Baseline-Dependent Biomarker Effects

Why Baseline Can Change an Exposure-Response Interpretation

A biomarker measured before dosing can help explain why participants have different responses. It can also make a drug effect appear different across participants: the same exposure may be associated with a larger response at one baseline value than at another. But a relationship between baseline and subsequent change is not, by itself, evidence that the drug works differently by baseline. Participants selected for unusually high or low measurements often have less extreme subsequent measurements even without treatment. This is regression to the mean.

The key is to distinguish three questions: does baseline predict the subsequent biomarker outcome; does baseline modify the exposure-associated effect; and how much of the observed baseline-change relationship could arise from measurement and natural variation alone? The model and the study design determine which of these questions the data can answer.

A Model That Separates Baseline Association From Effect Modification

For a specified post-baseline assessment, let \(E_i\) denote a relevant exposure summary for participant \(i\), and let \(\Delta Y_i\) denote the change from the observed baseline value to the post-baseline biomarker value. One useful model is

Here \(B^*\) and \(E^*\) are chosen reference values, often values near the center of the observed data. The parameter \(\alpha\) is the expected change at those reference values. The baseline coefficient \(\beta_B\) is the baseline association with change when exposure equals \(E^*\). The exposure coefficient \(\beta_E\) is the exposure slope at baseline \(B^*\). The interaction coefficient \(\beta_{BE}\) describes how that exposure slope changes for each one-unit increase in baseline.

The model makes its central interpretation explicit. At baseline \(b\), the expected difference in change between exposures \(e_1\) and \(e_0\) is

Thus \(\beta_{BE}\), not \(\beta_B\) alone, represents baseline dependence of the modeled exposure contrast. If \(\beta_{BE}=0\), the exposure contrast is constant across baseline values under this model, even if baseline strongly predicts change. Conversely, a nonzero interaction is meaningful only over baseline and exposure values with adequate data support; it should not be interpreted as proof of a biological mechanism.

The model assumes the conditional mean is adequately represented by the stated linear terms over the range used for interpretation. Its residual and dependence structure must also reflect the data. If several post-baseline measurements per participant are modeled, those observations are correlated; the analysis must account for within-participant dependence, as in repeated biomarker modeling. The single-assessment equation above describes a conditional mean, not an assumption that all observations are independent in a repeated-measures data set.

Why Baseline and Change Can Be Negatively Associated

Regression to the mean can create an apparent negative association between baseline and change without any drug effect that depends on baseline. A simple measurement model makes the mechanism precise. Suppose a participant has a stable underlying biomarker level \(X_i\), but the baseline measurement contains error \(e_{0i}\), so \(B_i=X_i+e_{0i}\). Assume \(X_i\sim N(\mu,\sigma_X^2)\), \(e_{0i}\sim N(0,\sigma_e^2)\), and that \(X_i\) and \(e_{0i}\) are independent. Also assume an untreated follow-up measurement is \(Y_{1i}=X_i+e_{1i}\), where \(e_{1i}\) has mean zero and is independent of \(X_i\) and \(e_{0i}\). The normality assumption for baseline measurement error is important: independence and variances alone do not establish the conditional-mean formula below.

When measurement error is present, \(0<\lambda<1\). An observed baseline above \(\mu\) therefore predicts a negative untreated change in this simplified stable-level model, and a baseline below \(\mu\) predicts a positive change. If the biomarker has a genuine untreated time trend, the formula must be extended to include that trend; it should not be treated as a universal prediction for every study.

Baseline Imbalance Can Reverse a Crude Comparison

In early-phase studies, exposure may differ across dose cohorts, and baseline distributions can differ as well. A crude comparison of mean change between exposure groups then mixes the exposure contrast with the baseline association. The following example separates those pieces algebraically.

Model Choices, Diagnostics, and Limits

Change-from-baseline models are convenient when the scientific quantity is change, but baseline appears both as a predictor and in the calculated outcome. This mathematical coupling can contribute to a negative baseline-change association. An alternative is to model the post-baseline biomarker as the outcome and include measured baseline as a covariate. That avoids subtracting baseline to form the outcome, but it does not eliminate measurement error, regression to the mean, or the need to model baseline-by-exposure effect modification when that is the question. The two approaches target related but not automatically identical quantities; the outcome, estimand, and assumptions should be stated.

A model with baseline as a main-effect covariate adjusts the expected outcome for baseline but does not allow the exposure contrast to vary with baseline. Adding a baseline-by-exposure interaction makes that variation estimable, at the cost of additional parameters and greater data requirements. Dividing baseline into categories can make summaries easy to display, but discards information and makes results depend on cut points. If the relationship is not plausibly linear, a more flexible form may be needed; a fitted linear interaction should not be extrapolated beyond observed baseline and exposure ranges.

Useful checks include plotting change against baseline separately across exposure ranges, checking whether the estimated exposure contrast is supported by participants at comparable baseline values, and examining residual patterns for curvature or unequal spread. Investigate the baseline assay's repeatability and collection conditions: a highly noisy single measurement can make baseline effects difficult to interpret. A strong negative association between baseline and change is not a diagnostic proof of regression to the mean, just as an interaction estimate is not proof of biological effect modification.

Interpretation also depends on design. Placebo or time-course controls can help distinguish drug-associated change from untreated evolution, while exposure comparisons in nonrandomized or sequential cohorts can be confounded by cohort differences. A statistical interaction describes how the modeled association changes; causal claims require defensible assumptions about treatment or exposure assignment and relevant confounding. Finally, a baseline-dependent biomarker response alone does not establish why the response varies or what it implies about a biological target.