ARE DISCOVERIES SPURIOUS? DISTRIBUTIONS OF MAXIMUM SPURIOUS CORRELATIONS AND THEIR APPLICATIONS

Multiblock Discriminant Analysis of Integrative 18F-FDG-PET/CT Radiomics for Predicting Circulating Tumor Cells in Early-Stage Non-small Cell Lung Cancer Treated With Stereotactic Body Radiation Therapy

PURPOSE

The main objective of the present study was to integrate 18F-FDG-PET/CT radiomics with multiblock discriminant analysis for predicting circulating tumor cells (CTCs) in early-stage non-small cell lung cancer (ES-NSCLC) treated with stereotactic body radiation therapy (SBRT).

METHODS

Fifty-six patients with stage I NSCLC treated with SBRT underwent 18F-FDG-PET/CT imaging pre-SBRT and post-SBRT (median, 5 months; range, 3-10 months). CTCs were assessed via a telomerase-based assay before and within 3 months after SBRT and dichotomized at 5 and 1.3 CTCs/mL. Pre-SBRT, post-SBRT, and delta PET/CT radiomics features (n = 1548 × 3/1562 × 3) were extracted from gross tumor volume. Seven feature blocks were constructed including clinical parameters (n = 12). Multiblock data integration was performed using block sparse partial least squares-discriminant analysis (sPLS-DA) referred to as Data Integration Analysis for Biomarker Discovery Using Latent Components (DIABLO) for identifying key signatures by maximizing common information between different feature blocks while discriminating CTC levels. Optimal input blocks were identified using a pairwise combination method. DIABLO performance for predicting pre-SBRT and post-SBRT CTCs was evaluated using combined AUC (area under the curve, averaged across different blocks) analysis with 20 × 5-fold cross-validation (CV) and compared with that of concatenation-based sPLS-DA that consisted of combining all features into 1 block. CV prediction scores between 1 class versus the other were compared using the Wilcoxon rank sum test.

RESULTS

For predicting pre-SBRT CTCs, DIABLO achieved the best performance with combined pre-SBRT PET radiomics and clinical feature blocks, showing CV AUC of 0.875 (P = .009). For predicting post-SBRT CTCs, DIABLO achieved the best performance with combined post-SBRT CT and delta CT radiomics feature blocks, showing CV AUCs of 0.883 (P = .001). In contrast, all single-block sPLS-DA models could not attain CV AUCs higher than 0.7.

CONCLUSIONS

Multiblock integration with discriminant analysis of 18F-FDG-PET/CT radiomics has the potential for predicting pre-SBRT and post-SBRT CTCs. Radiomics and CTC analysis may complement and together help guide the subsequent management of patients with ES-NSCLC.

Radiomics: from qualitative to quantitative imaging

Historically, medical imaging has been a qualitative or semi-quantitative modality. It is difficult to quantify what can be seen in an image, and to turn it into valuable predictive outcomes. As a result of advances in both computational hardware and machine learning algorithms, computers are making great strides in obtaining quantitative information from imaging and correlating it with outcomes. Radiomics, in its two forms "handcrafted and deep," is an emerging field that translates medical images into quantitative data to yield biological information and enable radiologic phenotypic profiling for diagnosis, theragnosis, decision support, and monitoring. Handcrafted radiomics is a multistage process in which features based on shape, pixel intensities, and texture are extracted from radiographs. Within this review, we describe the steps: starting with quantitative imaging data, how it can be extracted, how to correlate it with clinical and biological outcomes, resulting in models that can be used to make predictions, such as survival, or for detection and classification used in diagnostics. The application of deep learning, the second arm of radiomics, and its place in the radiomics workflow is discussed, along with its advantages and disadvantages. To better illustrate the technologies being used, we provide real-world clinical applications of radiomics in oncology, showcasing research on the applications of radiomics, as well as covering its limitations and its future direction.

Sparse Sliced Inverse Regression Via Lasso

For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if ρ = lim p n = 0 , where p is the dimension and n is the sample size. Thus, when p is of the same or a higher order of n, additional assumptions such as sparsity must be imposed in order to ensure consistency for SIR. By constructing artificial response variables made up from top eigenvectors of the estimated conditional covariance matrix, we introduce a simple Lasso regression method to obtain an estimate of the SDR space. The resulting algorithm, Lasso-SIR, is shown to be consistent and achieve the optimal convergence rate under certain sparsity conditions when p is of order o(n 2 λ 2), where λ is the generalized signal-to-noise ratio. We also demonstrate the superior performance of Lasso-SIR compared with existing approaches via extensive numerical studies and several real data examples.

Guarding against Spurious Discoveries in High Dimensions

Many data-mining and statistical machine learning algorithms have been developed to select a subset of covariates to associate with a response variable. Spurious discoveries can easily arise in high-dimensional data analysis due to enormous possibilities of such selections. How can we know statistically our discoveries better than those by chance? In this paper, we define a measure of goodness of spurious fit, which shows how good a response variable can be fitted by an optimally selected subset of covariates under the null model, and propose a simple and effective LAMM algorithm to compute it. It coincides with the maximum spurious correlation for linear models and can be regarded as a generalized maximum spurious correlation. We derive the asymptotic distribution of such goodness of spurious fit for generalized linear models and L₁-regression. Such an asymptotic distribution depends on the sample size, ambient dimension, the number of variables used in the fit, and the covariance information. It can be consistently estimated by multiplier bootstrapping and used as a benchmark to guard against spurious discoveries. It can also be applied to model selection, which considers only candidate models with goodness of fits better than those by spurious fits. The theory and method are convincingly illustrated by simulated examples and an application to the binary outcomes from German Neuroblastoma Trials.