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[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Study Objective ,[object Object],[object Object]
Population Description ,[object Object],[object Object],[object Object],[object Object],[object Object]
Unadjusted Kaplan-Meier Curves ,[object Object],[object Object],[object Object]
Log Rank Test ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Chi-Square  DF  p-value 156.91  2  <.0001
Testing the Proportional Hazards Assumption ,[object Object],[object Object],[object Object],[object Object],[object Object],____________ 1Patricia M. Grambsch and Terry M. Therneau.  Proportional hazards tests and  diagnostics based on weighted residuals.  Biometrics 81, 515-526 (1994).
Log(time) vs Log(-log(survival)) Plot  ,[object Object]
Statistical Test using Grambsch and Therneau ,[object Object],[object Object],[object Object],Chi-Square P-value Black 28.72 0.000 Hispanic 1.46 0.226 Global 36.67 0.000
Standardized KM Estimation ,[object Object],[object Object],[object Object],_____________________ 2 Amato, DA.  A generalized Kaplan-Meier estimator for heterogeneous populations.  Communications in Statistics, Theory and Methods 17, 263-286 (1988).
Weight Calculation ,[object Object],[object Object],[object Object],[object Object]
Weighting Example- Geographic Region Blacks: (60% South) Whites: (42% South) Study Population:  (57% South) 7% 57% 60% 42%
Weighting Example (cont’) 36201 36201 Group Race Region Cases Weight Weighted  Contribution 1 Black Northeast 7668 1.003 7691.004 2 Black South 17536 0.934 16378.624 3 Black North 2172 1.176 2554.272 4 Black West 1324 1.432 1895.968 5 White Northeast 2033 0.989 2010.637 6 White South 3117 1.373 4279.641 7 White North 1049 0.636 667.164 8 White  West 1302 0.417 542.934 Total      36201
[object Object],[object Object],[object Object]
Weighting accomplishes at least two things: ,[object Object],[object Object]
Standardized K-M  Crude K-M  d j = number of deaths at time t n j = number of persons at risk  at time t W D (u)= sum of weights for  cases who die at or before time t W R (u)= sum of weights for  cases at risk at time t
Comparison of KM and SKM   12 months (95% CI) 24 months (95% CI) 36 months (95% CI) Whites SKM 0.927 (0.924, 0.929) 0.892 (0.889, 0.894) 0.868 (0.867, 0.870) KM 0.922 (0.916, 0.927)    0.884 (0.877, 0.891) 0.858 (0.850, 0.866)  Hispanics SKM 0.927 (0.924, 0.930) 0.898 (0.896, 0.901) 0.871 (0.869, 0.873) KM 0.907 (0.901, 0.912) 0.872 (0.865, 0.878) 0.840 (0.832, 0.848) Blacks SKM 0.908 (0.906, 0.911) 0.863 (0.861, 0.866) 0.821 (0.819, 0.824) KM 0.907 (0.904, 0.910)  0.859 (0.855, 0.863)    0.815 (0.810, 0.819)
Results ,[object Object],[object Object],[object Object]
Conclusions- Advantages of SKM ,[object Object],[object Object],[object Object],[object Object]

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Evaluating Racial Disparities in Survival after AIDS Diagnosis using Standardized

  • 1.
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11. Weighting Example- Geographic Region Blacks: (60% South) Whites: (42% South) Study Population: (57% South) 7% 57% 60% 42%
  • 12. Weighting Example (cont’) 36201 36201 Group Race Region Cases Weight Weighted Contribution 1 Black Northeast 7668 1.003 7691.004 2 Black South 17536 0.934 16378.624 3 Black North 2172 1.176 2554.272 4 Black West 1324 1.432 1895.968 5 White Northeast 2033 0.989 2010.637 6 White South 3117 1.373 4279.641 7 White North 1049 0.636 667.164 8 White West 1302 0.417 542.934 Total     36201
  • 13.
  • 14.
  • 15. Standardized K-M Crude K-M d j = number of deaths at time t n j = number of persons at risk at time t W D (u)= sum of weights for cases who die at or before time t W R (u)= sum of weights for cases at risk at time t
  • 16. Comparison of KM and SKM   12 months (95% CI) 24 months (95% CI) 36 months (95% CI) Whites SKM 0.927 (0.924, 0.929) 0.892 (0.889, 0.894) 0.868 (0.867, 0.870) KM 0.922 (0.916, 0.927)    0.884 (0.877, 0.891) 0.858 (0.850, 0.866)  Hispanics SKM 0.927 (0.924, 0.930) 0.898 (0.896, 0.901) 0.871 (0.869, 0.873) KM 0.907 (0.901, 0.912) 0.872 (0.865, 0.878) 0.840 (0.832, 0.848) Blacks SKM 0.908 (0.906, 0.911) 0.863 (0.861, 0.866) 0.821 (0.819, 0.824) KM 0.907 (0.904, 0.910)  0.859 (0.855, 0.863)    0.815 (0.810, 0.819)
  • 17.
  • 18.