Acknowledgments

This research was supported by grants AI24643 from the National Institute of Allergy and Infectious Diseases. The authors are grateful to Drs. L. J. Wei, Michael Hughes, and the referees for their comments and suggestions.

Table 1. Asymptotic Power from a Simulation Study Using Independent Gap-time Exponential Distributions

hi,h2,h3,h4

K

Test(ek)

1,.8,.6,.4

.8,.8,.8,.8

.8,.8,1,1 1.25,.8,.8,1.25

1

Q2 = Q3

5.20

45.00

45.00

52.50

2

Q2

6.10

57.30

57.30

30.40

Q3

25.00

55.30

55.30

61.10

Qc(1, 2)

22.00

63.40

63.40

5.40

3

Q2

8.00

62.20

56.70

24.60

Q3

68.50

58.00

49.10

65.30

Qc(1, 2, 3)

62.90

71.60

47.30

10.70

4

Q2

9.30

62.40

56.80

26.00

Q3

91.80

56.20

44.10

63.30

Qc(1, 2, 3,4)

85.70

75.10

41.00

5.80

Qc(4, 3, 2, 1)

8.30

33.00

44.00

47.70

Table 2. Asymptotic Power from a Simulation Study for Unordered Events Using Joint Distributions of Four Exponential Variables.

hi,h2,h3,h4

Correlation K Test 1.67,1,1.67,1 1.25,1.25,1.25,1.25 1.25, .8, .8,1.25

Table 2. Asymptotic Power from a Simulation Study for Unordered Events Using Joint Distributions of Four Exponential Variables.

Correlation K Test 1.67,1,1.67,1 1.25,1.25,1.25,1.25 1.25, .8, .8,1.25

a i2 = 1

2

Q2

53.2

44.5

4.0

ai3 = 1

Q3

84.8

34.4

43.9

ai4 = 1

3

Q2

85.3

47.1

9.2

a23 = 1

Q3

95.1

33.5

56.1

a24 = 1

4

Q2

62.8

54.0

3.9

a34 = 1

Q3

97.0

33.8

74.2

a12 = 0.5

2

Q2

58.5

47.5

4.8

a13 = 0.5

Q3

83.8

38.0

40.8

a13 = 0.5

3

Q2

92.7

55.0

8.0

a23 = 0.5

Q3

96.0

40.5

49.7

a24 = 0.5

4

Q2

76.1

62.8

4.2

a34 = 0.5

Q3

95.4

44.7

60.7

a12 = —0.5

2

Q2

66.7

54.5

4.6

a13 = —0.5

Q3

83.3

45.3

38.5

a14 = —0.5

3

Q2

98.5

72.9

8.1

a23 = 0.5

Q3

99.0

53.4

43.7

a24 = 0.5

4

Q2

95.3

81.8

8.10

a34 = 0.5

Q3

98.8

62.3

62.8

a12 = —1

2

Q2

70.2

59.8

5.0

a13 = —1

Q3

83.5

51.3

38.9

a14 = —1

3

Q2

99.6

78.6

7.5

a23 = 1

Q3

99.4

62.1

41.4

a24 = 1

4

Q2

98.7

87.5

10.8

a34 = 1

Q3

99.3

68.2

72.5

Table 3. P-values for Different Test Statistics for HIV/AIDS Example

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