Comparing analysis and parameterisation approaches

In this chapter, FE-DSM analysis is compared with 2D-DSM analysis using the same dose parameterisation approach (dose-widths and EUD). Increasingly complex methods of dose parameterisation were then investigated, from spatially determined geometric subregions (SRRgeom), to subregions identified using statistically derived probability maps (SRRpmap)

based on unadjusted and adjusted p-values. Here, we compare the results presented for each analysis and parameterisation approach presented.

For planned and accumulated dose, the average AUC of the parameter found to be most discriminative of each toxicity endpoint, per analysis/parameterisation approach: 2D-

DSM dose-width/EUD, FE-DSM dose-width/EUD, FE-DSM SRRgeomregion, and FE-DSM

SRRpmap(unadjusted), are presented in Figures 6.11 and 6.12.

For planned dose, 9 of 12 endpoints resulted in significant associations between dose and toxicity. Of these, FE-DSM analysis (dose-width/EUD, SRRgeom, or SRRpmap) produced

greater AUCs than 2D-DSM analysis for 8 of 9 endpoints. Parameterising FE-DSMs using dose-widths resulted in larger AUCs than EUD for 5 of these 8 endpoints. SRRgeomproduced

the greatest AUCs for 2 endpoints, and SRRpmapfor 1 endpoint.

For accumulated dose, all 12 endpoints resulted in significant associations between dose and toxicity. Of these, the largest AUC was found using FE-DSM analysis (dose-width/EUD, SRRgeom, or SRRpmap) for 8 endpoints. The 4 endpoints where 2D-DSM analysis resulted in

the largest AUC were for the 3 different grades of bowel bother and G1 RTOG GI toxicity. For FE-DSM analysis, SRRpmap resulted in the greatest AUC for 4 endpoints, SRRgeom

for 1, and dose-widths for 2 endpoints. The general trend across individual endpoints with significant dose-toxicity associations was that AUC improved with increasing complexity of parameterisation technique.

Overall, results support the hypothesis that using FE-DSMs to analyse dose to the rectal wall improves the discriminative power of dose-toxicity predictions when compared to the 2D-DSM approach. However, this was not consistent across all endpoints examined, and the differences were generally not statistically significant. A direct comparison between 2D-DSM and FE-DSM using dose-widths and EUD found results to be significantly different. Where stronger dose-toxicity associations were observed with increasing complexity of dose parameterisation, this was generally more pronounced for accumulated dose than planned dose. Results are encouraging and further research into advanced parameterisation approaches tailored to FE-DSMs is recommended.

6.5 Concluding discussion 131

Fig. 6.11Area under the receiver operator characteristic curve (AUC) for the highest performing dose metric from planned 2D-DSM, FE-DSM, geometric subregion (SRRgeom), and probabilistic subregion (SRRpmap) for 12 toxicity endpoints. Errors have been discussed in corresponding sections.

Fig. 6.12Area under the receiver operator characteristic curve (AUC) for the highest performing dose met- ric from accumulated 2D-DSM, FE-DSM, geometric subregion (SRRgeom), and probabilistic subregion (SRRpmap) for 12 toxicity endpoints. Errors have been discussed in corresponding sections.

Chapter 7

Predictive models for rectal toxicity

Predictive models are used in radiotherapy to maximise tumour control probability (TCP) and minimise normal tissue complication probability (NTCP). In this chapter, we develop NTCP models specific to our data to address three questions:

1. Is accumulated dose a better predictor of toxicity than planned dose?

2. Does finite element dose accumulation improve the predictive power of NTCP?

3. Can finite element derived subregions improve toxicity prediction?

In previous chapters we explored different methods for parameterisation of planned and delivered dose to the rectal wall in prostate radiotherapy. In Chapter 4, two dimensional dose surface maps (2D-DSM) were generated by uniformly normalising the circumference of the rectal wall, assuming in-plane expansion only. 2D-DSMs were parameterised using equivalent uniform dose (EUD) and DSM dose-widths, the lateral extent of an ellipse fitted to a given isodose level. Chapter 5 describes generating dose surface maps using finite element analysis (FE-DSM), where voxels deform in 3D according to applied boundary conditions and biomechanical properties. For comparative measurement with 2D-DSM results, FE- DSMs were also parameterised using EUD and DSM dose-widths (Chapter 6). Spatial dose information contained within FE-DSMs was further parameterised by identifying rectal subregions at risk using geometric division (SRRgeom) and statistical mapping (SRRpmap).

