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zahrcast
The case study1 pools three historical metastatic colorectal cancer trials with a target trial, and forecasts the target trial's results at three cut-offs: trial months 6, 15 and 22, counted from when the target trial opened. The target trial is the Amgen PACCE trial (20040249). Its 739 patients are in two arms: panitumumab plus bevacizumab with chemotherapy (arm A), and bevacizumab with chemotherapy (arm B). The historical trials are HORIZON III (AstraZeneca cediranib, NCT00384176), a Pfizer sunitinib trial and Sanofi EFC5505. Each contributes one arm, and together they have 1,418 patients. At each cut-off Sia is refitted using only the data available at that date.
Sia models each patient's disease burden as a latent quantity over time and learns it from one marker, tumor size at each scan. The current burden changes the hazard of both progression routes, and the burden at the last scan changes the hazard of stopping treatment. The model has a fourth state for patients who stop treatment before progression. The baseline characteristics change the hazard of every transition out of the progression-free and progressed states, with a separate effect for each.
Every patient enters at enrollment as progression-free, marked by the dot. Each edge points to the state a patient enters. Solid edges: the hazard of the transition depends on the current latent burden. Dashed edges: it does not. The numbers match the table below.
| # | transition | when it is recorded | hazard depends on |
|---|---|---|---|
| 1 | progression at target lesionsprogression-free → progressed | At a scan. The date falls between two scans. | Current burden, baseline characteristics |
| 2 | other progressionprogression-free → progressed, in non-target or new lesions | At a scan. The date falls between two scans. | Current burden, baseline characteristics |
| 3 | death before progressionprogression-free → deceased | Exact date | Baseline characteristics |
| 4 | treatment discontinuationprogression-free → stopped treatment | At a visit | Burden at the last scan, baseline characteristics |
| 5 | progression after stopping treatmentstopped treatment → progressed | At a visit. The clock restarts when treatment stops. | Base hazard only |
| 6 | death after stopping treatmentstopped treatment → deceased | Exact date. The clock restarts when treatment stops. | Base hazard only |
| 7 | death after progressionprogressed → deceased | Exact date. The clock restarts at progression. | Baseline characteristics |
Transitions 1 and 2 follow the reader's recorded call. Only events after the date treatment stopped go through the stopped-treatment state.
ECOG is left out because it does not vary across the historical trials.
Each transition's base hazard is estimated in 4-week steps. Progression-free survival ends at transition 1, 2, 3, 5 or 6. Overall survival ends at transition 3, 6 or 7.
Amgen PACCE trial (20040249), 739 patients. Arm A: panitumumab plus bevacizumab with chemotherapy. Arm B: bevacizumab with chemotherapy.
HORIZON III, a Pfizer sunitinib trial and Sanofi EFC5505. Each contributes one arm, 1,418 patients in all.
Sia fits the historical data first. That fit, with its spread widened, is the prior for the target-trial fit. Patient-level terms are not carried over.
Each trial and arm has its own level for every burden parameter and every transition. Each patient also has their own term for each burden parameter.
Forecasts of tumor size for 6 target-trial patients who had not progressed at their last assessment, 3 per arm. Up to a patient's last assessment, marked by the vertical line, the median and 80% interval are Sia's fit to the measurements in hand. After it they are a forecast, which fades as the probability that the patient is still progression-free falls. Each panel has its own vertical scale.
The thin lines are 20 individual posterior draws for the patient. Each draw is one possible trajectory, so individual draws wander in and out of the band. A draw that runs above the top of a panel is cut at its edge. The posterior sample holds 8 such patients in arm A and 6 in arm B. A fitted line needs at least 2 assessments after baseline, which 4 of the 8 in arm A and 5 of the 6 in arm B have, so the three patients in each arm are picked from those. In each arm the three patients are the one whose tumor shrank the most relative to baseline, the one whose tumor shrank the least, and, of the remaining patients, the one with the largest forecast regrowth. These picks span the range of responses and are not a random sample. For this indication, Sia draws each progression from the hazard, and each progression adds a step to the forecast tumor size. A draw therefore jumps at the week it progresses, and draws that have not yet progressed stay smooth.
Target-trial accrual by trial month, counted from when the trial opened. The upper panel counts patients enrolled and, separately, patients with at least one tumor assessment after baseline. A patient enters the forecast only after their first assessment, so at trial month 15, 573 patients had enrolled and 467 were included. The lower panel counts tumor assessments. Dots mark the cut-offs at trial months 6, 15 and 22, when 114, 467 and 721 patients had an assessment. The counts are pooled across arms and by month.
Each cut-off is a separate fit that uses only the data available at that date. It forecasts survival in each arm for the patients who have had at least one tumor assessment after baseline by then, because only those patients enter the fit. Patients who enroll later are not in the forecast, and the observed curve includes all patients. The forecast is compared with the observed survival curve at the trial's final data cut. The observed median is where that curve crosses 50%.
