On the relationship between tumour growth rate and survival in non-small cell lung cancer

Introduction

A key question being posed in early oncology drug development at the end of phase II (and increasingly at the end of phase I expansion studies) is: given past imaging information, what is the overall survival (OS) outcome in a phase III study likely to be? This question has been primarily addressed by analysing efficacy data using RECIST criteria (Response Evaluation Criteria In Solid Tumours) (Therasse et al., 2000; Eisenhauer et al., 2009). RECIST v1.0 and v1.1 involves the evaluation of a drug’s efficacy against both target and non-target lesions. The drug’s effect on target lesions are reported via the Sum of Longest Diameters (SLD) marker which is a continuous variable whereas drug effect on non-target lesions is reported via qualitative descriptions: increase, decrease or no-change. Both are recorded over time as is the occurrence of a new lesion. The variables discussed above can also be combined to produce one variable, RECIST response classification which consists of four categories: Complete Response (CR), Partial Response (PR), Stable Disease (SD) or Progressive Disease (PD). CR represents complete disappearance of both target and non-target lesions. PR and SD are simply categorised versions of percentage change in SLD. PD as well as being a categorised version of percentage change in SLD also considers increase in non-target lesion size and occurrence of a new lesion. An important continuous metric of interest is progression free survival (PFS) time: the time from treatment initiation to PD or death. This time-point is of importance for two reasons; firstly it marks the end of imaging data collection and secondly, it also signals the end of the current treatment and the beginning of the next. Therefore, the imaging data collected can only provide one with information on the effect of the first treatment given during the trial. Without knowing what effect the treatment post progression has on the disease clearly makes survival prediction challenging. However, if one assumes the subsequent treatments have minimal effect on disease, compared to initial treatment, then survival prediction may be possible. The debate then moves onto how best to analyse the imaging data collected up until disease progression.

The option of using continuous measures involving changes in SLD over the categorisation scheme has been a long-standing debate when analysing early patient response to treatment (An et al., 2011; An et al., 2015; Toffart et al., 2014). These works have shown that there was no benefit in terms of survival concordance probability when using continuous changes in SLD compared to the current RECIST response classification. More elaborated approaches have therefore explored the use of mathematical models to fit the time-series of SLD (Stein et al., 2008; Stein et al., 2009; Stein et al., 2012; Wang et al., 2009; Blagoev et al., 2013; Claret et al., 2013; Bruno, Mercier & Claret, 2014; Han et al., 2016). Figure 1A shows the metrics that have been derived from these models of SLD time-series. These are the decay rate (DR), the re-growth rate (GR), the model estimated percentage change at a certain time-point and the time to tumour re-growth (TTG). In particular, TTG and GR have been claimed to be significant predictors of survival (Stein et al., 2008; Stein et al., 2009; Stein et al., 2012; Blagoev et al., 2013; Claret et al., 2013; Han et al., 2016) when calculated using an exponential decay/growth model. However, concerns about how these two metrics are estimated have been raised. The first relates to drop-outs not being accounted for through a joint longitudinal and survival model (Ibrahim, Chu & Chen, 2010; Mansmann & Laubender, 2013). The second concerns the time-dependent bias of TTG and GR, that is the time taken to estimate these quantities was never accounted for in those previous studies (Van Walraven et al., 2004; Mistry, 2016).

Contradictory results have been reported regarding the predictive power of these metrics. In one hand, Sharma et al. (2015) used TTG within a resampling of a single phase III study to assess phase II trial design and endpoints. They showed that TTG was equal if not superior to PFS in making the correct decision with regards to moving from phase II to III given an 18 week landmark time-point. On the other hand, Kaiser (2013) used a larger study and found that PFS was a superior endpoint compared to GR in five of his six trials. There are two possible reasons why the results from Sharma et al. and Kaiser differ: (i) the difference in PFS between treatments, in the studies used by Kaiser, were greater than that in the study used by Sharma et al. and/or (ii) the difference could be attributed to the choice of model based metric used: Sharma et al. used TTG whereas Kaiser chose GR.

