Prognostic value of different discretization parameters in ¹⁸fluorodeoxyglucose positron emission tomography radiomics of oropharyngeal squamous cell carcinoma

Abstract.

Purpose

We aim to interrogate the role of positron emission tomography (PET) image discretization parameters on the prognostic value of radiomic features in patients with oropharyngeal cancer.

Approach

A prospective clinical trial (NCT01908504) enrolled patients with oropharyngeal squamous cell carcinoma ($N=69$; mixed HPV status) undergoing definitive radiotherapy and evaluated intra-treatment ¹⁸fluorodeoxyglucose PET as a potential imaging biomarker of early metabolic response. The primary tumor volume was manually segmented by a radiation oncologist on PET/CT images acquired two weeks into treatment (20 Gy). From this, 54 radiomic texture features were extracted. Two image discretization techniques—fixed bin number (FBN) and fixed bin size (FBS)—were considered to evaluate systematic changes in the bin number ({32, 64, 128, 256} gray levels) and bin size ({0.10, 0.15, 0.22, 0.25} bin-widths). For each discretization-specific radiomic feature space, an LASSO-regularized logistic regression model was independently trained to predict residual and/or recurrent disease. The model training was based on Monte Carlo cross-validation with a 20% testing hold-out, 50 permutations, and minor-class up-sampling to account for imbalanced outcomes data. Performance differences among the discretization-specific models were quantified via receiver operating characteristic curve analysis. A final parameter-optimized logistic regression model was developed by incorporating different settings parameterizations into the same model.

Results

FBN outperformed FBS in predicting residual and/or recurrent disease. The four FBN models achieved AUC values of 0.63, 0.61, 0.65, and 0.62 for 32, 64, 128, and 256 gray levels, respectively. By contrast, the average AUC of the four FBS models was 0.53. The parameter-optimized model, comprising features joint entropy (FBN = 64) and information measure correlation 1 (FBN = 128), achieved an AUC of 0.70. Kaplan–Meier analyses identified these features to be associated with disease-free survival ($p=0.0158$ and $p=0.0180$, respectively; log-rank test).

Conclusions

Our findings suggest that the prognostic value of individual radiomic features may depend on feature-specific discretization parameter settings.

1. Introduction

Head and neck squamous cell carcinoma (HNSCC) represents $>90\%$ of head and neck cancers and commonly arises from the oral cavity, pharynx, and larynx.^1,2 The complexity of these disease sites introduces diagnostic and therapeutic challenges. For example, the small scale and morphological complexity of these tumors and nearby normal tissue can complicate the characterization of gross disease. Further, treatment-induced anatomic changes, and the subsequent variation in morphology of both primary and recurrent tumors, often make prognosis difficult to estimate.

Positron emission tomography (PET) with fluorodeoxyglucose (${}^{18}\mathrm{F}$-FDG) partially addresses these challenges with its capacity to identify distant disease and recurrence of HNSCC and specify uptake contrast at tumor edges. Importantly, PET imaging may be able to characterize biological heterogeneity of HNSCC tumors, leading to better representation of the disease. Quantitative radiomic analysis of PET images aims to capture such texture patterns to be used as potential biomarkers of therapeutic response.^1,3,4

An essential computational pre-processing step that is essential to PET radiomics is image discretization (i.e., the process of resampling voxel intensity, consequently narrowing the dynamic range of the image).^5–7 By resampling the intensity values into fewer discrete states, discretization is particularly important in PET radiomics because it reduces the sparsity of texture matrices that ultimately define metabolic heterogeneity.^8,9 This repartitioning is often accomplished using a fixed bin number (FBN) or fixed bin size (FBS) binning method. FBN discretization uses varying fixed bin widths to normalize a region of interest (ROI), clustering pixel intensities into a predefined number of bins. By contrast, FBS is an absolute resampling technique that uses predefined bin widths/sizes, but varying bin numbers, to resample an ROI’s intensity values.³

Image gray level discretization may have a major impact on the reproducibility of PET radiomics, in which different discretization techniques and parameterizations introduce variability of downstream PET radiomic features.¹⁰ For example, selecting too small of a bin number or too wide a bin size can average out features, leading to information loss.^4,11 By contrast, too many bin numbers or too small a bin size can obscure radiomic features with noise.⁴ Thus, it is important to determine an optimal discretization technique that can filter out noise without compromising the nature of the extracted data. Although some studies have concluded that radiomic features are most reproducible with FBS-discretized data,^4,12,13 others found FBN to be more stable.^14,15 Unstandardized approaches to quantizing image intensities limit the repeatability and reproducibility of radiomic extraction and analysis. Optimization of these feature extraction parameters is essential to producing reproducible radiomic biomarkers and evaluating their efficacy in linking imaging to outcomes.

