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

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 Change from Baseline Baseline Final Visit Intermediate Visit 0 Change from Baseline Intermediate Visit Final VisitBaseline 0 LOCF: Ignore Presumed Progression LRCF: Maintain Expected Relative Progression Individual Subjects

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 1. Use all available data: only in graphs, not analysis. in analysis with mixed models in analysis with imputation from modeling. 2. Use only completers: Sometimes only require final visit. Sometimes require all visits. 3. 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 12 -10.2 -8.3 Valid est of Δ 24 from N=94 Cumulative Change Valid est of Δ 02 from N=100 Δ 46 from N=87 -11.8 Δ 6-12 from N=83

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/mm 3 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 countsLog(count+1) Mean +/- 2SD Median w/ 95% limits -18

14. Subjects with Measured Changes Number of Subjects with Data Week 32: Yes Week 32: NoTotal Week 16: Yes701272 973 Week 16: No 58* Total7592721031 Thus, 1031 subjects with info on at least 1 change. Paper: 983, not 973; 766, not 759. (? Mistiming, +/- 4 weeks.) *268 Baseline 1299

15. Goal: Replace Median Counts using a Common N: 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. 1031? 1299 or 1031

16. LRCF: Algorithm 1.Rank subjects at visit 1 according to change from baseline to visit 1. [All subgroup groups pooled.] 2.Rank subjects at visit 2 according to change from baseline to visit 2. 3.Subjects unranked at visit 2 are assigned their rank from visit 1, if available. 4.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. 5.If necessary, make adjustment for tied ranks. See O’Brien. 6.Repeat at visit 3 using visit 2 assigned ranks; loop to end.

17. LRCF: Example IDT0T1T2T3 131211812 24028.. 334201716 4351916. 53719 15 IDΔ1Δ1R1Δ2Δ2S2R2Δ3Δ3S3R3LOCF 110113111923 2122..2..2 314317231811 41641945..5 5185 342234 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 MethodAlt’g w/ ddI+ Zalcitabine+ ddI+ ddI + NevAll Compl. N=759 -8.8 -15.0 to 1.0 -4.0 -16.0 to 2.0 -2.5 -17.0 to 5.5 0.5 -9.0 to 17.0 -3.0 -15.0 to 5.0 LOCF N=1031 -7.5 -15.0 to 1.0 -4.5 -15.0 to 2.0 -3.0 -15.0 to 5.0 0.5 -9.0 to 17.0 -3.0 -13.5 to 5.0 LRCF N=1031 -10.0 -19.3 to 1.0 -5.0 -19.0 to 0.5 -5.5 -18.0 to 2.5 -0.25 -10.5 t 11.5 -4.0 -16.0 to 3.0 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. 1.If a subject dropped out due to side effects, is he “administratively censored”? Why does it matter? 2.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. 3.Criticize the use of only completing subjects in the analysis. 4.Criticize the use last-observation-carried-forward. 5.Criticize the use of imputation methods. 6.Criticize the use of mixed models. 7.Criticize the use of today’s method of extrapolating ranks.