For overall survival, the 90% interval for the median contained the observed median in both arms at trial months 6 and 15. At trial month 22 it contained the observed median in neither arm. With the full data it contained the observed median in arm A but not in arm B. The intervals were about 20 months wide at trial month 6 and about 4 months wide at trial month 22. For progression-free survival, the interval contained the observed median in both arms at every cut-off and with the full data, and narrowed from 6 to 7 months wide to about 1 month.
The page uses two time scales. Cut-offs are in trial months, counted from when the target trial opened. The charts are in follow-up months, counted from each patient's enrollment. At trial month 6, no patient has more than 6 months of follow-up.
Trial month 6, 114 patients. The 90% interval for median overall survival runs from 13.5 to 33.1 months in arm A and from 14.3 to 34.0 months in arm B, about 20 months wide. Both contain the observed medians of 23.4 months in arm A and 26.3 months in arm B. The intervals for median progression-free survival run from 7.9 to 13.8 months in arm A and from 8.5 to 15.2 months in arm B, about 6 to 7 months wide, and contain the observed medians of 11.0 and 11.8 months.
Trial month 15, 467 patients. The intervals for median overall survival are 8.1 months wide in arm A and 9.8 months wide in arm B, and contain the observed medians in both arms. The intervals for median progression-free survival are 1.5 and 2.2 months wide and also contain the observed medians. The forecast median progression-free survival in arm B is 12.4 months, above the observed 11.8 months.
Trial month 22, 721 patients. The intervals for median overall survival are 3.8 months wide in arm A and 4.5 months wide in arm B. Neither contains the observed median. The arm A interval runs from 19.4 to 23.2 months against 23.4 observed, and the arm B interval runs from 21.1 to 25.6 months against 26.3 observed. The intervals for median progression-free survival are about 1 month wide and contain the observed medians in both arms.
Full data, 739 patients. The interval for median overall survival contains the observed median in arm A, running from 21.8 to 23.5 months against 23.4 observed. In arm B it runs from 23.9 to 25.9 months against 26.3 observed and does not contain it. This difference remains with the full data. The intervals for median progression-free survival contain the observed medians in both arms.
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Overall and progression-free survival for each arm of the target trial. The band is an 80% interval at each follow-up month, so the observed curve is expected to fall outside it at some time points.
Median overall and progression-free survival forecast at each cut-off. These are posterior summaries of the median itself, so they can differ from where the curves above cross 50%.
Diagnostics for each fit: survival curves replicated from the fitted model, and the sampler's and effective sample sizes.
At trial month 15, 573 patients had enrolled, and the intervals for median overall survival and median progression-free survival contained the medians observed at the final data cut. Enrollment continued until about trial month 20, and the last tumor assessment in the data is at about trial month 46.
The intervals for median overall survival narrowed from about 20 months wide at trial month 6 to about 4 months at trial month 22. They contained the observed medians in both arms at trial months 6 and 15, in neither arm at trial month 22, and in arm A only with the full data. The intervals for median progression-free survival narrowed from 6 to 7 months wide to about 1 month and contained the observed medians in both arms at every cut-off and with the full data. Overall survival is still heavily censored at the final data cut, so the observed median for overall survival is itself an estimate with its own uncertainty, which the charts do not show.
Whether an interval of a given width supports a decision depends on the decision. A forecast supports a go/no-go decision only against a benefit threshold and a cost of being wrong, and the trial sponsor sets both. For a given trial, the relevant question is the earliest cut-off at which the interval is narrow enough for that threshold. These results come from one disease and one target trial and should be checked on a sponsor's own data before they are applied elsewhere. The tails of the prior that carries the historical information are provisional, and their coverage has not been validated.
Sia's forecasts come from a fitted model whose parts can be read directly. Each panel below shows how one part of the model changes with a patient's baseline characteristics. The latent burden panels show the rate at which the burden shrinks and regrows and the share of the burden that shrinks. The event panels show hazard ratios for each transition between states. All effects are per standard deviation of the characteristic, from the fit to the full data. Progression has two routes. One is progression of the target lesions. The other is any other progression, such as a new lesion or progression of a non-target lesion. Each route has its own panel.
Both progression routes also depend on the latent burden at each point in time, and treatment discontinuation depends on the burden at the patient's most recent assessment. The rows under "current latent burden" show this: the burden in the shrinking and regrowing parts, and their shrink and regrowth rates.
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Medians and 80% intervals from the fit to the full data. The lighter bars behind them show the prior fit's 80% interval, before any data. Baseline rows are per standard deviation of each characteristic. Current latent burden rows are per e-fold (about 2.7-fold) change in the burden or rate. Event panels show hazard ratios on a log scale. Hover over a characteristic to highlight it across the panels.