAL DISPLAY FOR PRESENTATION
myTable
#        Deaths NonDeaths
#Obese        16      2045
#NotObese      7      1044
prop.test(16,(16+2045)) #For one proportion, est: 0.0078 95% CI: 0.0046 to 0.013
prop.test(7,(7+1044)) #For one proportion, est: 0067 95% CI: 0.0029 to 0.014
pHat    <- c(0.007763222, 0.006660324)*1000 # Get estimated deaths per 1,000 women
lower95 <- c(0.00459943, 0.002921568)*1000
upper95 <- c(0.01287243, 0.014318321)*1000

if(require(Hmisc)) { # Use Hmisc library 
  myObj   <- Cbind(pHat,lower95,upper95) 
  Dotplot(Obesity ~ myObj,   # Draw a dot plot of estimates and CIs
    xlab="Estimated CVD Deaths Per 1,000 Women (and 95% Confidence Intervals)",
    ylab="Weight Category", ylim=c(.5,2.5), cex=2)
}


detach(case1801)

Example output

'data.frame':	2 obs. of  3 variables:
 $ Obesity  : Factor w/ 2 levels "NotObese","Obese": 2 1
 $ Deaths   : int  16 7
 $ NonDeaths: int  2045 1044
         Deaths NonDeaths
Obese        16      2045
NotObese      7      1044

	2-sample test for equality of proportions without continuity
	correction

data:  myTable
X-squared = 0.11541, df = 1, p-value = 0.367
alternative hypothesis: greater
95 percent confidence interval:
 -0.004107007  1.000000000
sample estimates:
     prop 1      prop 2 
0.007763222 0.006660324 


	2-sample test for equality of proportions with continuity correction

data:  myTable
X-squared = 0.014031, df = 1, p-value = 0.4529
alternative hypothesis: greater
95 percent confidence interval:
 -0.004825345  1.000000000
sample estimates:
     prop 1      prop 2 
0.007763222 0.006660324 


	2-sample test for equality of proportions with continuity correction

data:  myTable
X-squared = 0.014031, df = 1, p-value = 0.9057
alternative hypothesis: two.sided
95 percent confidence interval:
 -0.005823425  0.008029221
sample estimates:
     prop 1      prop 2 
0.007763222 0.006660324 


	Pearson's Chi-squared test with Yates' continuity correction

data:  myTable
X-squared = 0.014031, df = 1, p-value = 0.9057


	Fisher's Exact Test for Count Data

data:  myTable
p-value = 0.4625
alternative hypothesis: true odds ratio is greater than 1
95 percent confidence interval:
 0.5161345       Inf
sample estimates:
odds ratio 
  1.166817 


	Fisher's Exact Test for Count Data

data:  myTable
p-value = 0.8277
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
 0.4524487 3.3646287
sample estimates:
odds ratio 
  1.166817 


Call:
glm(formula = myTable ~ Obesity, family = binomial)

Deviance Residuals: 
[1]  0  0

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)   -5.0049     0.3792 -13.198   <2e-16 ***
ObesityObese   0.1543     0.4548   0.339    0.734    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 1.1741e-01  on 1  degrees of freedom
Residual deviance: 9.8299e-13  on 0  degrees of freedom
AIC: 12.414

Number of Fisher Scoring iterations: 3

ObesityObese 
    1.166888 
Waiting for profiling to be done...
    2.5 %    97.5 % 
0.4964985 3.0439343 
         Deaths NonDeaths
Obese        16      2045
NotObese      7      1044

	1-sample proportions test with continuity correction

data:  16 out of (16 + 2045), null probability 0.5
X-squared = 1995.5, df = 1, p-value < 2.2e-16
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
 0.00459943 0.01287243
sample estimates:
          p 
0.007763222 


	1-sample proportions test with continuity correction

data:  7 out of (7 + 1044), null probability 0.5
X-squared = 1021.2, df = 1, p-value < 2.2e-16
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
 0.002921568 0.014318321
sample estimates:
          p 
0.006660324 

Loading required package: Hmisc
Loading required package: lattice
Loading required package: survival
Loading required package: Formula
Loading required package: ggplot2

Attaching package: ‘Hmisc’

The following objects are masked from ‘package:base’:

    format.pval, units

Sleuth3 documentation built on May 2, 2019, 6:41 a.m.