It is important to note that within the context of this study, risk can be allocated within two different categories, individual and group risk. An individual risk metric is assessed through survival concordance probabilities (Gönen & Heller, 2005; An et al., 2011; An et al., 2015), whereas a group risk metric is assessed on whether the correct decision was made to advance a compound from phase II to phase III. In this context, individual risk estimates the patient’s survival prognosis based on the patient’s historical imaging time series data. Therefore, for individual risk, the time taken to acquire sufficient time-series to estimate GR and TTG must be accounted for otherwise one assumes one can see into the future. This was not done in the approaches taken in Stein et al. (2008), Stein et al. (2009), Stein et al. (2012), Blagoev et al. (2013), Claret et al. (2013) and Han et al. (2016) and so a question remains as to whether GR and TTG can be used to predict individual risk.

For group risk the question of interest is different: given historical data on a standard of care treatment in a group of patients, is a new treatment (which has mature PFS data in a group of patients) likely to produce survival improvement? This would be assessed for instance through a future prospective head-to-head trial. In this different context, full time courses can indeed be considered for metrics estimation as was the case in the approaches taken by Stein et al. (2008), Stein et al. (2009), Stein et al. (2012), Blagoev et al. (2013), Claret et al. (2013) and Han et al. (2016). It could be argued that individual risk is mainly a concern to the practicing medical community whereas group risk is a concern for the pharmaceutical industry and regulatory agencies. However, given the growth of interest in personalised (precision) medicine, individual risk is also likely to become a critical factor of future drug development.

The objective of this study was to analyse both individual and group risk using three comparator arms of phase III NSCLC (Non-Small Cell Lung Cancer) studies in the following way. For individual risk the model derived metrics, GR and TTG, calculated using the exponential decay/growth model used in previous studies (Stein et al., 2008; Stein et al., 2009; Stein et al., 2012; Kaiser, 2013; Blagoev et al., 2013; Claret et al., 2013; Sharma et al., 2015), were assessed via calculation of the survival concordance probability. Concordance probability was chosen for two reasons: (1) it is a measure that is routinely used when reporting the predictive capability of a prognostic model developed for use in the clinic (Gönen & Heller, 2005; An et al., 2011; An et al., 2015); (2) it is a non-parametric approach which I preferred over a regression model to avoid the use of a specific functional form when measuring evidence of relationship between variables. I examined the correlation to overall survival times for these quantities using two different data alignment approaches, forward and reverse. Forward alignment refers to correlating TTG and GR to overall survival without accounting for the time taken to estimate them. Reverse alignment involves re-aligning patients time-series to their time of progression and correlating TTG and GR to overall survival time minus the progression time. This approach not only accounts for the time taken to estimate GR and TTG but also assesses if those metrics are significant correlates to survival post progression. For group risk, I tested the ability of the metrics, PFS, TTG and GR, derived from the control arms of two of the phase III studies, to predict the outcome of a phase III study, where the treatments in the control arms were placed in a head-to-head trial, was tested.

Methods

Results

Group risk

I then attempted to predict the outcome of the phase III test trial of Erlotinib versus Docetaxel, which showed an advantage of Docetaxel over Erlotinib, using GR, TTG or PFS. It can be seen in the histograms in Fig. 2A that the predicted distribution of OS HR using either GR (green) or PFS (grey) are close to the observed OS HR (solid vertical line) and sit well within the observed 95 percent confidence intervals (dashed vertical lines). This however is not the case for the OS HR predicted using TTG (pink) whose predicted distribution appears to sit outside the observed confidence intervals. The median and 95 percent prediction interval for the OS HR using each of the metrics, PFS, GR and TTG, were, 0.84 (0.62–1.13), 0.64 (0.53–0.77) and 0.42 (0.25–0.62) respectively. In comparing these to the actual OS HR observed, 0.73 (0.53–1), it is clear that the OS HR predicted using TTG is the furthest away. Both PFS and GR however are equally as close to the actual results with PFS under-estimating the effect and GR over-estimating the effect.

In order to investigate the difference between the predicted OS HR distributions of TTG and GR I assessed the correlation between the ratios of means between the two metrics, see Fig. 2B. The correlation plot shows that there is a relationship between the two variables (r² = 0.36) but that it is weak. This suggests that the information held within GR and TTG is moderately different and that the choice of metric could lead to different predictions. This may explain why TTG and GR did not give comparable predictions.

