------------------------------------------------------------------------------------------------------ log: c:\Imbook\bwebpage\Section4\mma17p2kmextra.txt log type: text opened on: 19 May 2005, 13:24:01 . . ********** OVERVIEW OF MMA17PP2KMEXTRA.DO ********** . . * STATA Program . * copyright C 2005 by A. Colin Cameron and Pravin K. Trivedi . * used for "Microeconometrics: Methods and Applications" . * by A. Colin Cameron and Pravin K. Trivedi (2005) . * Cambridge University Press . . * Chapter 17.5.1 pages 581-2 . * Nonparametric Survival Analysis . * Provides . * (1) K-M Survivor Function and N_A Cum Hazard Estimates (Table 17.2) . * using artificial data . . ********** SETUP ********** . . set more off . version 8.0 . set scheme s1mono /* Used for graphs */ . . ********** GENERATE DATA ********** . . * The time does not matter except for the hazard. . * Here arbitrarily let durations be 1, 4, 6, 11 and 20 (so irregularly spaced) . * 1. At t = 10 (time t1): 6 failures . * 2. At t = 15: 4 censored (lost) between t1 and t2 . * 3. At t = 20 (time t2): 5 failures . * 4. At t = 25: 3 censored (lost) between t2 and t3 . * 3. At t = 30 (time t3): 2 failures . * 4. At t = 35: 1 censored (lost) between t3 and t4 . * 3. At t = 40 (time t4): 1 failures . * 4. At t = 45: 32 failures (lost) between t4 and t5 . * 5. At t = 50 (time t5): 26 censored . . * Indicator failed = 1 if fail and 0 if censored . input duration failed duration failed 1. 10 1 2. 10 1 3. 10 1 4. 10 1 5. 10 1 6. 10 1 7. 15 0 8. 15 0 9. 15 0 10. 15 0 11. 20 1 12. 20 1 13. 20 1 14. 20 1 15. 20 1 16. 25 0 17. 25 0 18. 25 0 19. 30 1 20. 30 1 21. 35 0 22. 40 1 23. 45 0 24. 45 0 25. 45 0 26. 45 0 27. 45 0 28. 45 0 29. 45 0 30. 45 0 31. 45 0 32. 45 0 33. 45 0 34. 45 0 35. 45 0 36. 45 0 37. 45 0 38. 45 0 39. 45 0 40. 45 0 41. 45 0 42. 45 0 43. 45 0 44. 45 0 45. 45 0 46. 45 0 47. 45 0 48. 45 0 49. 45 0 50. 45 0 51. 45 0 52. 45 0 53. 45 0 54. 45 0 55. 50 1 56. 50 1 57. 50 1 58. 50 1 59. 50 1 60. 50 1 61. 50 1 62. 50 1 63. 50 1 64. 50 1 65. 50 1 66. 50 1 67. 50 1 68. 50 1 69. 50 1 70. 50 1 71. 50 1 72. 50 1 73. 50 1 74. 50 1 75. 50 1 76. 50 1 77. 50 1 78. 50 1 79. 50 1 80. 50 1 81. end . . sum Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- duration | 80 39.625 13.40166 10 50 failed | 80 .5 .5031546 0 1 . . ***** COMPUTATION USING STATA ********** . . * Stata st curves require defining the dependent variable . stset duration, fail(failed=1) failure event: failed == 1 obs. time interval: (0, duration] exit on or before: failure ------------------------------------------------------------------------------ 80 total obs. 0 exclusions ------------------------------------------------------------------------------ 80 obs. remaining, representing 40 failures in single record/single failure data 3170 total analysis time at risk, at risk from t = 0 earliest observed entry t = 0 last observed exit t = 50 . stsum failure _d: failed == 1 analysis time _t: duration | incidence no. of |------ Survival time -----| | time at risk rate subjects 25% 50% 75% ---------+--------------------------------------------------------------------- total | 3170 .0126183 80 50 50 50 . stdes failure _d: failed == 1 analysis time _t: duration |-------------- per subject --------------| Category total mean min median max ------------------------------------------------------------------------------ no. of subjects 80 no. of records 80 1 1 1 1 (first) entry time 0 0 0 0 (final) exit time 39.625 10 45 50 subjects with gap 0 time on gap if gap 0 time at risk 3170 39.625 10 45 50 failures 40 .5 0 .5 1 ------------------------------------------------------------------------------ . . * K-M survival graph . * sts graph, gwood . . * N-A Cumulative Hazard . * sts graph, cna . . * Kaplan-Meier Survivor Function listed (last column Table 17.2) . sts list failure _d: failed == 1 analysis time _t: duration Beg. Net Survivor Std. Time Total Fail Lost Function Error [95% Conf. Int.] ------------------------------------------------------------------------------- 10 80 6 0 0.9250 0.0294 0.8407 0.9656 15 74 0 4 0.9250 0.0294 0.8407 0.9656 20 70 5 0 0.8589 0.0395 0.7596 0.9193 25 65 0 3 0.8589 0.0395 0.7596 0.9193 30 62 2 0 0.8312 0.0428 0.7268 0.8984 35 60 0 1 0.8312 0.0428 0.7268 0.8984 40 59 1 0 0.8171 0.0443 0.7104 0.8875 45 58 0 32 0.8171 0.0443 0.7104 0.8875 50 26 26 0 0.0000 . . . ------------------------------------------------------------------------------- . . * Nelson-Aalen Cumulative Hazard Listed (second last column Table 17.2) . sts list, na failure _d: failed == 1 analysis time _t: duration Beg. Net Nelson-Aalen Std. Time Total Fail Lost Cum. Haz. Error [95% Conf. Int.] ------------------------------------------------------------------------------- 10 80 6 0 0.0750 0.0306 0.0337 0.1669 15 74 0 4 0.0750 0.0306 0.0337 0.1669 20 70 5 0 0.1464 0.0442 0.0810 0.2648 25 65 0 3 0.1464 0.0442 0.0810 0.2648 30 62 2 0 0.1787 0.0498 0.1035 0.3085 35 60 0 1 0.1787 0.0498 0.1035 0.3085 40 59 1 0 0.1956 0.0526 0.1155 0.3313 45 58 0 32 0.1956 0.0526 0.1155 0.3313 50 26 26 0 1.1956 0.2030 0.8571 1.6678 ------------------------------------------------------------------------------- . . ***** MANUAL COMPUTATION AS IN TABLE 17.2 (page 582) ********** . . scalar cumhaz1 = 6/80 . scalar cumhaz2 = 6/80 + 5/70 . scalar cumhaz3 = 6/80 + 5/70 + 2/62 . scalar surv1 = 1-6/80 . scalar surv2 = (1-6/80)*(1-5/70) . scalar surv3 = (1-6/80)*(1-5/70)*(1-2/62) . di "Cumulative hazard at t1: " cumhaz1 " at t2: " cumhaz2 " at t3: " cumhaz3 Cumulative hazard at t1: .075 at t2: .14642857 at t3: .17868664 . di "Survivor function at t1: " surv1 " at t2: " surv2 " at t3: " surv3 Survivor function at t1: .925 at t2: .85892857 at t3: .8312212 . . ********** CLOSE OUTPUT ********** . log close log: c:\Imbook\bwebpage\Section4\mma17p2kmextra.txt log type: text closed on: 19 May 2005, 13:24:01 ----------------------------------------------------------------------------------------------------