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The case study1 pools a historical first-line extensive-stage small-cell lung cancer trial with a target trial, and forecasts the target trial's results at three cut-offs: trial months 4, 11 and 19, counted from when the target trial opened. The target trial is a Lilly CXCR4 trial and the historical trial is Amgen 20010145. 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. Progression comes about in two ways. The RECIST rule, applied to the fitted tumor size of the target lesions, records progression when that size crosses its threshold. A hazard covers progression in non-target and new lesions. The current burden changes that hazard and the hazard of death before progression. The baseline characteristics change the hazard of every transition that has one, 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 heavier edge is the RECIST rule. It has no hazard, and the fitted tumor size of the target lesions alone decides it. The numbers match the table below.
| # | transition | when it is recorded | hazard depends on |
|---|---|---|---|
| 1 | progression at target lesionsprogression-free → progressed, by the RECIST 1.1 rule on the fitted tumor size | When the fitted tumor size crosses the RECIST threshold | Fitted tumor size only; no hazard |
| 2 | progression in non-target or new lesionsprogression-free → progressed | At a scan. The date falls between two scans. | Current burden, baseline characteristics |
| 3 | death before progressionprogression-free → deceased | Exact date | Current burden, baseline characteristics |
| 4 | death after progressionprogressed → deceased | Exact date. The clock restarts at progression. | Baseline characteristics |
The covariate chart below labels transition 2 as progression, because it is the only progression transition with a hazard.
Each transition's base hazard is estimated in 4-week steps. Progression-free survival ends at transition 1, 2 or 3. Overall survival ends at transition 3 or 4.
Lilly CXCR4 trial, 77 patients in arms A and B.
Amgen 20010145.
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 10 such patients per arm. 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.
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 11, 43 patients had enrolled and 39 were included. The lower panel counts tumor assessments. Dots mark the cut-offs at trial months 4, 11 and 19, when 9, 39 and 71 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 4 and 11. At trial month 19 it contained the observed median in arm A but not in arm B. With the full data it was above the observed median in both arms. The intervals were about 17 to 20 months wide at trial month 4 and 2 to 3 months wide at trial month 19.
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 4, no patient has more than 4 months of follow-up.
Trial month 4, 9 patients. Each arm has 4 or 5 patients, so the intervals are wide. The 90% interval for median overall survival runs from about 5 to 25 months in arm A and about 5 to 22 months in arm B, and contains the observed medians of 9.8 months in arm A and 11.6 months in arm B. The intervals for median progression-free survival also contain the observed medians.
Trial month 11, 39 patients. The intervals for median overall survival are about 5 and 6 months wide and contain the observed medians in both arms. For progression-free survival, the forecast median in arm A is 6.6 months. This is above the observed 5.6 months, though the interval now contains it. In arm B the forecast median is 4.6 months and the interval runs from 4.1 to 5.4 months, below the observed 5.8 months.
Trial month 19, 71 patients. The intervals for median overall survival are 3.1 months wide in arm A and 2.5 months wide in arm B. The arm A interval contains the observed median. The arm B interval runs from 8.9 to 11.4 months and does not contain the observed 11.6 months. The forecast median progression-free survival in arm A is 6.1 months, still above the observed 5.6 months. In arm B it is 5.5 months, and the interval runs from 5.2 to 5.8 months, just below the observed 5.8 months.
Full data, 77 patients. The interval for median overall survival runs from 10.3 to 12.2 months in arm A and from 11.6 to 13.9 months in arm B. Both intervals are above the observed medians of 9.8 and 11.6 months, the arm B interval only just. The interval for median progression-free survival in arm B contains the observed median. Sia estimates median progression-free survival in arm A at 6.0 months, against 5.6 months observed. This difference remains with the full data.
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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, out-of-sample scores for fits made once a month, and the sampler's and effective sample sizes.
At trial month 11, 43 patients had enrolled, and the intervals for median overall survival contained the medians observed at the final data cut. Enrollment continued until about trial month 19, and the last tumor assessment in the data is at about trial month 30.
The intervals for median overall survival narrowed from about 17 to 20 months wide at trial month 4 to 2 to 3 months at trial month 19. They contained the observed medians in both arms at trial months 4 and 11 and in arm A at trial month 19. With the full data both intervals are above the observed medians. The forecast median progression-free survival in arm A is above the observed median from trial month 11 onward. The interval excludes the observed median at trial month 19 and with the full data. The interval for median progression-free survival in arm B is below the observed median at trial months 11 and 19 and contains it 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 two trials 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 and death before progression also depend on the latent burden at each point in time. The rows under "current latent burden" show this for each of the two events: 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.