Marginal structural models with dose-delay joint-exposure for assessing variations to chemotherapy intensity

Abstract

Marginal structural models are causal models designed to adjust for time-dependent confounders in observational studies with dynamically adjusted treatments. They are robust tools to assess causality in complex longitudinal data. In this paper, a marginal structural model is proposed with an innovative dose-delay joint-exposure model for Inverse-Probability-of-Treatment Weighted estimation of the causal effect of alterations to the therapy intensity. The model is motivated by a precise clinical question concerning the possibility of reducing dosages in a regimen. It is applied to data from a randomised trial of chemotherapy in osteosarcoma, an aggressive primary bone-tumour. Chemotherapy data are complex because their longitudinal nature encompasses many clinical details like composition and organisation of multi-drug regimens, or dynamical therapy adjustments. This manuscript focuses on the clinical dynamical process of adjusting the therapy according to the patient's toxicity history, and the causal effect on the outcome of interest of such therapy modifications. Depending on patients' toxicity levels, variations to therapy intensity may be achieved by physicians through the allocation of either a reduction or a delay of the next planned dose. Thus, a negative feedback is present between exposure to cytotoxic agents and toxicity levels, which acts as time-dependent confounders. The construction of the model is illustrated highlighting the high complexity and entanglement of chemotherapy data. Built to address dosage reductions, the model also shows that delays in therapy administration should be avoided. The last aspect makes sense from the cytological point of view, but it is seldom addressed in the literature.

Keywords: Causal inference; bivariate exposure; marginal structural models; osteosarcoma; therapy delay.

Figure 1.

Illustration of the Euramos-1 preoperative treatment (a). Example patient (b) experienced a delay of one week in cycle 1 and a discontinuation of the second MTX course and a delay of 18 days in cycle 2.

Figure 2.

CONSORT-like diagram illustrating selection of patients.

Figure 3.

Event/censoring time (red and blue, respectively) for the subjects with both HRe and surgery date missing. The dashed line marks 77 days from registration, i.e. the nominal surgery time; all event/censoring times lie beyond it.

Figure 4.

Standardised dose of DOX plus CDDP against standardised dose of MTX. Points lying between the two horizontal (resp. vertical) dotted lines correspond to an administered dose of DOX + CDDP (resp. MTX) within 5% from the intended dosage. Points are coloured in red/blue depending on whether, according to the chemotherapy-registration-form dedicated field, at least a toxicity caused a delay/reduction. On the right part of the lower subfigure, it is possible to notice two groups of patients who received one and two extra courses of MTX.

Figure 5.

RDI of MTX against standardised dose of MTX. A cycle lasted less than expected for subjects above the solid line and more than expected (delay) for subjects below it.

Figure 6.

Direct Acyclic Graph (DAG) for the causal relationships between exposure and confounders in Euramos-1.

Figure 7.

Stacked bar-chart of the preoperative CTCAE grades for each class of toxicity.

Figure 8.

Diagnostic boxplot of subject-specific weights computed via equation (6). The scale on the y-axis is logarithmic. The left boxplot corresponds to the terms with k = 1 only, while the right one corresponds to the full product.