Exercise 2: Recreate Table 2.28 using any combination of the matrix, cbind, rbind, dimnames, or names functions

TABLE 2.28: Risk of Death in a 20-year Period Among Women in Whick- ham, England, According to Smoking Status at the Beginning of the Period

(Rothman, 2012)

England <- matrix(c(139, 443,230, 502), 2, 2,dimnames = list(VitalStatus = c('Dead', 'Alive'), 
Smoking=c('Yes', 'No')))
England

##            Smoking
## VitalStatus Yes  No
##       Dead  139 230
##       Alive 443 502

Exercise 3: Starting with the 2x2 matrix object we created in Table 2.28, using any combination of apply, cbind, rbind, names, and dimnames functions, recreate the Table 2.29

England2 <- cbind(England, Total = rowSums(England)) 
rbind(England2, Total = colSums(England2))

##       Yes  No Total
## Dead  139 230   369
## Alive 443 502   945
## Total 582 732  1314

Exercise 4: Using the 2 × 2 data from Table 2.28, use the sweep and apply functions to calculate row marginal, column marginal, and joint distributions (i.e., three tables)

 rtot <- apply(England, 1, sum) # row totals 
England.rowdist <- sweep(England, 1, rtot, '/');
England.rowdist

##            Smoking
## VitalStatus       Yes        No
##       Dead  0.3766938 0.6233062
##       Alive 0.4687831 0.5312169

ctot <- apply(England, 2, sum) # column totals 
ctot

## Yes  No 
## 582 732

England.coldist <- sweep(England, 2, ctot, '/')
England.coldist

##            Smoking
## VitalStatus       Yes        No
##       Dead  0.2388316 0.3142077
##       Alive 0.7611684 0.6857923

Row Marginal Distribution

rowdist<-sweep(England, 1, apply(England, 1, sum), '/')
rowdist #row distribution

##            Smoking
## VitalStatus       Yes        No
##       Dead  0.3766938 0.6233062
##       Alive 0.4687831 0.5312169

column marginal Distribution

coldist<- sweep(England, 2, apply(England, 2, sum), '/')
coldist #column distribution

##            Smoking
## VitalStatus       Yes        No
##       Dead  0.2388316 0.3142077
##       Alive 0.7611684 0.6857923

joint distributions

joindist <- England/sum(England)
joindist                 # joint distrib

##            Smoking
## VitalStatus       Yes        No
##       Dead  0.1057839 0.1750381
##       Alive 0.3371385 0.3820396

pEnglands<-list(row.distribution=rowdist, column.distribution=coldist, joint.distribution=joindist)
pEnglands

## $row.distribution
##            Smoking
## VitalStatus       Yes        No
##       Dead  0.3766938 0.6233062
##       Alive 0.4687831 0.5312169
## 
## $column.distribution
##            Smoking
## VitalStatus       Yes        No
##       Dead  0.2388316 0.3142077
##       Alive 0.7611684 0.6857923
## 
## $joint.distribution
##            Smoking
## VitalStatus       Yes        No
##       Dead  0.1057839 0.1750381
##       Alive 0.3371385 0.3820396

Exercise 5:Using the data from the previous problems, recreate Table 2.30 and interpret the results

risks <- England['Dead', ]/ctot
risk.ratio <- risks/risks[2] 
odds <- risks/(1 - risks) 
odds.ratio <- odds/odds[2] 
England

##            Smoking
## VitalStatus Yes  No
##       Dead  139 230
##       Alive 443 502

#risk ratio
#odds ratio
# display results

rbind(risks, risk.ratio, odds, odds.ratio)

##                  Yes        No
## risks      0.2388316 0.3142077
## risk.ratio 0.7601076 1.0000000
## odds       0.3137698 0.4581673
## odds.ratio 0.6848366 1.0000000

Interpretation: According to the output, the risk and odd of death among non-smokers is higher than the risk and odd of death among smokers, suggesting smoking may be protective.

Exercise 6: Install the mosaicData R package. Load the Whickham data set. Using the xtabs function create two-way and three-way contingency tables. Calculate “measures of associations.” What is your interpre- tation?

library(mosaicData)
data("Whickham")
y<-xtabs(~outcome + smoker, data =Whickham)
y

##        smoker
## outcome  No Yes
##   Alive 502 443
##   Dead  230 139

w <- xtabs(~outcome + age + smoker, data = Whickham) 
wtot <- apply(w, c(2, 3), sum)
wrisk<-sweep(w,c(2,3), wtot, "/")
wrisk2<-round(wrisk, 2)
wrisk2

