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zahrcast
The case study1 pools the placebo and docetaxel arms of two historical trials in metastatic castration-resistant prostate cancer, VENICE and MAINSAIL, with the placebo and docetaxel arm of a target trial, ENTHUSE-33. It forecasts the target arm's results at three cut-offs: trial months 7, 19 and 31. Only the control arm of each trial is available, so the forecasts cover one arm. Sia learns the latent burden here from PSA in place of tumor size, measured about every 3 weeks. Progression is the target trial's composite of pain progression, skeletal-related events, new bone lesions and soft-tissue progression on imaging. 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 one marker, PSA. The current burden changes the hazard of both progression routes. Progression has two states, clinical and imaging, and each has its own transition to death. 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 | clinical progressionprogression-free → clinical progression: pain progression, opioid start, radiotherapy for pain or a skeletal-related event | At a 3-weekly visit | Current burden, baseline characteristics |
| 2 | imaging progressionprogression-free → imaging progression: soft-tissue progression or new bone 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 | death after clinical progressionclinical progression → deceased | Exact date. The clock restarts at progression. | Baseline characteristics |
| 5 | death after imaging progressionimaging progression → deceased | Exact date. The clock restarts at progression. | Baseline characteristics |
Transition 2 can only be recorded at a trial's own scans. ENTHUSE-33 scans at weeks 24 and 48, VENICE about every 12 weeks and MAINSAIL every 9.
PSA progression itself is not a transition in the model.
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, 4 or 5.
ENTHUSE-33, the placebo and docetaxel arm, 436 patients.
The placebo and docetaxel arms of VENICE and MAINSAIL.
Sia fits the target and historical trials together. They share the population-level parameters and the patient-level spread.
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 PSA for 6 target-trial patients who had not progressed at their last PSA reading. Up to a patient's last reading, marked by the vertical line, the median and 80% interval are Sia's fit to the readings in hand. After it they are a forecast, shown for 52 weeks. The vertical scale is logarithmic, and each panel has its own scale, which stops at 100 times the top of the patient's fitted interval. A forecast that rises past that runs off the top of the panel. 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. A draw that runs above the top of a panel is cut at its edge. The six patients are the two whose PSA fell the most relative to baseline, the two whose PSA fell the least, and, of the remaining patients, the two with the largest forecast rise. The trial has one arm here, so it gets all six panels. These picks span the range of responses and are not a random sample.
Target-trial accrual by trial month on the simulated enrollment calendar. The upper panel counts patients enrolled and, separately, patients with at least one PSA reading after baseline. A patient enters the forecast only after their first reading after baseline, so at trial month 19, 264 patients had enrolled and 257 were included. The lower panel counts PSA readings. Dots mark the cut-offs at trial months 7, 19 and 31, when 97, 257 and 435 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 PSA 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 18.6 months at every cut-off and with the full data. The interval was 10.4 months wide at trial month 7 and 2.2 months wide at trial month 31. For progression-free survival, the interval contained the observed median of 6.9 months at trial month 7, was above it at trial months 19 and 31, and was below it 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 7, no patient has more than 7 months of follow-up.
Trial month 7, 97 patients. The 90% interval for median overall survival runs from 15.1 to 25.5 months and contains the observed median of 18.6 months. The interval for median progression-free survival runs from 6.90 to 9.08 months and contains the observed 6.93 months.
Trial month 19, 257 patients. The interval for median overall survival is 4.5 months wide and contains the observed median. The interval for median progression-free survival runs from 7.2 to 7.9 months, above the observed median.
Trial month 31, 435 patients. The interval for median overall survival is 2.2 months wide and contains the observed median. The interval for median progression-free survival runs from 7.4 to 7.8 months, above the observed median.
Full data, 436 patients. The interval for median overall survival runs from 18.3 to 19.2 months and contains the observed median. The interval for median progression-free survival runs from 6.58 to 6.90 months, below the observed 6.93 months.
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Overall and progression-free survival for the target trial's control 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 31, and the last PSA reading in the data is at about trial month 59.
The intervals for median overall survival narrowed from 10.4 months wide at trial month 7 to 2.2 months at trial month 31, and contained the observed median at every cut-off. The interval for median progression-free survival contained the observed median at trial month 7, was above it at trial months 19 and 31, and was below it with the full data. 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 the control 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 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. The model has two progressed states, clinical (pain progression or a skeletal-related event) and imaging (soft-tissue progression or new bone lesions), each with its own transition to death. All effects are per standard deviation of the characteristic, from the fit to the full data.
Both progression routes also depend on the latent burden at each point in time. The rows under "current latent burden" show this for each route: 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 PSA or rate. Event panels show hazard ratios on a log scale. Hover over a characteristic to highlight it across the panels.