The purpose of this work is to characterize the effect of PET image discretization on radiomic feature extraction in patients undergoing definitive (chemo)radiotherapy for HNSCC and to evaluate how specific discretization parameters modulate the association of radiomics data with clinical outcomes (Fig. 1).

Fig. 1.

General radiomics workflow, highlighting discretization. (a) PET image data were acquired using a Siemens Biograph mCT PET-CT scanner, and primary gross tumor volume (GTV) was segmented by a radiation oncologist. (b) The intensity values of the data were resampled into a specified bin size by the absolute resampling method FBS (bottom) and discretized into a predefined number of bins by the relative discretization method FBN (top). The disparate effects of two discretization techniques are illustrated by the discretized images of the region of interest (ROI). (c) Using an in-house algorithm benchmarked according to the Image Biomarker Standardisation Initiative (IBSI) standards, radiomic features were extracted from these discretized ROIs. (d) We performed statistical analysis of discretization-specific feature space (DSFS) variability (e) and statistical analysis of downstream model variability of disease-free survival based on differences in DSFS.

2. Methods

2.1. Patient Criteria and Characteristics

All research was conducted in keeping with best clinical practice and regulatory compliance. Prospective data (images, patient outcomes) were generated from Pro00108767 (NCT01908504) approved by the Duke University Institutional Review Board. In addition, the Duke University Institutional Review Board approved a secondary retrospective analysis (radiomics) of the original data with Pro00108767, which was completed under an approved waiver of consent, Health Insurance Portability and Protection Act Authorization, and decedent research notification. Patients enrolled ($N=69$; mixed HPV status) in NCT01908504 undergoing definitive radiotherapy and intra-treatment ${}^{18}\mathrm{F}$-FDG PET as a potential imaging biomarker of early metabolic response were included on this study. Inclusion criteria required squamous cell carcinoma of the oropharynx, an ECOG score of 0–1, and cancer staged I–III as defined in the 8th edition of the American Joint Committee manual.^16,17

Patients underwent repeat ${}^{18}\mathrm{F}$-FDG PET/CT and/or contrast-enhanced neck CT at 3 months after completing radiation therapy to evaluate the response. Subsequent follow-up was according to standard practice with a physical exam and fiberoptic laryngoscopy performed every 2-3 months in year 1 after radiation therapy, every 3 to 4 months in year 2, every 6 months in years 3-5, and annually after 5 years. Additional diagnostic imaging was performed as clinically indicated with biopsy performed to evaluate lesions suspicious for recurrent disease.

The primary clinical endpoint focused on the time-to-event measurement, specifically disease-free survival (DFS). DFS was defined as the duration from the completion of radiation therapy to the occurrence of residual or recurrent disease, including local, regional, and/or distant disease. Patient data was censored at the date of the last follow-up. The median follow-up time was determined using the reverse Kaplan–Meier method.

2.2. PET/CT Image Acquisition and Tumor Segmentation

All PET/CT scans were performed on a single Siemens Biograph mCT PET-CT scanner. Custom thermoplastic masks immobilized patients during PET-CT simulation with CT scans preceding PET acquisition.¹⁴ Attenuation correction and time-of-flight were performed according to clinical protocol based on manufacturer standards.¹⁷ Depending on patient weight, 8 to 15 millicuries (mCi) of ${}^{18}\mathrm{F}$-FDG were intravenously administered with PET imaging taking place 50 to 70 min post-injection,¹⁷ and standardized uptake value (SUV) was normalized to the blood pool.¹⁷ All image acquisition parameters were repeated for intra-treatment scans taken after 20 Gy. Primary gross disease was manually segmented on CT and transferred to the co-registered PET by a single radiation oncologist according to the clinical trial protocol.¹⁷ Radiomic features (outlined in the Table 2) were then extracted directly from the gross disease on the PET image expressed in terms of SUV.

Table 2.

Extracted features and mathematical definitions.

