Prostate Radiotherapy in Low-Burden STAMPEDE Metastatic Disease

Why Metastatic Burden Changes the Question

STAMPEDE’s prostate-radiotherapy comparison asks whether treating the primary prostate tumour improves outcomes for men with newly diagnosed metastatic prostate cancer. Its overall-survival result and its low-metastatic-burden result answer related but distinct questions. The overall estimate summarizes the randomized comparison across all eligible metastatic participants; the subgroup estimate asks whether the effect differs among men classified as having low metastatic burden.

The distinction matters because the overall result did not show a statistically significant survival benefit, while the low-burden subgroup showed evidence of longer survival with radiotherapy. Neither finding should be substituted for the other. The all-participant estimate does not establish that every subgroup has the same effect, and a favorable subgroup estimate does not mean the overall trial was positive.

Participants were randomly assigned to standard care with or without prostate radiotherapy. The principal survival outcome discussed here is overall survival (OS), the time from randomization until death from any cause. A hazard ratio (HR) compares the instantaneous event rates between groups over follow-up, among participants still at risk. An HR below 1 favors radiotherapy for mortality, under the stated comparison, but is not itself a ratio of survival probabilities.

The Overall Result and the Low-Burden Result

In STAMPEDE, the overall OS estimate for prostate radiotherapy was HR 0.92, with a 95% confidence interval (CI) of 0.80 to 1.06 and \(p=0.266\). The point estimate corresponds to an estimated 8% lower mortality hazard in the radiotherapy group. However, the interval includes 1, so the data are compatible with effects ranging from a 20% lower hazard to a 6% higher hazard. The result does not provide statistically significant evidence of an OS benefit across all participants at a conventional 0.05 significance level.

Among participants with low metastatic burden, the reported OS HR was 0.68 (95% CI 0.52 to 0.90; \(p=0.007\)). This estimate corresponds to a 32% lower mortality hazard with radiotherapy. The confidence interval is compatible with a hazard reduction between 10% and 48%. The study also reported estimated 3-year survival of about 81% with radiotherapy and 73% without it in this subgroup, an absolute difference of approximately 8 percentage points. These survival percentages and the HR summarize different aspects of the data: the former compare estimated survival at a particular time, while the latter compares hazards over follow-up.

Interpreting the Subgroup Evidence

The low-burden estimate is clinically important, but subgroup interpretation requires more than noticing that one subgroup’s \(p\)-value is below 0.05. A subgroup result estimates the treatment effect within that subgroup. A treatment-by-subgroup interaction asks a different question: is the treatment effect itself different between burden groups? In STAMPEDE, the reported evidence that the OS treatment effect differed by metastatic burden had an interaction \(p\)-value of 0.0098.

A significant result in one subgroup and a non-significant result in another does not, by itself, establish an interaction. The difference between “statistically significant” and “not statistically significant” is not automatically statistically significant. The formal interaction test evaluates the contrast between subgroup-specific treatment effects.

One way to express the interaction is to compare log hazard ratios. If \(\beta_L=\log(HR_L)\) is the low-burden treatment effect and \(\beta_H=\log(HR_H)\) is the high-burden treatment effect, then the interaction contrast is \(\Delta=\beta_L-\beta_H\). Under independent subgroup estimates, its standard error is \(SE(\Delta)=\sqrt{SE(\beta_L)^2+SE(\beta_H)^2}\). A test of \(H_0:\Delta=0\) assesses whether the log HRs differ. In a trial analysis, the interaction is typically estimated within a survival model; the reported test, rather than an informal comparison of subgroup \(p\)-values, is the relevant evidence.

A Wald Calculation and What It Does—and Does Not—Show

For a log hazard ratio estimate \(\hat\beta=\log(\widehat{HR})\) with estimated standard error \(SE(\hat\beta)\), a Wald statistic for \(H_0:\beta=0\) is \(z=\hat\beta/SE(\hat\beta)\). Under the null and the large-sample approximation, this statistic is approximately standard normal. A two-sided \(p\)-value is \(2P(Z\geq |z|)\), where \(Z\sim N(0,1)\). The corresponding approximate 95% CI on the log scale is \(\hat\beta\pm1.96SE(\hat\beta)\); exponentiating both endpoints returns an interval for the HR.

The Wald calculation relies on a suitable large-sample approximation and an estimated standard error appropriate to the survival model. The interpretation of an HR as a reasonably stable relative hazard over follow-up also relies on the proportional-hazards assumption. If treatment effects vary substantially over time, one HR may conceal that pattern; survival curves and time-specific estimates then provide useful context. Censoring must also be handled appropriately: the survival analysis assumes that censoring is non-informative, at least conditional on the variables included in the model.

What the Result Supports, and Its Limits

Randomization supports a causal comparison of assigned treatment strategies within the trial population, subject to issues such as adherence, outcome ascertainment, and missing follow-up. It does not make every subgroup comparison equally precise. Subgroups contain fewer participants and events than the full trial, so their estimates are generally less precise. The low-burden finding is strengthened by the reported interaction evidence, but it remains evidence from a subgroup analysis in a defined clinical setting.

The burden classification depends on imaging and the trial’s stated criteria. A different imaging method or a population with different patterns of disease could classify participants differently. The findings concern men with newly diagnosed metastatic disease in the trial’s treatment context; they should not automatically be extended to all men with metastatic prostate cancer, including those whose disease became metastatic later. The absolute survival difference is also tied to the follow-up period and background care in the trial. If systemic treatment and prognosis change, the absolute benefit may change even if a relative treatment effect were similar.

A common mistake is to describe HR 0.68 as “32% more men survived” or as an individual patient’s probability of benefit. The correction is that it is an estimated 32% lower instantaneous mortality hazard in the low-burden group, subject to the survival model and its assumptions. A second mistake is to call the overall trial positive because the subgroup \(p\)-value is significant. The correction is to report both the overall result and the subgroup evidence, specifying the population and outcome each describes.