Specification Testing in Econometric Models

The thesis consits of three independent articles. First, specification tests for the m-dimensional spatial autoregressive (SAR) panel model are provided. Therefore, we derive the limiting distribution of the specification test statistics and examine size and power properties in finite sample simulations. In the empirical application we analyze the Euro Stoxx 50 returns. Regarding this, a 3-dimensional SAR panel model incorporating global dependencies, dependencies inside industrial branches and local dependencies is assumed. The investigation shows the tests’ ability to detect inaccurate Value-at-Risk forecasts. Secondly, we propose a new non-parametric test for detecting relevant breaks in copula functions. We assume that the data is driven by two non-equal copulas C1 and C2. Under the null hypothesis, the copula difference within an appropriate norm is smaller than a certain positive adjustable threshold . Within the alternative hypothesis, the copula difference exceeds the fixed value. The test is based on a cumulative sum approach of the empirical copula with sequentially estimated marginals. We propose a bootstrap procedure to compute critical values. The Monte Carlo simulation study indicates that the test results in a reasonable sized and powered testing procedure. A real data application of the DAX30 up to cross sectional dimension N = 30 shows the test’s ability to detect relevant break points. Finally, we propose a novel consistent specification test for quantile regression models where we allow the covariate effects to be quantile dependent and nonlinear. To achieve this, we parameterize the conditional quantile functions by appropriate basis functions, rather than parametrically and hence allowing to test for functional forms beyond linearity while retaining the linear cases as special cases. Due to the dependence on the quantile itself covariate-quantile relations can differ for distinct quantiles. The induced class of conditional distribution functions can finally be tested with a Cramér-von Mises type test statistic. We derive the theoretical limit distribution and propose a practical bootstrap method. To increase the power of our test, we suggest a modified test statistic using quantile regression splines. A detailed Monte Carlo experiment shows that the test results in a reasonable sized testing procedure with large power. An application to conditional income disparities between East and West Germany over the period 2001 − 2010 indicates that there are still significant differences across the quantiles of the conditional income distributions, when conditioning on age

Flexible specification testing in quantile regression models

We propose three novel consistent specification tests for quantile regression models which generalize former tests in three ways. First, we allow the covariate effects to be quantile-dependent and nonlinear. Second, we allow parameterizing the conditional quantile functions by appropriate basis functions, rather than parametrically. We are thereby able to test for general functional forms, while retaining linear effects as special cases. In both cases, the induced class of conditional distribution functions is tested with a Cramér–von Mises type test statistic for which we derive the theoretical limit distribution and propose a bootstrap method. Third, a modified test statistic is derived to increase the power of the tests. We highlight the merits of our tests in a detailed MC study and two real data examples. Our first application to conditional income distributions in Germany indicates that there are not only still significant differences between East and West but also across the quantiles of the conditional income distributions, when conditioning on age and year. The second application to data from the Australian national electricity market reveals the importance of using interaction effects for modeling the highly skewed and heavy-tailed distributions of energy prices conditional on day, time of day and demand.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Peer Reviewe

Predictive Value of Total Metabolic Tumor Burden Prior to Treatment in NSCLC Patients Treated with Immune Checkpoint Inhibition

Objectives: We aimed to assess the predictive value of the total metabolic tumor burden prior to treatment in patients with advanced non-small-cell lung cancer (NSCLC) receiving immune checkpoint inhibitors (ICIs). Methods: Pre-treatment 2-deoxy-2-[18F]fluoro-D-glucose positron emission tomography/computed tomography (PET/CT) scans performed in two consecutive years for staging in adult patients with confirmed NSCLC were considered. Volume, maximum/mean standardized uptake value (SUVmax/SUVmean), metabolic tumor volume (MTV) and total lesion glycolysis (TLG) were assessed per delineated malignant lesion (including primary tumor, regional lymph nodes and distant metastases) in addition to the morphology of the primary tumor and clinical data. Total metabolic tumor burden was captured by totalMTV and totalTLG. Overall survival (OS), progression-free survival (PFS) and clinical benefit (CB) were used as endpoints for response to treatment. Results: A total of 125 NSCLC patients were included. Osseous metastases were the most frequent distant metastases (n = 17), followed by thoracal distant metastases (pulmonal = 14 and pleural = 13). Total metabolic tumor burden prior to treatment was significantly higher in patients treated with ICIs (mean totalMTV ± standard deviation (SD) 72.2 ± 78.7; mean totalTLG ± SD 462.2 ± 538.9) compared to those without ICI treatment (mean totalMTV ± SD 58.1 ± 233.8; mean totalTLG ± SD 290.0 ± 784.2). Among the patients who received ICIs, a solid morphology of the primary tumor on imaging prior to treatment was the strongest outcome predictor for OS (Hazard ratio HR 28.04, p < 0.01), PFS (HR 30.89, p < 0.01) and CB (parameter estimation PE 3.46, p < 0.01), followed by the metabolic features of the primary tumor. Interestingly, total metabolic tumor burden prior to immunotherapy showed a negligible impact on OS (p = 0.04) and PFS (p = 0.01) after treatment given the hazard ratios of 1.00, but also on CB (p = 0.01) given the PE < 0.01. Overall, biomarkers on pre-treatment PET/CT scans showed greater predictive power in patients receiving ICIs, compared to patients without ICI treatment. Conclusions: Morphological and metabolic properties of the primary tumors prior to treatment in advanced NSCLC patients treated with ICI showed great outcome prediction performances, as opposed to the pre-treatment total metabolic tumor burdens, captured by totalMTV and totalTLG, both with negligible impact on OS, PFS and CB. However, the outcome prediction performance of the total metabolic tumor burden might be influenced by the value itself (e.g., poorer prediction performance at very high or very low values of total metabolic tumor burden). Further studies including subgroup analysis with regards to different values of total metabolic tumor burden and their respective outcome prediction performances might be needed.Peer Reviewe

