1.69 Side effects of Avandia. Rosiglitazone is the active ingredient in the controversial type 2 diabetes medicine Avandia and has been linked to an increased risk of serious cardiovascular prob- lems such as stroke, heart failure, and death. A common alternative treatment is pioglitazone, the active ingredient in a diabetes medicine called Actos. In a nationwide retrospective observational study of 227,571 Medicare beneficiaries aged 65 years or older, it was found that 2,593 of the 67,593 patients using rosiglitazone and 5,386 of the 159,978 using pioglitazone had serious cardiovascular problems. These data are summarized in the contingency table below.

TxEffects <- data.frame("Treatment" = c("Rosiglitazone", "Pioglitazone", "Total"), "CardioProbs" = c(2593, 5386, 7979), "NoCardioProbs" = c(65000, 154592, 219592), "Total" = c(67593, 159978, 227571))
TxEffects
##       Treatment CardioProbs NoCardioProbs  Total
## 1 Rosiglitazone        2593         65000  67593
## 2  Pioglitazone        5386        154592 159978
## 3         Total        7979        219592 227571
  1. Determine if each of the following statements is true or false. If false, explain why. Be careful: The reasoning may be wrong even if the statement’s conclusion is correct. In such cases, the statement should be considered false.
  1. Since more patients on pioglitazone had cardiovascular problems (5,386 vs. 2,593), we can conclude that the rate of cardiovascular problems for those on a pioglitazone treatment is higher.

False: We must look at the denominator for cardio problems on each medication. There were far more people on Pioglitazone.

  1. The data suggest that diabetic patients who are taking rosiglitazone are more likely to have cardiovascular problems since the rate of incidence was (2,593 / 67,593 = 0.038) 3.8% for patients on this treatment, while it was only (5,386 / 159,978 = 0.034) 3.4% for patients on pioglitazone.

True

  1. The fact that the rate of incidence is higher for the rosiglitazone group proves that rosiglitazone causes serious cardiovascular problems.

False: It would be unwise to draw causal conclusions about a retrospective study. A randomized experiment is needed.

  1. Based on the information provided so far, we cannot tell if the difference between the rates of incidences is due to a relationship between the two variables or due to chance.

True

  1. What proportion of all patients had cardiovascular problems?
TxEffects[3,2]/TxEffects[3,4]
## [1] 0.03506159

0.035 Is the proportion of patients that had cardiovascular problems.

  1. If the type of treatment and having cardiovascular problems were independent, about how many patients in the rosiglitazone group would we expect to have had cardiovascular problems? If cardiovascular risk were independent from treatment, we could calculate it by using the overall cardiovascular rate for the entire sample: 2370
67593 * (7979/227571)
## [1] 2369.918
  1. We can investigate the relationship between outcome and treatment in this study using a randomization technique. While in reality we would carry out the simulations required for randomization using statistical software, suppose we actually simulate using index cards. In order to simulate from the independence model, which states that the outcomes were independent of the treatment, we write whether or not each patient had a cardiovascular problem on cards, shuffled all the cards together, then deal them into two groups of size 67,593 and 159,978. We repeat this simulation 1,000 times and each time record the number of people in the rosiglitazone group who had cardiovascular problems. Use the relative frequency histogram of these counts to answer (i)-(iii).

  1. What are the claims being tested? The claim being tested is if Rosiglitazone’s cardiovascular problems in the given data is due to chance.

  2. Compared to the number calculated in part (b), which would provide more support for the alternative hypothesis, more or fewer patients with cardiovascular problems in the rosiglitazone group? More patients with cardiovascular problems than chance would suggest that rosiglitazone increases the risk of such problems.

  3. What do the simulation results suggest about the relationship between taking rosiglitazone and having cardiovascular problems in diabetic patients? That rosiglitazone leads to more cardiovascular problems than chance in diabetic patients.