Feature families	Feature name	Feature equation/description
Intensity histogram features	Mean ($\mu$)	$\frac{1}{N}\sum _i^{N}I(i)$.
	Variance	$\frac{1}{N-1}\sum _{i=1}^N{(I(i)-\overline{I})}^2$
	Standard deviation ($\sigma$)	${(\frac{1}{N-1}\sum _{i=1}^N(I(i)-\overline{I}{)}^2)}^{\frac{1}{2}}$
	Skewness	$\frac{1}{N}\sum _{i=1}^N(I(i)-\overline{I}{)}^3/{\left(\sqrt{\frac{1}{N}\sum _{i=1}^N{(I(i)-\overline{I})}^2}\right)}^3$
	Kurtosis	$\frac{1}{N}\sum _{i=1}^N(I(i)-\overline{I}{)}^4/{\left(\sqrt{\frac{1}{N}\sum _{i=1}^N(I(i)-\overline{I}{)}^2}\right)}^2$
	Median	The median intensity value of I
	Maximum	The maximum intensity value of I
	90’th percentile $(P_{90})$	The 90’th percentile of I. It is more robust to outliers than the maximum
	Minimum	The minimum intensity value of I
	10’th percentile $(P_{10})$	The 10’th percentile of I It is more robust to outliers than the minimum
	Interquartile range	$P_{75}\text{-}{P}_{25}$
	Range	$\max (I)-\min (I)$
	Mean absolute deviation	$\frac{1}{N}\sum _i^N|I(i)-\overline{I}|$
	Robust mean absolute deviation	$\frac{1}{N_{10-90}}\sum _{i=1}^{N_{10-90}}|I_{10-90}-\overline{I_{10-90}}|$
	Median absolute deviation	$\frac{1}{N}\sum _i^N|I(i)-\text{median}(I)|$
	Coefficient of variation	$\frac{{(\frac{1}{N-1}{\sum }_{i=1}^N(I(i)-\overline{I}{)}^2)}^{\frac{1}{2}}}{\frac{1}{N}{\sum }_i^{N}I(i)}$
	Quartile coefficient of dispersion	$\frac{P_{75}-P_{25}}{P_{75}+P_{25}}$
	Entropy	$-\sum _{i=1}^L{P}_N(i){\log }_2{P}_N(i)$
	Uniformity	$\sum _i^L{P}_N(i{)}^2$
	Maximum histogram gradient	$\max (P(2)-P(1),\dots ,\frac{P(i+1)-P(i-1)}{2},\dots ,P(L)-P(L-1))$
	Minimum histogram gradient	$\min (P(2)-P(1),\dots ,\frac{P(i+1)-P(i-1)}{2},\dots ,P(L)-P(L-1))$
GLCM	Auto-correlation	$\sum _{i=1}^L\sum _{j=1}^{L}I(i)I(j)P_{ij}$
	Cluster prominence	$\sum _{i=1}^L\sum _{j=1}^L(I(i)+I(j)-2{\mu }_i{)}^4{P}_{ij}$
	Cluster shade	$\sum _{i=1}^L\sum _{j=1}^L(I(i)+I(j)-2{\mu }_i{)}^3{P}_{ij}$
	Cluster tendency	${\mu }_{i,j}=\sum _{i,j=1}^L(I(i),I(j))·P_{i,j}$
	Contrast	$\sum _{i=1}^L\sum _{j=1}^L(I(i)-I(j){)}^2{P}_{ij}$
	Correlation	$\frac{1}{{\sigma }_i{\sigma }_j}(-{\mu }_i{\mu }_j+\sum _{i=1}^L\sum _{j=1}^{L}I(i)I(j)P_{ij})$
	Differential entropy	$-\int \mathrm{d}i{P}_N(i){\log }_2{P}_N(i)$
	Dissimilarity	$\sum _{k=0}^{L-1}k{p}_{i-j}(k)$
	Joint energy	$\sum _{i=1}^L\sum _{j=1}^{L}I(i{)}^{2}I(j{)}^{2}N$
	Joint entropy	$-\sum _{i=1}^L\sum _{j=1}^L{P}_{ij}{\log }_2{P}_{ij}$
	Inverse difference	$\sum _{k=0}^L\frac{p_{i-j,k}}{1+k}$
	Inverse difference moment	$\sum _{k=0}^{L-1}\frac{p_{i-j,k}}{1+k^2}$
	Information measure correlation 1	$\frac{-{\sum }_{i=1}^L{\sum }_{j=1}^L{P}_{ij}{\log }_2{P}_{ij}+{\sum }_{i=1}^L{\sum }_{j=1}^L{P}_{ij}{\log }_2(P_i,P_j)}{-{\sum }_{i=1}^L{p}_i{\log }_2{p}_i}$
	Information measure correlation 2	$\sqrt{1-\exp \left(2\right(\sum _{i=1}^L\sum _{j=1}^L{P}_{ij}{\log }_2(P_i,P_j)-\sum _{i=1}^L\sum _{j=1}^L{P}_{ij}{\log }_2(P_{ij})\left)\right)}$
	Inverse difference moment normalized	$\sum _{k=0}^{L-1}\frac{p_{i-j,k}}{1+{\left(\frac{k}{L}\right)}^2}$
	Inverse difference normalized	$\sum _{k=0}^{L-1}\frac{p_{i-j,k}}{1+\frac{k}{L}}$
	Inverse variance	$\sum _{k=1}^{L-1}\frac{p_{i-j,k}}{k^2}$
	Joint maximum	$\max (P_{ij})$
	Sum average	$\sum _{k=2}^{2L}k{p}_{i+j,k}$
	Sum entropy	$-\sum _{k=2}^{2L}{p}_{i+j,k}{\log }_2{p}_{i+j,k}$
