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Binning of exposures in survival analysis for oncology – A simulation study
Matts Kågedal(1), Shang-Chiung Chen, Russ Wada (2), Jin Y. Jin (1)
(1) Genentech Inc., San Francisco, CA, (2) Quantitative Solutions, Menlo Park, CA
RESULTS
INTRODUCTION
 An exposure-response (E-R) analysis in oncology aims at describing the relationship between
drug exposure and survival and in addition aims at comparing efficacy in patients with low
exposure to control to understand if these patients should be given a higher dose or a different
treatment.
 In ER-analyses patients are commonly binned into equally sized groups based on exposure. Few
bins may result in a low probability in picking up an E-R trend since a wide range of exposures
with different efficacy will be pooled into one group, while many bins will result in few patients per
bin and large variability/uncertainty in the hazard ratio (HR) estimation.
 This simulation study was performed to assess the impact of binning by quartiles, tertiles or
twotiles on the ability to detect an E-R trend as well as to compare efficacy in the low exposure
treatment bin to control.
SIMULATION METHODS
 Study: A 2-arm oncology trial , N=100 per arm.
 Simulation method: A constant hazard corresponding to a median survival of 6 months for
control and 9 months for treatment was assumed. Censoring was assumed to occur based on
recruitment rate and study termination (patient recruited late were more likely to be censored).
Log normal distribution of the exposure metric Cmin was assumed. 1000 studies were simulated
per scenario.
 Simulation scenarios: Two scenarios for HR of treatment arm versus control were assumed
(Figure 1). Scenario 1 assumed a HR of 0.67 with no relation to drug exposure. Scenario 2
assumed an exposure response relation where the HR varied from 1 at low exposure (Quartile
1) to 0.4 at high exposure (Quartile 4). Overall, the HR was similar for the two scenarios.
Hazard Ratio Drug/Control
Q1
Q2
Q3
Scenario 1 - No ER relation
 When analyzing scenario 1 based on quartiles, the likelihood of correctly identifying a benefit of
treatment at low exposure was rather low at 61% based on CI80 and 76% based on the PE. This
was worse than tertiles and twotiles which had a likelihood of 70% and 79% respectively based
on CI80.
 With quartiles there were more spurious results based on the PE with 18% of the simulations
suggesting an ER-trend (HR of high bin lower than the low bin by at least 0.2).
Scenario 2 - With ER relation
 When analyzing simulations for scenario 2 based on binning by quartiles, the likelihood of
correctly showing similarity to control was 0% based on CI80 and 63% based on the point
estimate. Hence, clearly worse compared to tertiles and twotiles .
 The likelihood of finding a benefit over control was higher for twotiles reflecting the wider range of
exposure (and hence higher efficacy) in the low bin based on twotiles.
 The probability of obtaining an inconclusive results for the comparison between low exposure
group to control based on CI80 was high ranging from 54% for twotiles to 79% for quartiles.
 The risk of finding worse efficacy compared to control was highest based on quartiles where 22%
of the point estimates showed a HR>1.25.
 The likelihood of detecting an ER-trend was high based on quartiles at 91% based on CI80 and
95% based on point estimates which was clearly better than twotiles but only slightly better than
tertiles with a likelihood of 89% and 94% for CI80 and PE respectively.
Table 1. Percent correct/incorrect category assignment of the HR point estimate based on
different binning s for the two scenarios.
Criteria based on point
estimates
Q4
Scenario 1. No ER relationship,
HR=0.67, independent of
exposure.
Scenario 2. ER relation. HR is
reduced with increasing exposure
Scenario 1
HR(Q1-Q4) = 0.67
Scenario 2
HR(Q1)≈1, HR(Q4)≈0.4
Twotiles
Tertiles
Quartiles Twotiles Tertiles
Quartiles
Low bin better than
control (HR<0.80)
83%
78%
76%
32%
19%
15%
Low bin similar to
control (HR 0.80-1.25)
17%
22%
24%
66%
69%
63%
Low bin worse than
control (HR >1.25)
0.3%
0.1%
0.4%
3.0%
12%
22%
ER trend***
10%
14%
18%
85%
94%
95%
*** HR of high bin lower than low bin (by at least 0.2)
Figure 1 HR versus exposure for scenarios 1 and 2. Median exposure in quartiles (Q1-Q4) are
indicated with dashed horizontal lines.
 Criteria for evaluation of results: In this simulation study we assessed the probability of
concluding lower, similar or better efficacy in patients with low exposure based on the point
estimate (PE ) of the HR as well as the 80% confidence interval (CI80). An ER-trend was
concluded if the HR of the highest bin was lower by at least 0.2 compared to the lowest bin. If the
estimated HR of the highest bin was higher than control, no ER-trend was concluded, accounting
for the fact most people would be less likely to conclude and ER-trend is present when it goes in
the unexpected
direction.
RESULTS
and
DISCUSSION
RESULTS
 Samples of individual simulated studies are shown in figure 2 and the results are summarized in
table 1 and table 2.
Simulation scenario 1
1
2
Table 2. Percent correct/incorrect category assignment based on the 80% confidence interval
of the HR based for the different scenarios and binning.
Criteria based on CI80
Scenario 1
HR(Q1) = 0.67
Scenario 2
HR(Q1)≈1
Twotiles
Tertiles
Quartiles
Twotiles
Tertiles
Quartiles
Low bin better (CI<1)
79%
70%
61%
28%
13%
8%
Low bin similar (CI
0.75-1.33*)
Low bin worse CI >1
2%
1%
0%
16%
5%
0%
0%
0%
0%
2%
9%
13%
Inconclusive**
19%
29%
39%
54%
74%
79%
ER trend***
10%
9%
10%
85%
89%
91%
* CI80 should overlap 1
** Low bin comparison to control does not fulfil any of the other criteria
*** CI for HR (high bin/low bin) is less than 1.
DISCUSSION & CONCLUSION
3
HR
In this simulation exercise a set of pre-specified criteria was applied. In reality plots of exposure
response are explored graphically and the assessment of efficacy in the low exposure group is
made based on a subjective judgment. The assessment of benefit will also be influenced by the
safety profile of the new treatment versus standard of care.
Simulation scenario 2
5
6
HR
4
The proposed study appears small to draw firm conclusions on the comparison between patients
with low exposure to control. In particular binning based quartiles provided variable results and
seems not to be adequate based on the proposed trial design. While an analysis by twotiles
showed the most robust results, the exposure of the low exposure bin in this case includes drug
exposure up to the median. Binning by tertiles may be a better option to twotiles to ensure that
patients with near average plasma concentration is not influencing the comparison to control.
Tirtiles also provided a higher chance of detecting an ER-trend.
The ability to identify a marked exposure response relationship corresponding to scenario 2
appears to be relatively high with the study design evaluated.
Quartile
In conclusion, the proposed clinical trials simulation approach enabled a quantitative evaluation
of different ways of binning data and helps the development of a key component of the E-R
analysis plan.
Figure 2 Six examples of simulated studies showing HR (treatment/control) based on binning by
quartiles. Error bars represent 90% CI. Simulated studies 1-3 were based on scenario 1
(No ER trend) and 4-6 were based on scenario 2 (with ER trend)
Population Approach Group in Europe (PAGE)
Hersonissos, Crete, Greece. 2-5 June, 2015