STA442/1008 Assignment 9

Quiz on Friday Nov. 13th in Tutorial (Bring a calculator.)

1. A psychiatric consulting firm was hired by the Ontario Department of Corrections. Their task was to conduct in-depth interviews, and predict whether convicted felons released on parole would be arrested again within 12 months. The table below shows predicted re-arrest by observed re-arrest for a sample of 250 prisoners.

                                     Observed
                       Predicted    No     Yes
                            No      82      91
                           Yes      37      40
   

   1. What is the sensitivity of psychiatric prediction? Your answer is a single number. You may use a calculator.
   2. What is the specificity of psychiatric prediction? Your answer is a single number. You may use a calculator.
   3. What is the false positive rate? Your answer is a single number. You may use a calculator.
   4. What is the false negative rate? Your answer is a single number. You may use a calculator.
   5. Are the psychiatrists doing significantly better than chance? Use SAS to carry out the analysis. Give the Pearson chi-square and p-value. Do the shrinks want to feature your findings on their website? Answer Yes or No. For guidance on how to get the data into SAS, see the Berkeley example in Chapter Four. If you want to check your SAS work, I get a Phi Coefficient of -0.0060.
2. This question is based upon the Heart data again. Please start by creating a new variable with 3 categories:
   • Died from first heart attack (Sudden Death or Fatal Myocardial Infraction)
   • Died in next 10 years
   • Alive 10 years later
   This new 3-category variable will be your dependent variable. For interpretability, make the probability of being alive 10 years later the denominator in each generalized logit.
   1. To check, make tables of the new dependent variable by "First coronary heart disease event" and "Alive 10 years after entering study." Suppress all the percentages and include the missing values.
   2. Carry out a test of Number of cigarettes and Family history of CHD (considered simultaneously -- one test) controlling for Age and Blood pressure. Be able to state the value of the test statistic and the p-value (numbers from the printout), as well as whether the results are statistically significant, whether you reject the null hypothesis, and what (if anything) you'd conclude. For the conclusion, use plain, non-statistical language. I get b_0,2 = -14.2147.
   3. Why does it make sense that both regression coefficients for age are positive?
   4. Now fit a model with just Age and Blood pressure. For a 50 year old with a diastolic blood pressure of 100, estimate the probability of
      • Dying from a first heart attack.
      • Dying in the following 10 years.
      • Being alive 10 years later.
      Use proc iml. Should your probabilities add to one? For a 5 year old with disastolic blood pressure equal to 400, I get the follwing estimated probability of being alive 10 years later: 0.0057949.
   5. Be able to interpret all the parameter estimates and Wald chisquare tests (except those for the intercepts) under "Analysis of Maximum Likelihood Estimates" and "Maximum Likelihood Analysis of Variance."

Please bring your log file and your list file to the quiz. Bring a calculator.