We have developed a pharmacodynamic model to describe tumor growth in patients with mRCC enrolled in the phase 3 RECORD-1 trial. Although RECORD-1 did not have a separate arm in which all patients were administered a 5-mg dose of everolimus, the model was able to detect a difference in the effect of a 5-mg and a 10-mg dose on reducing the size of target lesions by taking into account the dosing histories of individual patients (Figure
1). It is worthy of note that when formulating the model, the effect of 5 mg everolimus was permitted to be less than, equal to, or even greater than the effect 10 mg everolimus. For the vast majority of patients, the model estimated a 10-mg dose of everolimus to be more effective than a 5-mg dose at shrinking their SLD. Our model assessed the effect of dose on growth of target lesions; thus, it did not capture any potential benefit that a reduced dose of everolimus may have on nontarget lesions and/or the prevention of new lesions. Subsequent efforts to model the dose–response of nontarget and new lesions demonstrated a marked difference between placebo and a 10-mg dose of everolimus, but no difference between 5-mg and 10-mg doses of everolimus was detected
. It may be that there is no difference between the two everolimus doses on nontarget and new lesions or that the lack of difference may have been because the measurements of these lesion types were categorical rather than continuous; characterization of the dose–response relationship for these variables requires additional data.
In a typical statistical analysis of a clinical trial, standard techniques such as the log-rank test are performed to compare outcomes in different treatment arms
. These techniques have the advantages of simplicity and a long history of use, but a disadvantage is that information about individual patients is ignored. The nonlinear mixed-effects modeling approach presented here can be used to describe not only the overall population, but also the tumor dynamics of each individual patient. This method offers the possibility to predict clinical observations as a function of time, and enables evaluation of the impact of actual dosing history and individual covariates on the drug effect observed. Modeling a continuous variable (tumor size) has enabled us to quantify a difference in the effect of 10 mg versus 5 mg everolimus, a difference that a coarser approach based on modeling categorical variables, such as RECIST response or PFS, might have missed.
In recent years, an increasing number of reports on modeling tumor dynamics have appeared in the literature and a variety of models have been employed that vary in the following three ways. 1) For placebo-treated patients, tumor growth has been described as linear, exponential, logistic, and/or gompertzian
[19–21, 24]. For the placebo growth model, we note that therapy is generally changed once a patient progresses; thus, the long-term steady state in the gompertz and logistic equations is rarely observed (Figure
1). 2) Furthermore, the drug effect can affect either the growth or decay term in the equation. In our case, we have tried both functional forms, but since they have similar analytic solutions, both describe our data reasonably well. 3) Finally, one can introduce a delay in the time it takes for a drug to affect the tumor
. We found that adding delay between the dose and the drug effect did not significantly improve the model fits, and we note that the time-scale for tumor shrinkage is on the order of months, whereas the terminal half-life of everolimus when dosed at 10 mg daily is around 30 h
, so any delay is likely short compared with the time scales of interest in the study. In future work, we plan to formally compare these different models. It should be noted that multiple models would likely be suitable to describe the data presented herein.
Tumor growth in the majority of RECORD-1 patients was well described by our model, with exceptions observed in <2% of patients. Of these patients (n = 7), 4 displayed initial shrinkage followed by growth over the course of treatment. Because of the small sample size, further modeling of the tumor dynamics in these particular patients was not conducted.
Simulations of tumor size in patients after 1 year of continuous treatment with everolimus show that a significant antitumor effect is achieved with either a 5-mg or 10-mg daily dose, but that a substantially improved response (tumor shrinkage) can be expected in patients receiving the 10-mg daily dose. These results support earlier clinical studies that identified 10 mg daily as the preferred clinical dose based on the complete inhibition of mTOR pathway signaling observed in tumor tissue from patients receiving this dosing regimen
[8, 9, 11]. While our results suggest that, whenever possible, clinical dosing of everolimus should be maintained at 10 mg daily, the model also demonstrates that a reduction in tumor burden compared with placebo can be achieved even in patients who require a dose reduction to 5 mg daily. This observation is noteworthy, as dose reductions to 5 mg daily are an integral part of the clinical strategy recommended by a panel of RECORD-1 investigators for the management of noninfectious pneumonitis (grade 2/3), infection (grade 2/3), stomatitis (grade 3), and metabolic abnormalities (grade 3) that arise as a result of everolimus therapy
To definitively show that a 10-mg dose of everolimus is superior to a 5-mg dose, a clinical trial would be required with 10 mg everolimus and 5 mg everolimus arms that is powered to measure an outcome difference (in PFS or overall survival [OS]) between the two doses. The RECORD-1 trial was not designed to compare these two different treatment arms (5 mg and 10 mg) to placebo, and such a 3-arm trial would have required more patients. Even if such data were available, one would need to consider that dose in the 10 mg everolimus arm might have been reduced in some patients due to AEs. The present analysis allows for the detection of a difference in the target lesion response to the 2 different doses in RECORD-1 by modeling the relationship between the dose given over time and tumor size. Thus, this work complements the initial biomarker analysis
 demonstrating that not only is a 10-mg daily dose of everolimus more effective than a 5-mg daily dose at reducing downstream mTOR signaling, but also that a 10-mg daily dose is more effective than a 5-mg daily dose at shrinking target lesions.