Additional Primary Tumors Detected Incidentally on FDG PET/CT at Staging in Patients with First Diagnosis of NSCLC: Frequency, Impact on Patient Management and Survival

We aimed to assess the frequency of additional primary malignancies detected incidentally on [18F]fluoro-D-glucose positron emission tomography/computed tomography (FDG-PET/CT) at staging in NSCLC patients. Moreover, their impact on patient management and survival was assessed. Consecutive NSCLC patients with available staging FDG-PET/CT between 2020 and 2021 were retrospectively enrolled. We reported whether further investigations of suspicious findings presumably not related to NSCLC were recommended and performed after FDG-PET/CT. Any additional imaging, surgery or multimodal management was considered as an impact on patient management. Patient survival was defined using overall survival OS and progression-free survival PFS. A total of 125 NSCLC patients were included, while 26 findings in 26 different patients were suspicious for an additional malignancy on FDG-PET/CT at staging. The most frequent anatomical site was the colon. A total of 54.2% of all additional suspicious lesions turned out to be malignant. Almost every malignant finding had an impact on patient management. No significant differences were found between NSCLC patients with suspicious findings versus no suspicious findings with regards to their survival. FDG-PET/CT performed for staging might be a valuable tool to identify additional primary tumors in NSCLC patients. Identification of additional primary tumors might have substantial implications for patient management. An early detection together with interdisciplinary patient management could prevent a worsening of survival compared to patients with NSCLC only.Peer Reviewe

An Innovative Non-Linear Prediction Model for Clinical Benefit in Women with Newly Diagnosed Breast Cancer Using Baseline FDG-PET/CT and Clinical Data

Objectives: We aimed to develop a novel non-linear statistical model integrating primary tumor features on baseline [18F]-fluorodeoxyglucose positron emission tomography/computed tomography (FDG-PET/CT), molecular subtype, and clinical data for treatment benefit prediction in women with newly diagnosed breast cancer using innovative statistical techniques, as opposed to conventional methodological approaches. Methods: In this single-center retrospective study, we conducted a comprehensive assessment of women newly diagnosed with breast cancer who had undergone a FDG-PET/CT scan for staging prior to treatment. Primary tumor (PT) volume, maximum and mean standardized uptake value (SUVmax and SUVmean), metabolic tumor volume (MTV), and total lesion glycolysis (TLG) were measured on PET/CT. Clinical data including clinical staging (TNM) but also PT anatomical site, histology, receptor status, proliferation index, and molecular subtype were obtained from the medical records. Overall survival (OS), progression-free survival (PFS), and clinical benefit (CB) were assessed as endpoints. A logistic generalized additive model was chosen as the statistical approach to assess the impact of all listed variables on CB. Results: 70 women with newly diagnosed breast cancer (mean age 63.3 ± 15.4 years) were included. The most common location of breast cancer was the upper outer quadrant (40.0%) in the left breast (52.9%). An invasive ductal adenocarcinoma (88.6%) with a high tumor proliferation index (mean ki-67 expression 35.1 ± 24.5%) and molecular subtype B (51.4%) was by far the most detected breast tumor. Most PTs displayed on hybrid imaging a greater volume (12.8 ± 30.4 cm3) with hypermetabolism (mean ± SD of PT maximum SUVmax, SUVmean, MTV, and TLG, respectively: 8.1 ± 7.2, 4.9 ± 4.4, 12.7 ± 30.4, and 47.4 ± 80.2). Higher PT volume (p < 0.01), SUVmax (p = 0.04), SUVmean (p = 0.03), and MTV (<0.01) significantly compromised CB. A considerable majority of patients survived throughout this period (92.8%), while five women died (7.2%). In fact, the OS was 31.7 ± 14.2 months and PFS was 30.2 ± 14.1 months. A multivariate prediction model for CB with excellent accuracy could be developed using age, body mass index (BMI), T, M, PT TLG, and PT volume as predictive parameters. PT volume and PT TLG demonstrated a significant influence on CB in lower ranges; however, beyond a specific cutoff value (respectively, 29.52 cm3 for PT volume and 161.95 cm3 for PT TLG), their impact on CB only reached negligible levels. Ultimately, the absence of distant metastasis M displayed a strong positive impact on CB far ahead of the tumor size T (standardized average estimate 0.88 vs. 0.4). Conclusions: Our results emphasized the pivotal role played by FDG-PET/CT prior to treatment in forecasting treatment outcomes in women newly diagnosed with breast cancer. Nevertheless, careful consideration is required when selecting the methodological approach, as our innovative statistical techniques unveiled non-linear influences of predictive biomarkers on treatment benefit, highlighting also the importance of early breast cancer diagnosis.Peer Reviewe

