Biostatistics Case Studies 2006

1. Biostatistics Case Studies 2006 Session 4: An Alternative to Last-Observation-Carried-Forward: Last-Rank-Carried-Forward Peter D. Christenson Biostatistician http://gcrc.LAbiomed.org/Biostat

2. Motivation for Session Topic • Setting: Baseline, intermediate, and final visits. • Primary outcome: change from baseline to final visit. • Not all subjects are measured at final visit. • Analysis of completers is not ITT. • Popular alternative: carry forward values at last intermediate visit to the final visit (LOCF). • If progressive disease: LOCF under-estimates placebo group. • If progressive treatment effect: LOCF under- estimates treated group.

3. Today’s Method: LRCF Idealized LOCF: Ignore Presumed Progression 0 Change from Baseline Individual Subjects Baseline Intermediate Visit Final Visit LRCF: Maintain Expected Relative Progression 0 Change from Baseline Intermediate Visit Baseline Final Visit

4. Basic Issues • Reasons for missing data: • Administrative choice: long-term study ends; early termination; interim analyses. • Related to treatment; subject choice. Unknown. • Time-specific or global differences between treatments: • Time course or Specific times or Only at end? • Do groups differ in the following Kaplan-Meier curves? “Well, in the long run, we’re all dead.” Milton Freidman, Economist

5. Some Typical Summaries • Use all available data: • only in graphs, not analysis. • in analysis with mixed models • in analysis with imputation from modeling. • Use only completers: • Sometimes only require final visit. • Sometimes require all visits. • Last-observation-carried-forward (LOCF): • Project last value to all subsequent visits • Sometimes interpolate for intermediate missing visits. Last session: Cumulative change is an alternative method that is better than (2) or (3).

6. Last Week’s Method: Use Successive Δs 0 Valid est of Δ02 from N=100 Cumulative Change Δ6-12 from N=83 -8.3 -10.2 Valid est of Δ24 from N=94 -11.8 Δ46 from N=87 12

7. Today’s Method • Used when only interest is in baseline to final visit change. • Need data at one or more intermediate visits. • Less bias than LOCF. • More power than Completer analysis. • More intuitive than mixed models for repeated measures (MMRM). • Less robust than MMRM if dropout is related to subject choice. • O’Brien(2005) Stat in Med; 24:341-358.

8. Case Study Henry K., et al, for the AIDS Clinical Trial Group 193A Study Team: A randomized, controlled, double-blind study comparing the survival benefit of four different reverse transcriptase inhibitor therapies for the treatment of advanced AIDS. J AIDS 1998;19:339-349.

9. ACTG Study 193A Outline • 1313 AIDS subjects with CD4 ≤ 50 cells/mm3 • Randomized to one of 4 regimens (combinations of HIV RT inhibitors, all with ZDV). • Clinical visits every 8 weeks; lab samples every 16 weeks up to 48 weeks; mortality status at study end. • Primary outcome is survival time. We will ignore. • A secondary outcome is CD4 count over time. • We will analyze several ways. • Table 3 – top half.

10. Comments on Study Only 25% of subjects completed the study or died. Most subjects discontinued due to toxicity, too ill, changing to other therapies. Intention-to-treat analysis was used. Paper only reports statistical comparisons for baseline to week 16 CD4 cell count changes.

11. Our Goal • Suppose outcome of interest is CD4 change from baseline to 32 weeks. • We have CD4 data between 0 and 40 weeks: N=1299 at baseline; 973 at week 16; 759 at week 32. • We compare three methods: • Use only the 759 week 32 “completers”. • Use last-observation-carried-forward to assign week 16 changes to week 32 for subjects not measured at 32 weeks. • Apply new method: carry forward ranks at week 16 to week 32.

12. Table 3 • Changing Ns over time may misrepresent time trends. • Side comment: Medians were used for baseline also due to skewness of cell count distributions; see next slide.

13. Table 3: Baseline CD4 Distribution Actual counts Log(count+1) -18 Median w/ 95% limits Mean +/- 2SD

14. Subjects with Measured Changes *268 Baseline 1299 • Thus, 1031 subjects with info on at least 1 change. • Paper: 983, not 973; 766, not 759. (? Mistiming, +/- 4 weeks.)

15. Goal: Replace Median Counts using a Common N: 1031? 1299 or 1031 • The published method requires at least one post- baseline value. • We will thus use N=1031. Applying to N=1299 would probably be preferable to LOCF on 1299.

16. LRCF: Algorithm • Rank subjects at visit 1 according to change from baseline to visit 1. [All subgroup groups pooled.] • Rank subjects at visit 2 according to change from baseline to visit 2. • Subjects unranked at visit 2 are assigned their rank from visit 1, if available. • Some of the other subjects at visit 2 (who have actual ranks then) have their ranks shifted upward to accommodate the non-completers who are using visit 1 rank. • If necessary, make adjustment for tied ranks. See O’Brien. • Repeat at visit 3 using visit 2 assigned ranks; loop to end.

17. LRCF: Example N=5 subjects T0 = baseline N=2 missing final visit T3 Δ=Change R=Rank S=Temp Rank

18. LRCF: This study: CD4 Changes at Week 32 • All methods give same overall conclusions; p- values similar. • Completer and LOCF tend to attenuate change estimates, relative to LRCF.

19. More General: O’Brien Simulations

20. Summary for LRCF Method • More powerful than completer method and less biased than LOCF. Similar to cumulative change from last week. • Use standard non-parametric tests (Wilcoxon, Kruskal - Wallis) on final visit ranks of changes. • Identical to standard test (Wilcoxon, K-W)if no dropout. • Developer O’Brien suggests use of %iles rather than ranks, if computational simplicity is desired. • More intuitive than mixed model repeated measures (MMRM – see Case Studies 2004 Session 3). • More potential for bias than MMRM if subjects choose to drop out. • Same lack of bias as MMRM if administratively censored.

21. Self Quiz • For all questions, consider a study with 2 treatment groups that has scheduled visits at baseline and at study end. Primary outcome is change from baseline to study end, but not all subjects are measured at study end. • If a subject dropped out due to side effects, is he “administratively censored”? Why does it matter? • What additional information is necessary in order to use the method we discussed today?

22. Self Quiz • Now, suppose we also have intermediate visits with measurements for some subjects, for the remaining questions. • Criticize the use of only completing subjects in the analysis. • Criticize the use last-observation-carried-forward. • Criticize the use of imputation methods. • Criticize the use of mixed models. • Criticize the use of today’s method of extrapolating ranks.