Here, we combine dosimetric parameters from planned and delivered dose with pre- treatment clinical factors to construct multivariate NTCP models for 12 toxicity endpoints. Final model performance indicates whether delivered dose is a better predictor of toxicity than planned dose, whether dosimetric information extracted from FE-DSMs improves model performance with respect to features from 2D-DSMs, and whether subregions reveal areas of heightened radiosensitivity.

The knowledge base of the underpinning statistical methods for constructing NTCP mod- els within this PhD was largely formed by attending the European Society for Radiotherapy & Oncology (ESTRO) school ‘Quantitative Methods in Radiation Oncology: Models, Trials and Clinical Outcomes’, as well as following approaches described in the literature. The format adopted for documenting model development and validation follows the recommendations of the Transparent Reporting of a multivariate prediction model for Individual Prognosis Or Diagnosis (TRIPOD) Statement [45] where possible.

7.1

Introduction

The aim of radiotherapy treatment planning is to maximise radiation dose to the tumour whilst minimising dose to nearby healthy organs. In prostate radiotherapy, the planning target volume (PTV) is the prostate, and the organs at risk (OARs) include the rectum, bladder, femoral heads. With advances in radiotherapy imaging and hardware, greater conformity and targeting accuracy has enabled dose escalation to the PTV, which has led to improvements in biochemical control of the tumour [84, 85, 130]. However, as a consequence, this can lead to higher dose being received by the healthy OARs. During the iterative radiotherapy treatment planning process, the plan is optimised such that the PTV receives the prescribed radiation dose and the OARs do not exceed certain normal tissue dose thresholds, or constraints. These OAR constraints are generally based on consensus guidelines (e.g. Quantitative Analyses of Normal Tissue Effects in the Clinic, QUANTEC [94]), or the outcomes of randomised clinical trials [10, 54, 148]. The overarching goal is to maximise tumour control probability (TCP) and minimise normal tissue complication probability (NTCP).

NTCP is based on dose-response modelling. OARs generally receive non-homogeneous doses, so the complex 3D dose distribution, often presented as a dose-volume histogram (DVH,) is reduced to a simplified dose metric for NTCP modelling. For example, the proportion of volume receiving a percentage of the prescribed dose or more, the mean dose, and the equivalent uniform dose (EUD), are commonly used. A limitation of these metrics is the loss of spatial dose information due to dimension reduction.

Many studies have investigated the relationship between dose and rectal toxicity using NTCP models[87, 131]. Often, dose has been considered to the entire rectum, but more recent studies have parameterised dose to specific regions of the rectum [34, 35, 61, 115]. This allows potential inhomogeneous intra-organ radiosensitivities to be investigated. Furthermore, various rectal toxicity endpoints have been reported in the literature, and the difference in underlying pathophysiology [70, 126] may be associated with different dose levels. A study by Schaake et al. [140] presented the first multivariate NTCP model considering dose to

7.2 Material and methods 135

specified regions of the rectum, for different toxicity endpoints, as well as clinical prognostic factors. They conclude that different rectal subregions and dose levels are associated with different toxicity effects, which may be useful for plan optimisation to reduce side-effects in future studies.

A common limitation of the published literature is that, to date, rectal NTCP models have been based on planned dose data. This is calculated from the pre-treatment CT scan that represents the anatomy at a static point in time. These data are readily available in radiotherapy as they form the basis of each patient’s radiation treatment. However, planned dose does not incorporate the effects of interfraction motion, which introduces deviations to dose parameters [139, 142] and spatial dose patterns [34], and may be more pronounced in hollow structures such as the rectum [140].

Here we present, for the first time, multivariate NTCP models developed for both planned and motion-inclusive accumulated delivered dose to the rectum. The effect of incorporating different spatial dose features of dose surface maps (DSMs) and patient prognostic vari- ables, are investigated for 12 different toxicity endpoints. The approach follows published methodologies [16, 140] for building robust NTCP models in order to demonstrate the merits of different dose parameterisation approaches, and the differences between planned and accumulated dose models.

The risk of toxicity approximately follows a sigmoidal curve when plotted against dose due to radiation dose response relationships. This supports the use of logistic regression to predict the probability of a binary outcome, or the proportion of patients with a given toxicity endpoint. Schakke et al [140] developed multivariable model for rectal bleeding, faecal incontinence and stool frequency based on planned dose volume histograms and found different dose levels and patient characteristics to be associated with each of the discrete endpoints. Following a similar approach, binary logistic regression was selected to develop NTCP models based on VoxTox data. Patient baseline cofactors were included in model development, as well as the spatial dose parameters derived throughout this thesis for planned and accumulated dose.

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7.2

Material and methods