Data source: PRODIGE 9 trial
PRODIGE 9 is an open label randomized phase 3 maintenance trial [
6,
24]. The trial randomized 494 patients newly diagnosed with a histologically proven, unresectable metastatic colorectal cancer (mCRC), between March 2010 and July 2013, in one of the 66 participating centers in France. Inclusion criteria included life expectancy greater than 3 months, and no previous chemotherapy or anti-angiogenic therapy for metastatic disease. Consenting participants were first stratified according to: study site, previous primary tumor resection and Köhne prognostic classification (good, intermediate or poor), and then assigned, within each stratum, to either the maintenance or the CFI arm, using simple 1:1 randomization [
6].
The original aim was to compare (a) bevacizumab during CFI versus (b) no treatment during CFI after an induction sequence with FOLFIRI (folinic acid, 5-fluoro-Uracile and irinotecan) combined with bevacizumab (5 mg/kg every 2 weeks). The main outcome was tumor control duration, defined as the time to tumor progression (diagnosed on CT-scan according to the Response Evaluation Criteria in Solid Tumors) during a sequence of chemotherapy [
6]. Patients who died without progression were censored.
The induction sequence lasted 12 treatment cycles (24 weeks), followed by a CFI whose length was determined by the clinical state of individual patients [
6]. For both groups, a new sequence of chemotherapy of 16 weeks (8 treatment cycles) began after the CFI in case of progression or investigator-based decision. Patients underwent CFI and chemotherapy alternatively until they left the study protocol [
6].
Outcomes that occurred until December 2016 were include in the study. Sociodemographic characteristics, tumor characteristics (localization, size, primitive tumor resection, KRAS, NRAS and BRAF status) were assessed at randomization. A standard examination (including WHO Performance Status (PS) and biological samples) associated with a CT scan to assess signs of progression according to RECIST criteria [
25], and toxicity evaluation were repeated every 8 weeks during the treatment protocol [
6]. The reported ITT analyses yielded generally negative results with no evidence of systematic differences in median tumor control duration (HR=1.07 for maintenance with the control arm as reference; 95%-CI=0.85–1.34;
p=0.57], progression free survival (HR=0.91; 95%-CI=0.76–1.09;
p=0.316) or overall survival (HR=1.07; 95%-CI=0.88–1.29;
p=0.500) [
6]. The original PRODIGE 9 trial was approved by the Committee for the Protection of Persons Ile de France VIII and was registered on clinicaltrials.gov (NCT00952029) [
6].
Statistical analysis
Our re- analyses of PRODIGE9 data relied on statistical methods for survival (time-to-event) analyses, and used death of any cause as the endpoint. Because the PRODIGE 9 protocol did not differ between the two groups during the initial 6-month induction sequence [
6], we shifted time 0 (baseline) to 6 months after randomization, the expected date of the beginning of the first CFI. Accordingly, our analyses were limited to only those patients who remained alive until 6 months post-randomization. The main objectives of the re-analyses was to explore potential benefits of using time-varying exposure metrics and accounting for possibly cumulative effects of bevacizumab treatment. To this end, we compared how the estimated associations with the overall survival varied across five alternative time-varying bevacizumab exposure metrics, included in multivariable Cox proportional hazards (PH) model and its flexible extensions [
22], using either the exposure to bevacizumab administered only during CFI (CFI exposure) or exposure during all the study protocol including in the induction sequence (overall exposure). We then contrasted their results with the conventional ITT analysis that defined a time-invariant exposure as binary indicator of randomization group (model 1).
Models 2a (for CFI exposure) and 2b (for overall exposure) defined the time-varying metric as a continuous variable (CE) representing the updated current value of the cumulative administrated dose at any time t, calculated as the sum of all doses received until a given time
t:
$$ {CE}_i(t)={\sum}_{t_0<\dots <{t}_k<\dots <t}^t{X}_i\left({t}_k\right) $$
(1)
with Xi(tk), the dose received at time tk by patient i; t0, the time of origin;
Models 3a (for CFI exposure) and 3b (for overall exposure) relied on a categorical variable (CEQ), defined by quantiles of the distribution of the cumulative dose
CEi(
t) in [1].
$$ {\mathrm{C}\mathrm{EQ}}_{\mathrm{i}}\left(\mathrm{t}\right)={\sum}_{\mathrm{k}=1}^{\mathrm{p}}\mathrm{k}\times {\mathrm{I}}_{\left\{\mathrm{E}{\mathrm{C}}_{\mathrm{i}}\left(\mathrm{t}\right)\in {\mathrm{A}}_{\mathrm{k}}\right\}} $$
(2)
with Ak corresponding to the keme quartile range for p=4 (keme tertile range for p=3, respectively).
Model 3a consisted in five categories corresponding to (i) the control group (reference category) (ii) patients of the maintenance group who did not receive any bevacizumab at time t (iii)-(v) tertiles of the updated cumulative dose CE(t) among those subjects who had non-zero cumulative dose at a given time. Model 3b consisted in four categories corresponding to the quartiles of the updated cumulative dose CE(t) among those subjects who had non-zero cumulative dose at a given time.