	Sum variance	$\sum _{k=2}^{2L}(k-\mu {)}^2{p}_{i+j,k}$
	Joint variance	$-\sum _{i=1}^L\sum _{j=1}^L(i-\mu {)}^2{P}_{ij}$
GLRLM	Short run emphasis	$\sum _{i=1}^L\sum _{j=1}^R\frac{r_{\mathrm{ij}}}{j^2}/\sum _{i=1}^L\sum _{j=1}^R{r}_{\mathrm{ij}}$
	Long run emphasis	$\frac{{\sum }_{i=1}^L{\sum }_{j=1}^R{j}^2{r}_{\mathrm{ij}}}{{\sum }_{i=1}^L{\sum }_{j=1}^R{r}_{\mathrm{ij}}}$
	Gray level non-uniformity	$\frac{1}{N_s}\sum _{i=1}^{N_r}\sum _{j=1}^{N_g}{r}_{\mathrm{ij}}^2$
	Gray level non-uniformity normalized	$\frac{1}{N_s^2}\sum _{i=1}^{N_r}\sum _{j=1}^{N_g}{r}_{\mathrm{ij}}^2$
	Run length non-uniformity	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_r}{r}_{\mathrm{ij}}^2$
	Run length non-uniformity normalized	$\frac{1}{N_s^2}\sum _{i=1}^{N_g}\sum _{j=1}^{N_r}{r}_{\mathrm{ij}}^2$
	Run percentage	$N_s/N_v$
	Low gray level run emphasis	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_r}\frac{r_{\mathrm{ij}}}{i^2}$
	High gray level run emphasis	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_r}{i}^2{r}_{\mathrm{ij}}$
	Short run low gray level emphasis	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_r}\frac{r_{\mathrm{ij}}}{i^2{j}^2}$
	Short run high gray level emphasis	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_r}\frac{i^2{r}_{\mathrm{ij}}}{j^2}$
	Long run low gray level emphasis	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_r}\frac{j^2{r}_{\mathrm{ij}}}{i^2}$
	Long run high gray level emphasis	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_r}{i}^2{j}^2{r}_{\mathrm{ij}}$
	Gray level variance	$\sum _{i=1}^{N_g}\sum _{j=1}^{N_r}(i-\mu {)}^2{p}_{\mathrm{ij}}$
	Run length variance	$\sum _{i=1}^{N_g}\sum _{j=1}^{N_r}(j-\mu {)}^2{p}_{\mathrm{ij}}$
	Run entropy	$-\sum _{i=1}^{N_g}\sum _{j=1}^{N_r}{p}_{\mathrm{ij}}{\log }_2(p_{\mathrm{ij}})$
GLSZM	Small zone emphasis	$\frac{1}{N_s}\sum _{j=1}^{N_z}\sum _{i=1}^{N_g}\frac{s_{ij}}{j^2}$
	Large zone emphasis	$\frac{1}{N_s}\sum _{j=1}^{N_z}\sum _{i=1}^{N_g}{j}^2{s}_{\mathrm{ij}}$
	Gray level non-uniformity	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_z}{s}_{\mathrm{ij}}^2$
	Gray level non-uniformity normalized	$\frac{1}{N_s^2}\sum _{i=1}^{N_g}\sum _{j=1}^{N_z}{s}_{\mathrm{ij}}^2$
	Size zone non-uniformity	$\frac{1}{N_s}\sum _{j=1}^{N_z}\sum _{i=1}^{N_g}{s}_{\mathrm{ij}}^2$
	Size zone non-uniformity normalized	$\frac{1}{N_s^2}\sum _{j=1}^{N_z}\sum _{i=1}^{N_g}{s}_{\mathrm{ij}}^2$
	Zone percentage	$N_s/N_v$
	Low gray level size emphasis	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_d}\frac{d_{ij}}{i^2}$
	High gray level size emphasis	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_d}{i}^2{d}_{ij}$
	Small size low gray level emphasis	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_d}\frac{d_{ij}}{i^2{j}^2}$
	Small size high gray level emphasis	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_d}\frac{i^2{d}_{ij}}{j^2}$
	Large size low gray level emphasis	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_d}\frac{j^2{d}_{ij}}{i^2}$
	Large size high gray level emphasis	$\frac{1}{N_s}\sum _{i=1}^{N_g}\sum _{j=1}^{N_d}{i}^2{j}^2{d}_{ij}$
	Gray level variance	$\sum _{i=1}^{N_g}\sum _{j=1}^{N_r}(i-\mu {)}^2{p}_{ij}$
	Zone size variance	$\sum _{i=1}^{N_g}\sum _{j=1}^{N_z}(j-\mu {)}^2{p}_{ij}$
	Zone size entropy	$-\sum _{i=1}^{N_g}\sum _{j=1}^{N_z}{p}_{\mathrm{ij}}{\log }_2(p_{\mathrm{ij}})$

