Biostatistics Case Studies 2008
Session 1: Survival Analysis Fundamentals
Same material repeated three times:
Tuesday May 6, 3:30-4:30
Wednesday May 7, 4:00-5:00
Friday May 9, 12:00-1:00
Location: RB-1 Chopra Conference Room (2nd Floor, just left of elevators)
Case Study Paper:
Miller K, et al. Paclitaxel plus Bevacizumab versus Paclitaxel Alone for Metastatic Breast Cancer, NEJM
2007;357:2666-76.
http://gcrc.labiomed.org/Biostat/Education/CaseStudies2008/Session1/MillerNEJM2007.pdf
Survival analyses are a collection of methods for studies that measure whether, and if so when an event
such as death or cure occurs. In this session, we use a paper on progression of metastatic breast cancer
as an example to discuss – through the questions listed below – the logic of these methods, and
differences in measuring treatment effects with hazard ratios, relative risks, and odds ratios. Although
more common in clinical studies, survival methods can also sometimes increase the sensitivity of basic
science and translational experiments to detect effects.
We will discuss the following questions, and any others that participants may have:
1. Fourteen more subjects were assigned to one of the treatment groups, compared to the other
(Figure 1). In most randomized studies there is a difference of at most a few subjects. Why is it so
far off here?
2. In Figure 2B, survival is 20% in the mab group at the end of the study, yet Figure 1 says that only
243/347=70% (or perhaps 6 more to give 72%) in that group died, so why isn’t survival 30%?
3. The main positive conclusion is that adding mab therapy doubled median time until disease
progression (Fig 1). Why are median, rather than mean, times always reported in survival
analyses?
4. Even more fundamentally, why is time-to-event the primary outcome anyway, instead of, say, 1, 2
or 3-year survival rates?
5. As a follow-up question, the authors responded to a letter to the editor that basically said, “Big
deal, no effect on mortality”, with “In our view, the improvement in 1-year survival with the addition
of bevacizumab (81.2% vs. 73.4%, P = 0.01) confirms our original conclusion [sic. They meant
“conjecture”].” Comments?
6. In the abstract and the second paragraph of the results section, the authors report “objective
response rates” without definition. What is this outcome?
7. A supplement to the paper states that the original study design limited treatment to18 months, but
it was later amended to allow treatment until disease progression. Comments?
8. In the second paragraph of the results section, the authors state that the effect (on disease
progression) of adding mab therapy decreases with time. Is this apparent in Figure 2A? What
should we look at: the horizontal differences in the curves over time, vertical? Does it matter? In
any case, won’t this always occur, given enough time?
9. Relative risk (RR) is the probability of progression (at a specified time) for taxol + mab, divided by
the probability for taxol alone. At end of study, would this be 316/347 divided by 308/326, equals
0.96 (from Fig 1)? Use Fig 2 to show that approximately RR=50/73=0.68 at 1-year and
84/96=0.88 at 2-years.
10. The authors do not report RRs. In the second paragraph of the results section, they report a
hazard ratio of 0.60 for disease progression and 0.88 for mortality. What is a hazard ratio, or for
that matter a “hazard”?
11. What does the requirement of “proportional hazards” used in their (page 2670, paragraph 2, and
in most paper’s) survival analyses mean? Sketch a figure like Fig 2A where this obviously does
not occur. What could we do in that case, since the standard analysis needs it, and would
therefore be wrong?
12. The authors look at many subgroups (Fig 3) to try to find subjects who might benefit most. Is this
“data mining”; are you concerned about false positive conclusions? See NEJM 354(16):16671669.
13. Regarding the previous question #12: Nevertheless, older (>65) subjects may not benefit as
much as others. What should be done about this observation? Does the multivariate analysis
(bottom of page 2671) satisfy you? Has it addressed whether age itself, and/or other factors
related to age, are associated with apparent decreased mab efficacy?
14. We have compared hazard ratios and relative risks. But odds ratios (OR) are an alternative to RR
in measuring group differences in characteristics, and like RR are for a fixed period of time. How
different are they from RRs? Assume that at one year 0.50*347=173 subjects receiving taxol +
mab were still progression-free, but only 0.27*326=88 subjects receiving taxol only were, and that
all subjects were followed for at least 1 year. What is the RR for taxol + mab vs. taxol only? What
is the OR? What generally makes OR more or less appropriate than RR? Are there situations
where (1) one or the other must be used, or (2) it doesn’t really matter since they will both be
almost identical?