Strep throat is a common virus. To detect whether someone has this virus, doctors administer a swab test. Even though the swab test helps doctors make a diagnoses, it does, at times, give the wrong results. Specifically, the test could come back negative when in fact a patient has strep (false negative) or the test could come back positive when in fact a patient does not have strep (false positive). As a doctor, it is important to understand the chances of these false positives and false negatives occurring so that risks could be communicated accurately with patients. A doctor asks: What is the probability of not having the virus given that you get a positive test result?

*Must do this problem through simulation in R (or other software) AND after you have simulated, you must compute the probability theoretically. Check that answers “match.” Minimum of 10,000 runs for the simulation. Open up a new RMarkdown file. Complete the activity. Make sure you are using complete sentences, different sections for different parts of the problem, etc.

P(having strep) = .15 P(has no strep) = .85 P(false negative) = .10 P(false positive) = .01 P(true positive∣has strep) = 1−0.10 =0.90

xdata = c()
for (i in 1:10000)
{
  strep <- rbinom(1,1,.15)
  # false_negative <- rbinom(1,1,.10)
  # false_positive <- rbinom(1,1,0.01)
  #the .15 chance strep is given
  if (strep == 1)
  {
    test <- rbinom(1, 1, .90)
    #we test the prob. of .9 
    if (test == 1)
    {
      xdata = c(xdata, "true_positive")
    }
    # fails the .9 test 
    if (test == 0)
    {
      xdata = c(xdata, "false_negative")
    }
  }
#strep is not given
  if (strep == 0)
  {
    #test for false positive .01 prob.
    test <- rbinom(1, 1, .01)
    #is false positive
    if (test == 1)
    {
      xdata = c(xdata, "false_positive")
    }
    # does not have strep and tests negative
    if (test == 0)
    {
      xdata = c(xdata, "true_negative")
    }
  }
}

xdata[1:10]
##  [1] "true_negative" "true_negative" "true_negative" "true_negative"
##  [5] "true_negative" "true_negative" "true_negative" "true_positive"
##  [9] "true_negative" "true_negative"
falsePositives <- length(which(xdata == "false_positive"))
truePositives <- length(which(xdata == "true_positive"))

falsePositives / (falsePositives + truePositives)
## [1] 0.06058543

The chances of not having Strep and not have the test be positive, it will be around a 5.88% chance.

##The theoretical calculation would be: P(no strep and positive)=(0.85)(0.01)=0.0085 P(strep and positive)=(0.15)(0.90)=0.135

P(no strep∣positive)<- 0.0085/(0.0085+ 0.135)

 no_strep_positive <- (0.0085/(0.0085+ 0.135))
print(no_strep_positive)
## [1] 0.05923345

The theoretical probability of not having strep and it showing up as positive will would be around 5.92%. We have 5.88% based on simulation and 5.92% based off of theoretical probability.Both are fairly close and off by a margin of less than 0.1%, we cam assume both will “match” ifwe were to add more trials in our simulation.