2.3. Discretization Framework and Feature Extraction

Following segmentation, an in-house algorithm¹⁷—benchmarked according to the Image Biomarker Standardisation Initiative (IBSI) standards^18,19 – was used for radiomic feature extraction. Image preprocessing and radiomic feature extraction were performed according to prior work^5,9,20 and IBSI standards^18,19 as follows. PET image data and masks of the region of interest (ROI) were resampled to an isotropic voxel size of $0.97{\mathrm{mm}}^3$ using linear interpolation. Two approaches to discretization were then explored: FBN and FBS. Each resampling method generated discretized ROIs and subsequent feature spaces ${\mathcal{F}}_{\mathrm{BN}}$ and ${\mathcal{F}}_{\mathrm{BS}}$, where BN/BS denotes the value of the chosen bin number/size. These resampled feature matrices both comprise 74 features (Appendix) that can be organized into two broad categories: first-order histogram/intensity features that describe the spread of grey-level intensity values and second-order histogram (i.e., texture) features that measure the degree of heterogeneity throughout the image.

2.3.1. Fixed bin number

The FBN method depicted in Fig. 2 is a relative discretization technique that clusters pixel intensities into an integer number of bins (BN). BNs 32, 64, 128, and 256 were chosen, according to values as described in the most recent literature.^3,10,13,15 The discretized gray-levels $I_{\mathrm{FBN}}$ were generated using the following equation:

$$I_{\mathrm{FBN}}=\{\begin{array}{ll}1& I(x)=I_{\min }\\ \mathrm{BN}·\frac{I(x)-I_{\min }}{-I_{\min }}& \text{otherwise}\end{array},$$ (1)

where a given voxel $I(x)$ of pixel $x$ was resampled according to the chosen BN and the maximum ($I_{\max }$) and minimum ($I_{\min }$) intensity values of an ROI.

Fig. 2.

Toy model representing relative discretization. The left histogram (and accompanying image) demonstrates pixel intensity values at the full dynamic range. The rightmost image shows an example of FBN-discretized feature space ${\mathcal{F}}_{\mathrm{BN}}$, with BN = 12, and the resulting resampled image.

2.3.2. Fixed bin size

FBS is an absolute discretization technique that, as illustrated in Fig. 3, assigns the same bin for every voxel intensity $I(x)$ corresponding to the bin size (BS).^10,15 Resampled intensity values $I_{\mathrm{FBS}}$ were quantized into equal widths of BS 0.10, 0.15, 0.22, and 0.25 according to the following equation:

$$I_{\mathrm{FBS}}=\{\begin{array}{ll}1& I(x)=I_{\min }\\ \frac{I(x)-I_{\min }}{\mathrm{BS}}& \text{otherwise}\end{array}.$$ (2)

Fig. 3.

Schematic depicting absolute discretization. The image on the left demonstrates pixel intensity values at the full dynamic range, with a pre-defined bin size chosen to resample intensity values into a variable number of bins.

Discretizing the extracted features at a given BN or BS generated feature spaces characterized by that chosen bin number (${\mathcal{F}}_{\mathrm{BN}}$) or bin size (${\mathcal{F}}_{\mathrm{BS}}$), each of size $74\times 69$, for pre- and intra-treatment datasets.

2.4. Variability Among Discretization-Specific Radiomic Feature Spaces

The sensitivity of feature extraction to these common discretization techniques was systematically evaluated by measuring radiomic feature values at monotonically increasing bin numbers and bin sizes. From the discretized data, 54 features were extracted from intra-treatment PET images at monotonically increasing bin numbers (BN = {32, 64, 128, 256} gray levels) and bin size (BS = {0.10, 0.15, 0.22, 0.25} bin widths). Disparities in the feature spaces parameterized by these different resampling settings were quantified based on t-tests of individual features. T-tests were applied to each row vector of each ${\mathcal{F}}_{\mathrm{BN}}$ and ${\mathcal{F}}_{\mathrm{BS}}$ to compare the distribution of features across the discretization techniques, with a $p\text{value}\le 0.05$ denoting a statistically significant difference in this distribution. A matrix $M^{(k)}$ was constructed to encode the response of parameterization combinations of the $k^{th}$ feature. Additionally, to assess the impact of the discretization methods on entire feature spaces, we calculated the cross correlation (CC) between feature spaces parameterized by differences in discretization techniques.

