Introduction
Pancreatic cancer is a common cause of cancer-related death and is difficult to treat as diagnosis is often made late and patients present with metastatic disease [
1]. Despite recent improvements in diagnostic techniques, the prognosis of patients with pancreatic cancer is poor, with a 5-year survival rate of 0.4–4 % [
2]. The only potential curative treatment is surgical resection although only 15–20 % of patients are eligible for surgery [
1]. Gemcitabine chemotherapy is the standard palliative care [
3], with a median survival of 5.7 months and 20 % 1-year survival rate [
4]. However, the prognosis of patients receiving palliative chemotherapies varies depending on their clinical characteristics [
5]. It is therefore important to identify subgroups of patients that would benefit from chemotherapies. Several prognostic factors for patients with metastatic pancreatic cancer (MPC) have been previously identified: pancreatic cancer location [
6], albumin level (ALB), carbohydrate antigen 19-9 level (CA19-9), alkaline phosphatase level (ALP), lactate dehydrogenase level, white blood cell count, aspartate aminotransferase level, blood urea nitrogen level [
7], long-standing diabetes [
8], Eastern Cooperative Oncology Group (ECOG) performance status, C-reactive protein level [
9], the status of unresectable disease, carcinoembryonic antigen level and neutrophil–lymphocyte ratio [
10].
Identifying prognostic factors with predictive value for patient risk stratification is an important task in cancer research to monitor and assess clinical trials, and individualise patient care. Multivariate statistical modelling methods are commonly used to investigate survival in relation to a factor of interest (e.g. treatment exposure) while adjusting for others (e.g. genotype). The Cox proportional hazards (CPH) model [
11] is the most frequently used multivariate regression method, mainly because no assumption on the distribution of survival times is required (“semi-parametric” method) although it relies on the key assumption that the group-specific hazards are proportional over time. A useful alternative when the proportional hazards assumption does not hold is to use the accelerated failure time (AFT) model [
12] which offers the advantage of an easier interpretation of the covariate effects (directly on the survival time) as compared to the CPH model (effects on the hazard rate). Since the AFT model is fully parametric, it is also more suitable for simulations that can be of value to extrapolate patient survival data and to optimise the design of oncology clinical trials. Nevertheless, the assumption on the survival time distribution might be deemed too strict as most of the time the distribution (or even a close approximation) is unknown.
In oncology drug development, decision-making and trial design are traditionally based on the Response Evaluation Criteria In Solid Tumours (RECIST), an empirical categorical measure of antitumor activity [
13,
14]. More recently, several studies have shown that model-derived tumour size (TS) metrics can also be used as predictors for survival of patients with solid tumours [
15‐
18]. In drug development, a parametric survival model that includes early change in TS as predictor variables might be beneficial for trial design and early assessment of drug efficacy. To our knowledge, this approach has not been evaluated in MPC.
The objective of this study is to apply a fully parametric drug development approach (referred to as the “PAR approach”) that utilises longitudinal TS data, to predict the mortality risk of patients with MPC. We used the control arm data from two Phase III MPC studies to build and validate the models as it would be done in the clinic. Early changes in TS were interpolated by hierarchical nonlinear modelling of the TS time-series and were tested as predictors for survival in an AFT model. We also compared the predictive performance between the PAR approach and a more conventional clinical approach that uses a CPH regression of empirical risk factors.
Discussion
Prognostic models for survival of patients with MPC are essential to identify stratification variables and control for known important variability in the data when conducting large, prospective, Phase III randomised controlled trials. It is also essential to individualise care and treat patients more effectively. In this study, two different survival modelling approaches have been evaluated retrospectively using the control arm data of two independent Phase III studies of patients under gemcitabine treatment. The first approach, referred to as the PAR approach, aims at incorporating model-predicted TS reduction metrics into a parametric survival model that can be used for clinical trial simulations. This approach utilises time-series of imaging data to interpolate early change in TS for all patients. The second approach, referred to as the COX approach, simply aims at identifying empirical prognostic factors with the commonly used multivariate CPH regression model. Our results suggest that the two approaches perform similarly in predicting survival probability of new MPC patients, as indicated by the 95 % CIs of the integrated AUROC values.
