Using Biomarker Thresholds for Phase I Progression Decisions

From a Biomarker Threshold to a Development Decision

A Phase I biomarker can provide evidence that a drug has a biological effect, but a measured change alone does not say whether the effect is large enough to matter for development. A progression rule makes that judgment explicit: it identifies a meaningful response, specifies how much response is required in the intended population, and states how uncertainty and the consequences of a wrong decision will be handled.

Two thresholds must not be confused. The biomarker-response threshold defines the size of change considered biologically meaningful for an individual. A separate progression criterion specifies how much evidence of such responses is needed to proceed. For example, a development team might define a meaningful reduction of at least 20 units, then require evidence that at least 70% of the target population would achieve that reduction at a proposed regimen. The first number defines response; the second governs the decision.

The threshold \(\delta\) should be supported by biological or translational evidence, not selected simply because it makes the observed Phase I results look favorable. Its justification may draw on target engagement, pharmacology, assay characteristics, and the size of effect considered relevant to the next development question. It must also refer to a clear measurement scale and time point. A threshold in absolute units is not interchangeable with one defined as a percentage change, and a transient change at one sampling time does not automatically establish a sustained response.

The response probability is also conditional on context. A probability estimated at one dose, exposure distribution, population, and sampling window should not be presented as though it applies to all doses or populations. These specifications are part of the estimand: they define what the probability describes. Biomarker evidence can inform whether to progress, but by itself does not establish clinical benefit or validate the biomarker as a surrogate endpoint.

Measurement Uncertainty and Response Probability

The observed change is not necessarily the participant's true change. A simple measurement model is \(D_i=\theta_i+\varepsilon_i\), where \(D_i\) is the observed change and \(\varepsilon_i\) is measurement error. If baseline and follow-up assays have independent, unbiased errors with standard deviation \(\sigma_a\), the error standard deviation for their difference is \(\sqrt{2}\sigma_a\). In practice, replicate measurements, assay validation, and the sampling schedule help determine whether that assumption is reasonable.

If the decision concerns the proportion of participants whose true response exceeds \(\delta\), classifying every observed change above \(\delta\) as a true response can misclassify participants near the boundary. One way to account for this is to fit a population response model that separates between-participant variation from assay error. For a simple illustration, suppose true changes at the regimen of interest follow a normal distribution with mean \(\mu\) and between-participant standard deviation \(\tau\). Then:

where \(\Phi\) is the standard normal cumulative distribution function. This formula describes variability in true participant responses, not the spread of uncorrected measurements. Under the model \(D_i=\theta_i+\varepsilon_i\), with independent normal measurement error of standard deviation \(\sigma_m\), the observed-change variance is \(\tau^2+\sigma_m^2\). The model must therefore account for measurement error rather than interpreting all observed variability as true differences between participants.

This calculation assumes the chosen distribution is adequate, the measurement-error model is appropriate, and the fitted parameters apply to the population and regimen being considered. If the response distribution is markedly skewed, has a substantial ceiling effect, or contains distinct subgroups, a single normal distribution may give a misleading tail probability. Diagnostics should include checking model fit, comparing predicted and observed response distributions, and examining whether results are unduly driven by a few participants or by measurements close to the threshold.

Setting and Applying a Progression Criterion

A progression criterion translates the estimated response probability into a decision. A simple rule might require \(p\) to exceed a prespecified minimum \(p_0\). For example, the rule could be to progress only if the estimated probability of a meaningful response is at least 0.70. A point-estimate rule is easy to communicate, but it can be unstable when the sample is small or the estimate is near \(p_0\). A more cautious rule can require the lower limit of an uncertainty interval to exceed \(p_0\), or require a specified probability that \(p\) exceeds \(p_0\). The chosen rule should be set before reviewing the results and its interpretation stated plainly.

Uncertainty in \(p\) matters because the estimated response probability depends on estimated model parameters as well as measurement assumptions. A confidence interval or a resampling interval can express sampling uncertainty under the specified analysis; model-based uncertainty may also be explored by propagating uncertainty in parameter estimates through the response-probability calculation. An interval that spans the progression criterion signals that the decision is sensitive to uncertainty. It does not, on its own, dictate whether the team should progress: that also depends on the decision context and the consequences of errors.

Decision Consequences and Alternative Rules

A fixed probability criterion can be supplemented by considering the consequences of false decisions. A false progression occurs when development proceeds despite inadequate biological activity; a false stop occurs when development is stopped despite adequate activity. If \(p\) is the probability that the activity is adequate, let \(C_{FG}\) be the loss from false progression and \(C_{FS}\) the loss from false stopping. Under a simplified two-state decision model, the expected loss of progressing is \((1-p)C_{FG}\), while the expected loss of stopping is \(pC_{FS}\). Progress when the first is smaller:

This derivation assumes the two states and losses capture the relevant consequences, and that \(p\) is the probability of the adequate-activity state. Real decisions can involve additional evidence, costs, and safety constraints. The result nevertheless shows why a universal probability cutoff is not automatically appropriate: if the cost of false progression is relatively high, the required probability rises. Safety assessment remains a separate, necessary part of a Phase I progression decision.

These approaches answer related but different questions. A responder-proportion rule asks how many participants are expected to cross a meaningful threshold. A mean-response rule asks whether the average change is large enough, but a favorable mean can conceal a mixture of strong responders and participants with little or no response. A threshold on the mean therefore cannot be substituted for a criterion on \(p\). A cost-based rule makes the trade-off between decision errors explicit, but it depends on defensible consequences and a clear definition of adequate activity. Each rule should be aligned with the development question rather than selected for convenience.

Practical diagnostics include checking assay precision and the timing of samples, reviewing the distribution of changes relative to the threshold, evaluating the response model's fit, and assessing how the decision changes under plausible alternative assumptions. A large fraction of measurements near the threshold deserves particular attention because small assay or model changes may alter responder classifications. Missing or mistimed samples can also undermine the estimated response probability if the observed participants do not represent the target population. If results are unstable, report that instability and consider whether additional data or a different analysis is needed; do not adjust the biological threshold after seeing the results merely to obtain a desired decision.

Common Pitfall

Another limitation is that a biologically plausible threshold is not necessarily a clinically validated one. In early development, it may be a useful decision aid for testing a pharmacological hypothesis, but it should not be overstated as proof of clinical benefit. The conclusion should remain scoped to the biomarker, regimen, population, and assessment time actually studied.