Fecal Calprotectin and Relapse in Inflammatory Bowel Disease

Why Relapse Definition and Marker Timing Matter

Fecal calprotectin is a stool biomarker of intestinal inflammation, commonly reported in micrograms per gram. In a study of inflammatory bowel disease (IBD), measurements may be collected repeatedly while patients are in remission, and relapse may occur between scheduled assessments. The statistical question is not simply whether one measurement differs between patients who do and do not relapse. It is how a patient’s evolving marker level relates to their risk of relapse over time, while allowing for measurement error and differences in individual trajectories.

The endpoint must be defined before fitting a model. For example, a study might define relapse as a protocol-specified clinical recurrence confirmed by a clinician, or as a prespecified combination of symptoms and treatment escalation. These are not interchangeable events. If the endpoint definition includes fecal calprotectin itself, an association between calprotectin and relapse can partly arise because the marker is built into the outcome. A useful design therefore states exactly what qualifies as relapse, how the date is assigned, and whether calprotectin contributes to that definition.

A Joint Model for Calprotectin and Relapse

Let \(Y_{ij}\) be the fecal calprotectin measurement for patient \(i\) at time \(t_{ij}\), measured in months from a clearly defined baseline. Because concentrations are positive and often right-skewed, consider \(Z_{ij}=\log(Y_{ij})\), where the logarithm is natural. A linear mixed model can describe the latent mean log concentration:

Here \(D_i(t)\) indicates whether a specified treatment intensification is in effect at time \(t\); the exact coding and effective date must be defined in the analysis plan. The patient-specific random intercept \(b_{0i}\) and random slope \(b_{1i}\) allow baseline levels and trends to vary. A standard working assumption is that the random effects follow a mean-zero multivariate normal distribution with covariance matrix \(G\), and that the measurement errors are independent normal variables with mean zero and variance \(\sigma^2\), conditional on the random effects and included covariates. These assumptions should be checked against the measurement scale and observed trajectory patterns.

Let \(T_i\) be time from baseline to the study-defined relapse, and let \(C_i\) be the censoring time. The observed follow-up time is \(X_i=\min(T_i,C_i)\), with event indicator \(\delta_i=1\) if relapse is observed and \(0\) if the patient is censored first. A current-value association model is:

where \(h_i(t\mid b_i)\) is the instantaneous relapse hazard among patients still relapse-free at \(t\), \(h_0(t)\) is an unspecified baseline hazard, \(W_i(t)\) contains specified baseline or time-varying covariates, and \(m_i(t)\) is the latent log calprotectin mean. The parameter \(\alpha\) describes the association between the latent current log marker and the relapse hazard, conditional on the included covariates and the model. It is not, by itself, a causal effect of changing calprotectin.

This formulation assumes that the marker trajectory relevant to risk is adequately represented by the chosen mean function, that the hazard link is appropriate, and that the event and measurement processes are conditionally independent given the shared random effects and modeled covariates. It also requires a defensible censoring assumption: conditional on modeled information, censoring should not carry additional information about the unobserved relapse time. If visits are missed because a patient is worsening, or because a treatment change prompts extra testing, the observation process may be informative and deserves attention.

Interpreting the Link and Its Derivation

The current-value link gives a direct hazard-ratio interpretation for two latent marker levels at the same time, with the other covariates held fixed. Taking the ratio of their hazards cancels the common baseline hazard. If their latent log concentrations differ by \(\Delta\), the hazard ratio is \(\exp(\alpha\Delta)\). A one-unit increase in log concentration corresponds to multiplying concentration by \(e\), not increasing it by one microgram per gram.

The justification follows directly from the hazard definition. For patients A and B at time \(t\), suppose their covariate values are equal and their latent log-marker values differ by \(\Delta=m_A(t)-m_B(t)\). Then:

This ratio is conditional on the specified model. It does not imply that intervening to lower a patient’s calprotectin by \(\Delta\) would produce that hazard change; treatment, disease severity, and other processes may affect both the marker and relapse.

Treatment Changes, Relapse Dates, and Joint Likelihood

Treatment changes are especially important in IBD. Worsening symptoms or rising calprotectin may prompt intensification, and intensification may then alter subsequent marker values and relapse risk. Including \(D_i(t)\) can describe an adjusted association under the chosen model, but it does not remove confounding by indication automatically. Treatment timing should be recorded, the exposure definition should be explicit, and a coefficient for treatment should not be described as causal without a design and assumptions supporting causal interpretation.

A joint model combines the longitudinal and event information through the shared random effects. In schematic form, a patient’s contribution to the likelihood is obtained by integrating the product of the measurement likelihood and event-time likelihood over the random-effects distribution. For an observed event or censoring time, the event contribution conditional on the random effects is \(h_i(X_i\mid b_i)^{\delta_i}S_i(X_i\mid b_i)\), where \(S_i\) is the conditional probability of remaining relapse-free through \(X_i\). The integration matters: it accounts for uncertainty about each patient’s latent trajectory rather than treating estimated marker values as error-free.

The event date also needs careful handling. If relapse is assessed only at visits, the true event may be known to have occurred between the last relapse-free assessment and the first assessment showing relapse. Assigning the first positive visit as the exact event date can shift event times and distort the hazard analysis. The endpoint protocol should state whether the event is dated at onset, confirmation, or another rule; if only an interval is known, the analysis should reflect interval censoring rather than silently treating the visit date as exact.

Diagnostics, Alternatives, and Limitations

Diagnostics should examine both parts of the model and the link between them. For the longitudinal component, inspect residual patterns, the distribution of residuals, and whether the assumed trajectory captures curvature or abrupt changes. For the event component, assess whether the chosen hazard structure and covariate effects are adequate. Check whether fitted trajectories systematically miss patients with high or low values, whether treatment changes coincide with unexpected residual patterns, and whether estimates are sensitive to influential patients or sparse measurements near relapse.

The current-value link is one choice, not a universal biological law. A slope association asks whether the rate of marker change is related to hazard; an accumulated exposure link asks about a summary of prior trajectory. These alternatives answer different questions and require their own specification and justification. A separate survival model using only baseline calprotectin is simpler, but discards later measurements. A model using the most recent observed measurement is also simpler, but treats that noisy value as the risk predictor and may handle irregular visits or measurement error poorly. Joint modeling can address the shared trajectory and event process under its assumptions, but is more computationally demanding and can be sensitive to misspecified trajectory, association, or observation models.

A practical failure mode is circularity: if relapse is defined partly by a calprotectin threshold and the same measurements predict relapse, the apparent predictive relationship may be strengthened by construction. Another is informative monitoring: patients with suspected worsening may be tested more often, so observed measurement times are not merely administrative. Finally, a shared-parameter joint model does not automatically account for every source of dependence, treatment confounding, competing events, or informative dropout. Its estimates should be reported with the endpoint definition, units, time origin, treatment coding, and assumptions.