Regardless of the modelling approach applied, the baseline variable TS
0 appears to be a significant prognostic factor for patients with MPC, although the effect is weak overall: in the COX
1 model for instance, the hazard ratio (HR) for 1-cm increase in TS
0 is 1.07 (95 % CI 1.03–1.14); in the AFT
LN model, the ratio of median survival time (AF) for 1-cm increase in TS
0 is 0.990 (95 % credible interval 0.985–0.995). The other risk factors identified were different depending on which approach was applied. With the PAR approach, the metric PTR at week 2 was identified as strong survival predictors in the AFT
LN model (AF ratio of 2.92 for 1 unit increase, with 95 % credible interval from 1.21 to 7.46) although it was not in the AFT
WB model. The fact that the predictive value of the PTR metric was similar at each time point assessed (week 2–10) is consistent with the predicted median TS-dynamic trend in the studied patients treated with gemcitabine (Figure S1 in the Online Resource). Also, patients with higher albumin levels were found to survive slightly longer (AF ratio of 1.08 with 95 % credible interval from 1.01 to 1.16), which is consistent with biology (inflammation marker) and with a previously reported MPC prognostic model [
7]. Finally, increase in BSA was related to increase in median survival time (AF ratio of 2.14 with 95 % credible interval from 1.11 to 4.22) in the AFT
WB model. Since patients undergoing gemcitabine chemotherapy are dosed by BSA, this means that patients with higher doses might survive longer, which suggests that the standard dose for gemcitabine (1000 mg/m
2) might not be optimal for all studied MPC patients. Using the COX approach, PTR
max was identified as significant risk factor with HR estimate of 0.275 (95 % CI 0.0123–0.832). However, the CPH model that includes only NEUT as covariate (COX
2 model) performed as well as the model with both TS
0 and PTR
max (COX
1 model) in predicting patient survival, thereby suggesting that variables derived from TS imaging data might not be better prognostic factors for patients with MPC than some of the toxicology markers like baseline neutrophils. Patients with high pre-treatment neutrophil counts are probably more at risk than patients with lower counts (HR ratio of 2.14 with 95 % CI from 1.40 to 5.58), as it was suggested in a previous study [
10]. It should be noted that only NEUT was retained in the CPH model when analysing the reduced-training set (excluding TS-related variables) compared to 8 variables when analysing the original training set using the LASSO method. This can be explained by the decreased power of the analysis when reducing the training set and probably also by the difference of variable selection method.
The choice of the modelling approach clearly depends on the purpose of the survival analysis. The PAR approach has been recommended to aid oncology drug development decisions such as compound screening, dose selection and trial design [
15‐
18]. In the present example for MPC, this approach could reasonably predict the mortality risk of patients from an independent study, with similar performance compared to the more conventional COX approach. However, our work suggests caveats against the PAR approach. Firstly, a unique AFT model could not be selected on the basis of the training set (see Figure S2 in the Online Resource), possibly due to the small study sample size (120 patients, 58 deaths). This emphasises the difficulty of defining the distribution of survival times when using parametric models with limited survival data. Although the AFT
LN and AFT
WB models could predict the validation data with similar global predictive accuracy, the distributional assumption on time to death seems to affect the identification of prognostic factors (Table
3) as well as the extrapolation ability of the model (Fig.
3). It should be stressed that using the Weibull distribution, longitudinal TS metrics were not identified as better survival predictors than other baseline characteristics. Nevertheless, we acknowledge that other commonly used AFT models, such as the log-logistic and generalised gamma distributions, were not assessed in this analysis and might provide a better description of the training data than the lognormal and Weibull distributions. Secondly, the PAR approach is more time-consuming than the COX approach as it involves modelling the TS dynamics rather than simply evaluating empirical metrics. Also, the individual model parameters, used to interpolate early change in TS for each patient, always carry uncertainty. For simplicity, we ignored parameter uncertainty in the present analysis by using the posterior means of the individual parameters. However, this can introduce bias in the subsequent evaluation of these variables as survival predictors. Ideally, several sets of TS reduction metrics should be produced by sampling from the posterior distribution of the individual parameters, if a Bayesian approach is applied. This issue has also been addressed in a frequentist modelling approach where shrinkage of individual parameter estimates can affect the type I error of falsely detecting or failing to detect TS metrics as predictors of survival [
32].
We developed the parametric AFT models using a Bayesian approach mainly because we found a probabilistic programming language convenient for the analysis of censored data and because credible intervals for the covariate effects are obtained. The identification of prognostic factors was simply done by forward selection based on LOO estimates and the 95 % credible intervals of the coefficients. Alternatively, methods that use shrinkage priors could be employed for variable selection [
33,
34]. These methods are similar to frequentist penalised regressions, in the sense that the coefficients of (apparently) irrelevant covariates would have credible intervals that include zero, although it offers the advantage of readily producing the uncertainty distribution of the parameters.
In conclusion, the PAR modelling approach that utilises model-derived TS metrics in addition to baseline patient characteristics could predict reasonably well survival of patients with MPC undergoing gemcitabine chemotherapy. However, determining the distribution of survival times appeared challenging with data from only one small study and seems to affect the identification of risk factors. Moreover, the predictive performance was not significantly better than a simple CPH model that incorporates only baseline neutrophil count as covariate. Nevertheless, our findings should be confirmed by analysing data sets that have higher power for multivariable survival regression. In particular, the predictive value of the new potential prognostic factors BSA (gemcitabine dose) and TS-related metrics should be reassessed together with established risk factors on a larger MPC study.