Discussion

In this work I examined the relationship between on-treatment changes in imaging and survival outcomes, which has been gaining favour recently (Stein et al., 2008; Stein et al., 2009; Stein et al., 2012; Wang et al., 2009; Blagoev et al., 2013; Claret et al., 2013; Bruno, Mercier & Claret, 2014; Han et al., 2016). Based on the cases I have analysed, I found that:

1. Model derived metrics TTG and GR were not significant covariates of survival post progression.

2. The outcome of the phase III study using historical data was predicted just as well by conventional PFS HR as TTG and GR.

Regarding the first point, model derived metrics TTG and GR were found to be significant correlates for overall survival when the time taken to estimate them was not accounted for i.e., they were considered to be biased. However, by re-phrasing the question to, do TTG and GR correlate to survival post progression? I accounted for this bias, since imaging data ceases to be collected once a patients disease progresses. The result of re-phrasing the question highlighted that the dynamics of the disease leading up to progression have no bearing on the prognosis of a patient post progression. This result may seem surprising however it may not be once one considers what happens at the time of progression. The patient stops taking the current line of treatment and at some time-point post-progression may start a new treatment. Furthermore, this new treatment may be quite variable if there is no standard treatment approved. Therefore unless there is a correlation between the dynamics leading up to progression and the dynamics under the new unknown treatment one would expect the results found here to hold in most clinical trials.

Regarding the second finding, I assessed three metrics in their ability to correctly predict the outcome of a phase III trial, an assessment of group risk, which was a head-to-head test of two of the drugs used in this analysis, Erlotinib and Docetaxel. The three metrics assessed were PFS HR, TTG and GR. Both PFS and GR were as far away to the actual result as each other; with GR over-predicting and PFS under-predicting the advantage of Docetaxel over Erlotinib. TTG, however, was furthest away from the actual result; it overestimated the advantage of Docetaxel over Erlotinib more so than GR. These results confirm previous findings where PFS was equal or superior to GR in making the correct decision in moving from phase II to phase III (Kaiser, 2013). This is in contrast with the study by Sharma et al. (2015) where PFS was found to be slightly less predictive than TTG. A reason for this could be that the study used here as the test case was powered to show a PFS difference which was not the case in the study done by Sharma et al., where they stopped the re-sampled study after 18 weeks and so was not powered to detect a PFS difference which is usually done for phase II studies. Sharma et al. proposed that the difference in magnitude of PFS between their study arms and that of Kaiser explained why the latter found PFS superior to GR. However, the PFS HR I investigated here (0.71) was similar to the one in the study by Sharma et al. (HR: 0.79). I suggest that the reason for the difference in results between Sharma et al. and Kaiser is related to the choice of model derived metric. Sharma et al. used TTG whereas Kaiser et al. used GR. The results here show that the ratio of means of those metrics between treatment arms do not correlate strongly. Therefore, the discrepancy could be due to choice of metric and not to differences in PFS. It is interesting to note that although TTG and GR were not strong covariates for survival post-progression, they performed well at predicting group risk. Thus, it is possible that a different approach should be used for modelling individual and group risk.

Although the analyses performed were for only one disease type, NSCLC, and were within a limited pharmacological space, they highlight the importance of accounting for the time it takes to estimate model derived metrics when assessing their prognostic value for individual risk. In addition to the approach described here regarding re-aligning a patients time-series to their time of progression an alternative approach would be to perform a landmark analysis in forward alignment at a specific time-point as was done by Sharma et al. (2015). Both of these approaches account for the time taken to estimate TTG and GR. For group risk, although the results here show that PFS HR can predict OS HR, it has been shown that in general this may not be the case (Blumenthal et al., 2015). However, this does not suggest that PFS cannot be used for decision making as I found that for majority of patients radiological progression precedes death; it merely implies that it may not always predict quantitatively what the OS difference could be.

Overall, when comparing the results seen here with previous published studies assessing the decision making value of tumour size metrics, it suggests that PFS remains the best metric to use for decision making when considering group risk. For individual risk, model derived metrics derived from SLD time-series might be inappropriate. This is in contrast to prognostic models developed using standard pre-treatment clinical variables (e.g., lactate dehydrogenase, alkaline phosphatase etc.) which have been shown to be predictive for a specific drug within a specific disease setting (Halabi et al., 2014; Wendling et al., 2016). It would be interesting to further investigate how prognostic models developed using routine clinical variables could be adapted to be used for predicting group risk and how well these perform compared to PFS for decision making and quantitatively predicting treatment differences in OS.

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