## , , smoker = No
## 
##        age
## outcome   18   19   20   21   22   23   24   25   26   27   28   29   30
##   Alive 0.91 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.95 1.00 0.89 1.00
##   Dead  0.09 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.05 0.00 0.11 0.00
##        age
## outcome   31   32   33   34   35   36   37   38   39   40   41   42   43
##   Alive 1.00 0.94 0.94 1.00 0.87 0.86 1.00 0.92 1.00 1.00 1.00 0.88 0.80
##   Dead  0.00 0.06 0.06 0.00 0.13 0.14 0.00 0.08 0.00 0.00 0.00 0.12 0.20
##        age
## outcome   44   45   46   47   48   49   50   51   52   53   54   55   56
##   Alive 1.00 0.80 0.67 0.86 1.00 0.60 0.80 0.85 0.89 1.00 0.80 0.71 0.56
##   Dead  0.00 0.20 0.33 0.14 0.00 0.40 0.20 0.15 0.11 0.00 0.20 0.29 0.44
##        age
## outcome   57   58   59   60   61   62   63   64   65   66   67   68   69
##   Alive 0.71 0.83 0.56 0.50 0.69 0.60 0.78 0.71 0.23 0.46 0.40 0.11 0.00
##   Dead  0.29 0.17 0.44 0.50 0.31 0.40 0.22 0.29 0.77 0.54 0.60 0.89 1.00
##        age
## outcome   70   71   72   73   74   75   76   77   78   79   80   81   82
##   Alive 0.14 0.13 0.12 0.09 0.42 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
##   Dead  0.86 0.87 0.88 0.91 0.58 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
##        age
## outcome   83   84
##   Alive 0.00 0.00
##   Dead  1.00 1.00
## 
## , , smoker = Yes
## 
##        age
## outcome   18   19   20   21   22   23   24   25   26   27   28   29   30
##   Alive 1.00 1.00 0.88 0.88 1.00 1.00 1.00 1.00 1.00 0.88 1.00 1.00 1.00
##   Dead  0.00 0.00 0.12 0.12 0.00 0.00 0.00 0.00 0.00 0.12 0.00 0.00 0.00
##        age
## outcome   31   32   33   34   35   36   37   38   39   40   41   42   43
##   Alive 0.93 1.00 0.94 1.00 1.00 0.94 1.00 0.90 0.90 0.60 1.00 0.82 0.82
##   Dead  0.07 0.00 0.06 0.00 0.00 0.06 0.00 0.10 0.10 0.40 0.00 0.18 0.18
##        age
## outcome   44   45   46   47   48   49   50   51   52   53   54   55   56
##   Alive 0.91 0.64 0.80 0.86 0.82 0.80 0.87 0.73 0.77 0.67 1.00 0.67 0.50
##   Dead  0.09 0.36 0.20 0.14 0.18 0.20 0.13 0.27 0.23 0.33 0.00 0.33 0.50
##        age
## outcome   57   58   59   60   61   62   63   64   65   66   67   68   69
##   Alive 0.58 0.73 0.44 0.27 0.46 0.75 0.56 0.70 0.00 0.17 0.67 0.00 0.00
##   Dead  0.42 0.27 0.56 0.73 0.54 0.25 0.44 0.30 1.00 0.83 0.33 1.00 1.00
##        age
## outcome   70   71   72   73   74   75   76   77   78 79   80   81   82
##   Alive 0.00 0.12 0.00 0.00 0.67 0.00 0.00 0.00 0.00    0.00 0.00 0.00
##   Dead  1.00 0.88 1.00 1.00 0.33 1.00 1.00 1.00 1.00    1.00 1.00 1.00
##        age
## outcome   83   84
##   Alive 0.00 0.00
##   Dead  1.00 1.00

Homework 2

Auwal

9/15/2019

Exercise 2: Recreate Table 2.28 using any combination of the matrix, cbind, rbind, dimnames, or names functions

TABLE 2.28: Risk of Death in a 20-year Period Among Women in Whick- ham, England, According to Smoking Status at the Beginning of the Period

Exercise 3: Starting with the 2x2 matrix object we created in Table 2.28, using any combination of apply, cbind, rbind, names, and dimnames functions, recreate the Table 2.29

Exercise 4: Using the 2 × 2 data from Table 2.28, use the sweep and apply functions to calculate row marginal, column marginal, and joint distributions (i.e., three tables)

Row Marginal Distribution

column marginal Distribution

joint distributions

Exercise 5:Using the data from the previous problems, recreate Table 2.30 and interpret the results

Interpretation: According to the output, the risk and odd of death among non-smokers is higher than the risk and odd of death among smokers, suggesting smoking may be protective.

Exercise 6: Install the mosaicData R package. Load the Whickham data set. Using the xtabs function create two-way and three-way contingency tables. Calculate “measures of associations.” What is your interpre- tation?

Risk of death increases with age among both smokers and Non-smokers