1. Suppose on the basis of one dataset we obtained the following model

,

where Y is a binary outcome (CHD69), X₁ is a binary variable of interest (arcus) and X₂ is a binary variable (age group 35-49 vs 50-60).

Calculate odds ratios (which group you would select as a reference?) and give their interpretations. Find predictive probabilities for all possible outcomes and build all possible diagnostic tools based on different cutoff points. Estimate sensitivities and specificities of these diagnostics on the dataset given below. Plot these diagnostic properties in ROC space (it will not be a curve b/c you have only several possible diagnostic tools).

2. Assume that age (X₂) is a continuous variable (unit = 10 years) and the following model was obtained

Calculate predictive probabilities for the first 20 outcomes in the table. Plot ROC curve (select cutoff points yourself).

+---------------------------+

chd69 arcus bage_50

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1. yes present 50-60

2. no absent 50-60

3. no present 50-60

4. yes present 50-60

5. no absent 35-49

6. yes absent 35-49

7. no absent 35-49

8. yes absent 35-49

9. no present 50-60

10. no absent 35-49

11. no absent 50-60

12. no present 50-60

13. no absent 35-49

14. yes absent 35-49

15. no absent 35-49

16. no present 50-60

17. no absent 35-49

18. yes present 50-60

19. no absent 35-49

20. no absent 35-49

21. no present 35-49

22. no absent 35-49

23. no present 35-49

24. no absent 50-60

25. no absent 35-49

26. yes present 35-49

27. no present 35-49

28. no absent 50-60

29. no absent 35-49

30. no present 35-49

31. no absent 35-49

32. no absent 35-49

33. no present 50-60

34. yes present 35-49

35. no present 50-60

36. no absent 35-49

37. no absent 35-49

38. no absent 50-60

39. no absent 35-49

40. no absent 35-49

41. no absent 35-49

42. no absent 35-49

43. no present 35-49

44. no absent 35-49

45. no absent 50-60

46. no absent 50-60

47. no present 50-60

48. yes absent 35-49

49. no present 35-49

50. no absent 35-49

51. no present 50-60

52. no absent 35-49

53. yes absent 35-49

54. no absent 50-60

55. no absent 50-60

56. no absent 35-49

57. no present 35-49

58. no absent 35-49

59. no present 35-49

60. no absent 35-49

61. no absent 35-49

62. yes absent 50-60

63. no present 35-49

64. no present 35-49

65. no absent 50-60

66. no present 50-60

67. no present 50-60

68. no present 50-60

69. no absent 35-49

70. no present 50-60

71. no present 50-60

72. no present 50-60

73. no absent 50-60

74. no present 35-49

75. no absent 35-49

76. no absent 35-49

77. no absent 50-60

78. no absent 35-49

79. no absent 35-49

80. no absent 50-60

81. no absent 35-49

82. no present 35-49

83. no absent 50-60

84. no absent 35-49

85. no absent 35-49

86. no absent 35-49

87. no absent 50-60

88. no absent 35-49

89. no absent 35-49

90. yes present 35-49

91. no absent 35-49

92. no absent 35-49

93. no present 35-49

94. no absent 35-49

95. no present 50-60

96. no absent 50-60

97. no absent 50-60

98. yes absent 50-60

99. no absent 35-49

100. no present 50-60