2.5. Variability in Model Performance for Predicting Recurrence

A LASSO-regularized logistic regression model training employed Monte Carlo cross- validation with a 20% testing hold-out, 50 permutations, and minor-class up-sampling to account for imbalanced outcomes data. To assess the performance of the models, receiver operating characteristic curve analysis was utilized to quantify performance differences among the discretization-specific models. The goal was to identify the optimal combination of parameters that would yield the highest predictive power. This was achieved by developing a final logistic regression model that incorporated different parameter settings into the same model. The performance of the trained models was systematically evaluated to ferret out the most effective method for predicting recurrence in oropharyngeal tumors based on radiomic features. To enhance the understanding of the predictive power of the models, Kaplan–Meier estimates were also performed. This added analysis allowed for a comparative assessment of the relative effectiveness of the discretization-specific approaches, providing additional information to assist in identifying an optimal combination of parameters that would yield radiomic features with the highest predictive power for recurrence in oropharyngeal tumors.

2.6. Sensitivity Analysis of Discretization Methods Based on Tumor Size and Pixel Standard Deviation

The impact of discretization was further investigated by performing sensitivity analyses of FBN and FBS by tumor size and pixel variation. All tumors were first sorted by their volume (units: cc) and partitioned into two groups by the median tumor volume of the cohort. For each group, we tested for differences in normalized cross-correlation (NCC) measurements at the extremes of each binning technique (i.e., FBN: [32, 256]; FBS: [0.10, 0.25]). Differences in NCC were evaluated based on the Student t-test, where $p<0.05$ was considered statistically significant when comparing extreme binning techniques across extreme tumor volumes (Fig. 4).

Fig. 4.

Visual differences in discretized tumors at extreme values of tumor volume and pixel standard deviation. (a) and (b) FBN values of 32 and 256, respectively, demonstrating differences in tumor volume (e.g., smallest versus largest) and pixel standard deviation (e.g., smallest versus largest). (c) and (d) FBS values of 0.10 and 0.25, respectively, demonstrating differences in tumor volume (e.g., smallest versus largest) and pixel standard deviation (e.g., smallest versus largest). Although the pixel standard deviation demonstrated a significant influence ($p=8.32\mathrm{E}\text{-}05$) on discretization based on FBN, significant differences in structural similarity were not observed in FBS ($p=0.1983$). The structural similarity was not influenced by tumor volume when discretized by both FBN ($p=0.5712$) and FBS ($p=0.5255$).

Next, all tumors were then sorted by their standard deviation (units: SUV) and partitioned into two groups by the median standard deviation of the cohort. For each group, we tested for differences in normalized cross-correlation (NCC) measurements at the extremes of each binning technique (i.e., FBN: [32, 256]; FBS: [0.10, 0.25]). Differences in NCC were evaluated based on the Student t-test, where $p<0.05$ was considered statistically significant when comparing extreme binning techniques across extreme intensity variations.

3. Results

3.1. Variability Among Discretization-Specific Radiomic Feature Spaces

Individual features demonstrated a non-linear response to systematic changes in discretization parameters. As summarized in Table 1, matrices $M$ with a high frequency (i.e., $\ge 5$) of statistically significant $p$-values denote features that were sensitive to changing BN or BS. By contrast, $M$ matrices with low occurrence of $p\le 0.05$ were less variable. The resultant values are the number of features in each range.

Table 1.

Frequency of significant variation as a function of discretization technique in intra-treatment images.

	Number of statistically significant $p$-values in $M^{(k)}$	0	1	2	3	4	5	6
Fixed Bin number		3	0	0	3	0	1	47
Fixed bin size		6	0	0	2	0	46	0

Of the FBN-discretized intra-treatment images, 5.56% were invariant to (i.e., stable against) changing discretization parameters. This is compared with 87.0% of individual features, all of which were impacted by variability in the bin number. Comparatively, 85.2% of FBS-discretized intra-treatment data exhibited sensitivity to a chosen BS value; 11.1% of this data, however, were stable against varying BS (Fig. 5).

Fig. 5.

Illustrative example of encoding the frequency of a variable for individual features. The leftmost feature exhibits sensitivity to all changing bin parameters; the middle feature shows partial binning parameter dependency; and the rightmost feature depicts no response to alterations in discretization parameters.

3.1.1. Fixed bin number

Discretizing PET images with BNs equal to 128 and 256 had equal effects on the extracted radiomics data, with CC values being one (1) for the pre-treatment images. All other off-diagonal elements of the $F$ matrices demonstrated decreasing correlation proportional to increasing differences in BN: ${\mathcal{F}}_{32}$ maintained the lowest CC values with ${\mathcal{F}}_{128}$ (CC = 0.04811) and ${\mathcal{F}}_{256}$ (CC = 0.04735), showing a small increase in correlation with ${\mathcal{F}}_{64}$ (CC = 0.455). The correlation of ${\mathcal{F}}_{64}$ with unidentical feature spaces ${\mathcal{F}}_{128}$ (CC = 0.8284) and ${\mathcal{F}}_{256}$ (CC = 0.8285) substantially increased. Similarly, feature spaces of FBN-discretized radiomics data increased with decreasing differences in the BN value (${\mathrm{\Delta }}_{\mathrm{BN}}$) (Fig. 6).