Models 4a (for CFI exposure) and 4b (for overall exposure) used the updated standardized cumulative dose (StCE), obtained by converting the values of the cumulative dose CE(t) in [1] observed for individual subjects at time t into z-scores:
$$ {\mathrm{StCE}}_{\mathrm{i}}\left(\mathrm{t}\right)=\frac{{\mathrm{EC}}_{\mathrm{i}}\left(\mathrm{t}\right)-\overline{\mathrm{EC}\left(\mathrm{t}\right)\ }}{\upsigma_{\mathrm{EC}\left(\mathrm{t}\right)}} $$
(3)
where \( \overline{EC(t)\ } \) is the mean of the cumulative doses at time t and σEC(t) is their standard deviation.
This approach eliminated the systematic differences between the values of cumulative doses CE(t) in [1], calculated at different times during the follow-up.
Model 5 defined the time-varying exposure metric as the expected theoretical blood concentration (TBC) of bevacizumab, at time
t, for a given individual. This metrics is defined as the weighted sum of past bevacizumab doses received by the patient, with weights following the exponential decay model [
26]. The weights were calculated assuming the half-life of bevacizumab was h = 20 days, based on previous pharmaco-kinetics studies [
27].
$$ {TBC}_i(t)={\sum}_{t0<\dots <{t}_k<\dots <t}^t{X}_i\left({t}_k\right)\times 0,{5}^{\left(\frac{t_k-t}{h}\right)} $$
(4)
Finally, model 6 relied on a weighted cumulative exposure (WCE) metric, in which weights also depend on the time elapsed since the dose was taken
(tk – t) [
15]. However, in contrast to model 5 in [4], in the WCE model the weights are estimated directly from the data, using a very flexible cubic spline model, that requires only minimal assumptions, resulting in a weight function w
(tk – t) that is continuous and smooth, but can take an arbitrary shape [
22]:
$$ {WCE}_i(t)={\sum}_{t0<\dots <{t}_k<\dots <t}^t{X}_i\left({t}_k\right)\times w\left({t}_k-t\right) $$
(5)
The use of un-penalized cubic regression splines is based on several earlier statistical papers that have built the WCE methodology and validated it in comprehensive simulations [
22,
16,
28,
29]. This approach combines sufficient flexibility to recover a wide range of functional shapes (as demonstrated in simulations) with ease of statistical inference (due to use of un-penalized maximum likelihood estimation) and is implemented in the R program [
30]. The underlying assumptions are that (i) the weight function is a smooth function (with continuous 1st and 2nd derivatives) of time elapsed between the exposure and the current time when the risk is being assessed; and (ii) this function can take an arbitrary shape, including both monotone and non-monotone curves, and (iii) can take positive (indicating risk increases) and/or negative (risk decrease) values for different times in the past [
22]. Because of uncertainty regarding the maximum duration of the effect of past exposures, we estimated three alternative WCE models with exposure windows of 120, 365 (1 year) or 730 (2 years) days, respectively, and selected the best-fitting WCE model based on the minimum AIC [
22]. Adjusted Hazard Ratios corresponding to some clinically plausible bevacizumab exposure patterns were reconstructed based on the estimated weight function, as described by Sylvestre & Abrahamowicz 2009 [
22].
Section 1 of
Online Appendix describes how we tested for the linearity and proportional hazards (PH) hypotheses. Goodness of fit of alternative models was compared through the Akaike Information Criterion (AIC), a decrease of 4 points was deemed a moderate improvement, and a decrease of more than 10 points was deemed important [
31].
Because time-varying changes in bevacizumab use during the follow-up were based on multiple factors (patient general condition, tumor evolution, patient and investigator choices …), we had to control for potential confounding bias. To ensure the comparability of results, all multivariable models adjusted the bevacizumab exposure for the same a priori selected potential confounders. Adjustment variables included both time-invariant covariates (age at randomization, sex, group of randomization, resection of the primitive tumor, initial level of phosphatase alkaline, localization of the primitive tumor), and time-varying variables (updated values of WHO performance status, a binary indicator of any toxicities related to bevacizumab, as well as updated values of weight, hemoglobin concentration, bilirubin concentration, blood pressure level). A directed acyclic graph representing the main risk factors and disease history in patients with colorectal metastatic cancer in the PRODIGE 9 study is presented in Appendix
2.
In sensitivity analyses, we assessed the effect of adjusting for time-varying variables. To this end, we re-estimated all the models adjusting only on the baseline values of all aforementioned time-varying variables. In further sensitivity analyses, in the TBC and WCE models we adjusted for an additional time-dependent binary indicator of “having received a treatment dose in the last 20 days”. The goal was to reduce concerns about the potential reverse causality bias that could occur if having received any dose recently may be a marker very poor health indicating a patient is likely to die very soon.