zahrcast
zahrcast
The case study1 pools the gemcitabine arms of two historical trials in metastatic pancreatic cancer, VANILLA and CO-1.01, with the gemcitabine arm of a target trial, MPACT. It forecasts the target arm's results at three cut-offs: trial months 5, 14 and 24. Only the gemcitabine arm of MPACT is available, so the forecasts cover one arm. Sia learns the latent burden here from two markers. One is tumor size, the sum of target lesion diameters, measured at scans about every 8 weeks. The other is the blood marker CA19-9, drawn every 4 to 8 weeks. Both markers follow the one latent burden, and each has its own level and noise. CO-1.01 released no tumor sizes, so its patients enter the fit through CA19-9 alone. Progression is each trial's own investigator assessment. The data do not include enrollment dates, so the target trial's enrollment is simulated, spread evenly over about 30 months, and the cut-offs are set on that simulated calendar. 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 two markers, tumor size from scans and the blood marker CA19-9. The current burden changes the hazard of progression. The baseline characteristics change the hazard of every transition, 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 | progressionprogression-free → progressed, by the investigator's assessment | At a scan. The date falls between two scans. | Current burden, baseline characteristics |
| 2 | death before progressionprogression-free → deceased | Exact date | Baseline characteristics |
| 3 | death after progressionprogressed → deceased | Exact date. The clock restarts at progression. | Baseline characteristics |
Age and sex are the only baseline characteristics all three trials record. For CO-1.01, which released no tumor sizes, the baseline tumor size is imputed from them.
Patients at 2 U/mL or less of CA19-9 at baseline give no CA19-9 readings.
Each transition's base hazard is estimated in 4-week steps. Progression-free survival ends at transition 1 or 2. Overall survival ends at transition 2 or 3.
MPACT, the gemcitabine arm.
The gemcitabine arms of VANILLA and CO-1.01.
Sia fits the target and historical trials together. They share the population-level parameters and the patient-level spread.
Each trial has its own level for every burden parameter, every transition and the CA19-9 baseline. Each patient also has their own term for each burden parameter.
Forecasts of tumor size and CA19-9 for 6 target-trial patients who had not progressed at their last reading. Each panel has two rows on the same follow-up axis: tumor size in mm above, and CA19-9 in U/mL on a logarithmic scale below. Each row has its own vertical line at that measure's last reading, because scans and blood draws fall on different weeks. Up to that line, the median and 80% interval are Sia's fit to the readings in hand. After it they are a forecast. The tumor size forecast runs 52 weeks from the last scan, and the CA19-9 forecast stops at the same point. Each row's scale stops at 100 times the top of the patient's fitted interval, so a forecast that rises past that runs off the top of the row. This model gives no probability that a patient is still progression-free, so the forecast does not fade.
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, and the same 20 draws appear in both rows. A draw that runs above the top of a row is cut at its edge. The posterior sample holds 6 target-trial patients who had not progressed, have at least 2 scans after baseline and have CA19-9 readings, so the panels show all six. The panel titles name the pick rules used on the other case studies, which here only set the order: the two whose fitted tumor size fell the most relative to baseline, the two whose tumor size fell the least, and the two with the largest forecast rise.
Target-trial accrual by trial month on the simulated enrollment calendar. The upper panel counts patients enrolled and, separately, patients with at least one scan or CA19-9 reading after baseline. A patient enters the forecast only after their first such reading, so at trial month 14, 185 patients had enrolled and 146 were included. The lower panel counts scans and CA19-9 readings. Dots mark the cut-offs at trial months 5, 14 and 24, when 32, 146 and 267 patients had a reading. The counts are by month. The enrollment dates are simulated, so the timing in this chart is not the trial's own.
Each cut-off is a separate fit that uses only the data available at that date. It forecasts survival in the target arm for the patients who have had at least one scan or CA19-9 reading 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 of 6.6 months at trial months 5 and 14 and with the full data, and was above it at trial month 24. The interval was 3.1 months wide at trial month 5 and 0.3 months wide at trial month 24. For progression-free survival, the interval contained the observed median of 3.5 months at every cut-off and with the full data.
The page uses two time scales. Cut-offs are in trial months on the simulated enrollment calendar. The charts are in follow-up months, counted from each patient's enrollment. At trial month 5, no patient has more than 5 months of follow-up.
Trial month 5, 32 patients. The 90% interval for median overall survival runs from 5.1 to 8.2 months and contains the observed median of 6.6 months. The interval for median progression-free survival runs from 3.2 to 4.8 months and contains the observed 3.5 months.
Trial month 14, 146 patients. The interval for median overall survival is 1.1 months wide and contains the observed median. The interval for median progression-free survival runs from 3.40 to 3.55 months and contains the observed median.
Trial month 24, 267 patients. The interval for median overall survival runs from 6.67 to 6.99 months, above the observed 6.60 months. The interval for median progression-free survival runs from 3.45 to 3.54 months and contains the observed median.
Full data, 403 patients. The interval for median overall survival runs from 6.52 to 6.65 months and contains the observed median. The interval for median progression-free survival runs from 3.48 to 3.50 months and contains the observed 3.49 months.
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Overall and progression-free survival for the target trial's gemcitabine arm. 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.
The enrollment dates are simulated, so the trial months on this page are not the trial's own. On the simulated calendar, enrollment ends at trial month 30, and the last reading in the data is at about trial month 52.
The intervals for median overall survival narrowed from 3.1 months wide at trial month 5 to 0.3 months at trial month 24. They contained the observed median at trial months 5 and 14 and with the full data, and were above it at trial month 24. The interval for median progression-free survival contained the observed median at every cut-off and with the full data. The observed medians are themselves estimates with their 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 arm of one trial and should be checked on a sponsor's own data before they are applied elsewhere.
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 only baseline characteristics all three trials record are age band and sex. The latent burden panels show the rate at which the burden shrinks and regrows and the share of the burden that shrinks. The baseline tumor size panel shows how the model sets the starting tumor size of a patient with no tumor sizes, which here means the CO-1.01 patients. 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 also depends on the latent burden at each point in time. The rows under "current latent burden" show this: the burden in the shrinking and regrowing parts, and their shrink and regrowth rates. Death before and after progression do not depend on the latent burden in this model.
The last panel is the elasticity of CA19-9. It is the change in log CA19-9 for a change in the log latent burden. An elasticity of 1 means CA19-9 changes by the same proportion as the burden.
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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. The elasticity is on its own scale, starting at 0. Hover over a characteristic to highlight it across the panels.