Fig. 6.

Matrices encoding the response of FBN-discretization combinations between complete feature spaces.

3.1.2. Fixed bin size

Feature spaces exhibited a high degree correlation across all chosen values in the absolute intensity interval discretization method. ${\mathcal{F}}_{0.10}$ showed nearly maximal correlation with ${\mathcal{F}}_{0.15}$ (CC = 0.991) with decreasing similarity proportional to increasing difference in BS (${\mathrm{\Delta }}_{\mathrm{BN}}$) value between ${\mathcal{F}}_{0.22}$ (CC = 0.8984) and ${\mathcal{F}}_{0.25}$ (CC = 0.7127). ${\mathcal{F}}_{0.15}$ reiterates this trend: ${\mathrm{\Delta }}_{\mathrm{BN}}$ is inversely proportional to the similarity value. ${\mathrm{\Delta }}_{\mathrm{BS}}=|0.15-0.22|=0.07$ had an associated CC of 0.9158, whereas ${\mathrm{\Delta }}_{\mathrm{BS}}=|0.15-0.25|=0.1$ corresponds to a CC of 0.741. For non-identical feature spaces, ${\mathcal{F}}_{0.25}$ and ${\mathcal{F}}_{0.22}$ shared the second highest value (CC = 0.9461). The results of these similarity calculations are given in Fig. 7.

Fig. 7.

Matrices encoding the response of FBS-discretization combinations between complete feature spaces.

3.2. Variability in Model Performance for Predicting Recurrence

FBN-specific discretization outperformed FBS in predicting disease recurrence. The LASSO regression model trained on each discretization-specific radiomic feature space to predict residual and/or recurrent disease generated the following AUC values: FBN models were 0.63, 0.61, 0.65, and 0.62 for 32, 64, 128, and 256 gray levels, respectively, and FBS models were 0.51, 0.52, 0.55, and 0.53 for 0.10, 0.15, 0.22, and 0.25 bin widths, respectively. The parameter-optimized model that incorporated these texture features achieved the highest AUC of 0.70, as displayed in Fig. 8.

Fig. 8.

Bar rank plot of AUC values from each discretization model, with the highest AUC value from the parameter-optimized model highlighted in gold.

This optimal model facilitated the additional findings in the Kaplan–Meier survival analysis, which, as shown in Fig. 9, indicated that individual features may benefit from having feature-specific discretization parameters to enhance their prognostic potential. The analysis identified joint entropy discretized at FBN = 64 and information measure correlation 1 at FBN = 128 to be associated with disease-free survival ($p=0.0158$ and $p=0.0180$, respectively).

Fig. 9.

Kaplan–Meier curves measure disease-free survival probability for joint entropy at FBN = 64 (left) and information measure correlation (IMC) 1 at FBN = 128 (right).

3.3. Sensitivity Analysis of Discretization Methods Based on Tumor Size and Pixel Standard Deviation

Based on NCC calculations, our results imply that structural similarity is not significantly perturbed by tumor size for both FBN ($p=0.5712$) and FBS ($p=0.5255$) discretization. Similarly, differences in intensity variation exhibited no significant impact on FBS discretization ($p=0.1938$). By contrast, our results demonstrate that differences in intensity variation led to significant changes in structural similarity when discretized via FBN ($p=8.3020$ E-05).

4. Conclusions

Radiomic features quantitatively reflect the characteristics of a region of interest, capable of assessing locoregional heterogeneity.⁹ Their application to PET imaging requires a discretization step to facilitate the delineation of pixel intensity values. However, standardized discretization recommendations are limited, and their effect on prognostic value are largely unknown. This impacts radiomic analysis and disrupts the potential of radiomic implementation in a clinical setting. In this work, we systematically addressed this problem using a cohort of HNSCC patients previously enrolled on a prospective clinical trial to receive definite (chemo)radiation therapy.

Our results illustrate that the impact of discretization is largely feature-dependent. Individual features demonstrated a non-linear response to systematic changes in discretization parameters. Our data describe varying bin numbers and widths that produce an overall measurable effect on a given texture feature value. These discretization-dependent feature values are vital to predicting recurrence, as evidenced by the Kaplan–Meier survival analysis.

Two demonstrative features—joint entropy and information measure correlation 1—were found to be prognostically relevant given a specific discretization technique (i.e., FBN) and value (i.e., 64 and 128, respectively). Both features lacked Kaplan–Meier separation for all other parametrizations, indicating an association between radiomic features and outcome that is discretization-dependent. The evaluation of model variability for predicting recurrence supports this notion, in which the relative AUC values indicated a mixture of discretization parameters that is essential to capturing the predictive value of radiomic features. Our findings therefore suggest that the prognostic value of individual features may depend on feature-specific discretization parameter settings. FBN-discretized texture features may serve as a potential biomarker for predicting the recurrence in oropharyngeal tumors, and optimization of texture feature selection and parameterization can improve the predictive power of radiomic models.

