This study was conducted at the Netherlands Cancer Institute-Antoni van Leeuwenhoek hospital (NKI-AvL), Amsterdam, The Netherlands. Patients were included in this study if they were treated with alectinib, if they started treatment between February 2017 and December 2021, and if pharmacokinetic data were available. At the NKI-AvL, plasma samples of patients receiving alectinib were collected during routine follow-up visits to the outpatient clinic as part of the standard of care. In the majority of the cases, the collected plasma samples could not be considered to be trough concentrations, as this is often not feasible to arrange in clinical practice. Therefore, date and time of the last drug intake and plasma sampling were used to calculate trough concentrations of alectinib using log-linear extrapolation in which a plasma elimination half-life of 32 h was used [13]. Plasma concentrations were measured by validated liquid chromatography with tandem mass spectrometry detection [14].

Patient characteristics and survival outcomes were extracted from the electronic medical records, whereas data on plasma samples were extracted from the laboratory database. The conduct of this study was approved by the Investigational Review Board of the NKI-AvL and the need for written informed consent was waived.

Alectinib plasma trough concentrations were transformed to normalize the data as this is one of the assumptions of linear mixed effects models [15]. In addition, exposure–response relationships are usually described by the sigmoid Emax model, in which a certain drug exposure corresponds non-linearly to a certain drug effect. In these type of models, the response reaches a plateau above a certain exposure, as one can imagine that an alectinib trough concentration of 1000 ng/mL does not result in double the response compared to an alectinib trough concentration of 500 ng/mL. Alectinib plasma trough concentrations were normalized by transformation into transformed trough concentrations (TTC) using this equation:

$$TTC =\frac^}^+ ^}\times 100$$

Ctrough is the alectinib trough concentration, EC50 is the alectinib trough concentration that represents the center of the sigmoid curve, and γ is curve-fitting parameter, describing the steepness of the concentration-effect relationship. The EC50 was set at 600 ng/mL, which is slightly above the target trough concentration of 435 ng/mL used in other studies [16]. Above 600 ng/mL, the TTC increases less than proportional with the trough concentration compared to trough concentrations under 600 ng/mL. Lastly, γ was empirically fixed to ensure that the resulting TTC approximately follows a normal distribution. The factor 100 in the formula ensures that the TTC takes values between 0 and 100, enhancing the interpretability of the results of the Cox models and joint models. The resulting sigmoid curve describing the relationship between the alectinib trough concentration and TTC is shown in the supplementary materials.

The survival outcome was progression-free survival (PFS), which was defined as the time from treatment initiation until the first signs of disease progression by either radiology or clinical signs, or death by any cause in the absence of progression. PFS was estimated using the Kaplan–Meier method and the median follow-up time was estimated with the reverse Kaplan–Meier method [17].

Variables taking into account were weight, sex, previous number of treatment lines, the use of previous ALK inhibitors (e.g. crizotinib and ceritinib), ECOG performance status and the presence of brain metastases at baseline and alectinib dose at time of plasma sampling. Except for weight, all covariates were used as categorical variables with no order.

Joint models consist of two sub-models that are then joined together: a linear mixed effects model and a Cox proportional hazards model.

The linear mixed effects model was used to fit the longitudinal data, in which covariates at baseline and time of plasma sampling were tested on their association with the TTC of alectinib as longitudinal outcome measurements. Subject level random effects for both the intercept and slope were added to cluster the outcome measurements within subjects together, as the linear mixed effects model assume variability in measurements within subjects to be smaller than variability in measurements between different subjects [15]. A Cox proportional hazards model was used to fit the second sub-model using the time-to-event data. Using this sub-model, the association between baseline covariates and PFS were estimated [12, 18].

Lastly, the joint model was fitted using the two sub-models to estimate the association between the longitudinal TTC of alectinib and PFS. In the joint model, the complete trajectory of the TTC is estimated for each individual patient using the included covariates in the first sub-model and the actual TTC measurements. This trajectory of the TTC is then associated with the hazard, i.e. the risk of experiencing an event at a specific time point, in the second sub-model. Via this hazard, the association between the longitudinal measurements of TTC and PFS were determined.

Joint models with different functional forms were tested [18]. These functional forms describe the association structure between the historic trajectory of the TTC of alectinib and the hazard for progression. The basic association structure is to relate the estimated TTC at the time of the most recent measurement, directly to PFS, in which all historic TTCs are used to estimate the current TTC. Using other functional forms, it is possible to associate the average TTC of alectinib, which is the area under the historical TTC trajectory divided by the time, with PFS. In addition, it is possible to combine different association structures together in one joint model. In this study, joint models with the current value, the average exposure and the combination of these two functional forms were tested. In case functional forms are combined, separate hazard ratios are estimated for each functional form. Another functional form is the time-dependent slope of the TTC of alectinib, i.e. how fast the TTC decreases or increases at the time of most recent measurement. Joint models using the time-dependent slope as association structure were not performed in this study as this approach does not reflect the mechanism of action of oral targeted anticancer agents and is more suited for biomarkers. The Watanabe-Akaike information criterion (WAIC) was used to select the best model, in which smaller values are preferred as this indicates better models. Joint models were fitted using the JMbayes2 package in R version 4.3.1 (R Foundation for Statistical Computing, Vienna, Austria). In order to assess the dependence of our results on the precise form of the sigmoid curve used to transform the trough concentrations, a sensitivity analysis was performed for the joint model with the best association structure, in which the EC50 was set at 500 and 700 ng/mL and the γ was set at 2.

In addition to the joint models, basic Cox proportional hazards models were fitted on the same dataset using the median TTC for each patient as a numerical variable and as a categorical variable. In the model with TTC as a categorical variable, patients were divided into two groups describing whether the median exposure of each patient was adequate or inadequate (reference group) based on the target trough concentration of 435 ng/mL. Similarly, the corresponding time-dependent Cox proportional hazards models were also fitted, as this is the traditional approach to study the association between repeated measurements and the occurrence of an event over time. For the time-dependent Cox proportional hazards models, the time-dependent variable was assumed constant in the time period after the measurement, i.e. the last value was carried forward. The backward elimination procedure was used to determine which covariates are kept in the Cox proportional hazards models. A p-value <0.05 was considered statistically significant.