Texture feature values must be directly comparable if they are to have substantial impact in clinical routine. Robust radiomics features ensure reproducibility, facilitating the translation of feature analysis into a clinical setting. The clinical utility of PET radiomics for patient stratification, decision support, and other potential uses demands an understanding of how specific features behave with a chosen pre-processing parameter. Selecting a generic approach to discretization PET data can average out radiomic features and lead to information loss. Alternatively, a nonspecific resampling choice does not address variability in radiomic features due to stochastic PET image acquisition noise—a complication that an appropriate choice in the discretization parameter may help alleviate.

Features belonging to the gray level co-occurrence matrix (GLCM) quantify texture by expressing how combinations of neighboring voxel pairs of discretized grey levels are spatially distributed. These features measure image heterogeneity. Our univariate analysis for these texture features implies that the bin values chosen in this study have considerable impact: these features (e.g., joint entropy and information measure correlation 1) are dynamic under monotonic grey-level transformations (i.e., discretization). Kaplan–Meier estimates and LASSO regression analysis further the suggestion that the predictive potential of GLCM features is not agnostic, but rather depends on optimally chosen discretization parameters.

Complementary sensitivity analyses further illustrate the intricate relationship between discretization methods and the characteristics of PET images, offering additional insights into the nuanced interplay between intensity patterns, tumor size, and the chosen resampling strategies. The non-significant $p$-value for NCC between patients with small and large tumors when discretized by either FBN or FBS suggests that, according to NCC, structural similarity is not significantly impacted by variations in tumor size. This implies that certain structural features are preserved across different tumor sizes when using either resampling method. The findings underscore the importance of considering tumor size when choosing a discretization method. Both FBN and FBS demonstrate sensitivity to tumor size variations in terms of mutual information, but the impact on structural similarity, as measured by NCC, appears to be consistent across different tumor sizes. The significance in NCC between patients with small and large heterogeneous intensity when discretized by FBN suggests that, according to NCC, structural similarity is significantly impacted by the heterogeneity of intensity. This might indicate that certain structural aspects are not preserved across different intensity patterns when using FBN. The non-significant $p$-value for NCC with FBS adds a layer of complexity. NCC suggests that structural similarity is less influenced by the intensity heterogeneity when using FBS. This nuanced result points to a method-specific interaction between FBS and intensity patterns in preserving structural information.

These findings highlight the intricate relationship between discretization methods and the characteristics of PET images, namely, how different aspects of the images, such as intensity heterogeneity, interact with the chosen discretization strategies, offering insights that could inform the selection of appropriate resampling parameters.

Radiomic features derived from PET images offer unique advantages in characterizing tissue function and molecular activity. PET radiomics excel in providing sensitivity to metabolic changes within tissues, making them particularly valuable for monitoring treatment response and assessing disease progression in oncology. The functional information captured by PET radiomics reflects the metabolic heterogeneity within tumors. However, it is important to acknowledge the limitation of PET images in offering detailed anatomical resolution compared with high-resolution CT (HRCT). As this research depended on intra-treatment PET/CT, we did not have access to diagnostic-grade or high-resolution CT imaging. Intra-treatment imaging of any variety is a novelty in radiation oncology and is the key innovation of the prospective clinical trial on which this study is based. The availability of intra-treatment PET/CT is a significant advantage for radiomic applicability in radiation oncology, particularly for future biologically-guided adaptative treatment paradigms. Future work studying CT-based radiomic features, particularly those on HRCT systems such as photon-counting CT, may provide complementary information about the biology of HNSCC tumors.²¹ Combining radiomic features from both modalities can provide a more comprehensive understanding of the disease phenotype. Of course, optimal discretization techniques (i.e., FBN and FBS) are likely modality-specific, and future work will need to characterize accordingly.

Additionally, a limitation of this study is that it did not evaluate additional pre-processing steps (e.g., segmentation) and their confounding effects on downstream radiomic efficacy. The reported results only recount features stable across discretization effects; a natural extension of this work would be to add other sources of variability (i.e., different segmentation methods) to discern the sensitivity of downstream radiomic biomarkers.

5. Appendix

Table 2 presents a comprehensive list of extracted radiomic features along with their corresponding mathematical definitions, sourced from the IBSI database.

Biography

Biographies of the authors are not available.

Disclosures

The authors declare no conflicts of interest.

Code and Data Availability

All source code is publicly available on GitHub, at https://github.com/breylon/toph. Data generated during and/or analyzed during the current study are also publicly available. Raw data associated with clinical trial (Grant No. NCT01908504) will be made available from the corresponding author on reasonable request.