Testing for relevant dependence change in financial data: a CUSUM copula approach

We propose a new nonparametric test for detecting relevant breaks in copula functions. We assume that the data is driven by two non-equal copulas C-1 and C-2. Under the null hypothesis, the copula difference within an appropriate norm is smaller than a certain positive adjustable threshold Delta. Within the alternative hypothesis, the copula difference exceeds the fixed value Delta. The test is based on a cumulative sum approach of the empirical copula with sequentially estimated marginals. We propose a bootstrap procedure to compute critical values. The Monte Carlo simulation indicates that the test results in a reasonable sized and powered testing procedure. A real data application of the DAX30 up to cross-sectional dimension N = 30 shows the test's ability to detect relevant break points

Malignancy Rate of Indeterminate Findings on FDG-PET/CT in Cutaneous Melanoma Patients

Background: The use of 18F-2-Fluor-2-desoxy-D-glucose Positron Emission Tomography/Computed Tomography FDG-PET/CT in clinical routine for staging, treatment response monitoring and post treatment surveillance in metastatic melanoma patients has noticeably increased due to significant improvement of the overall survival rate in melanoma patients. However, determining the dignity of the findings with increased metabolic activity on FDG-PET/CT can be sometimes challenging and may need further investigation. Purpose: We aimed to investigate the malignancy rate of indeterminate findings on FDG-PET/CT in metastatic cutaneous melanoma patients. Methods: This single-center retrospective study included cutaneous melanoma patients who underwent FDG-PET/CT in clinical routine between 2015 and 2017 with findings reported as indeterminate and therefore requiring further evaluation. The dignity of the included findings was determined by subsequent imaging and, if required, additional histopathology. The impact of the outcome on the clinical management was also reported. Results: A total of 842 FDG-PET/CT reports of 244 metastatic cutaneous melanoma patients were reviewed. Sixty indeterminate findings were included. Almost half of all indeterminate findings were lymph nodes, lung nodules and cerebral lesions. In total, 43.3% of all included findings proved to be malignant. 81% of all malignant lesions were metastases of cutaneous melanoma, while 19% of all malignant lesions could be attributed to other primary malignancies, such as lung, breast, thyroid and colorectal cancers. Malignant findings influenced clinical management in 60% of the cases. Conclusion: Indeterminate findings on FDG-PET/CT in metastatic cutaneous melanoma patients should be further investigated. Almost one out of every two indeterminate findings on FDG-PET/CT is malignant. The majority of the findings are melanoma manifestations, however, in a significant percentage, other primary tumors are found. Upon verification, patient management is changed in most cases.Peer Reviewe

Malignancy Rate of Indeterminate Findings on FDG-PET/CT in Cutaneous Melanoma Patients

Background: The use of 18F-2-Fluor-2-desoxy-D-glucose Positron Emission Tomography/Computed Tomography FDG-PET/CT in clinical routine for staging, treatment response monitoring and post treatment surveillance in metastatic melanoma patients has noticeably increased due to significant improvement of the overall survival rate in melanoma patients. However, determining the dignity of the findings with increased metabolic activity on FDG-PET/CT can be sometimes challenging and may need further investigation. Purpose: We aimed to investigate the malignancy rate of indeterminate findings on FDG-PET/CT in metastatic cutaneous melanoma patients. Methods: This single-center retrospective study included cutaneous melanoma patients who underwent FDG-PET/CT in clinical routine between 2015 and 2017 with findings reported as indeterminate and therefore requiring further evaluation. The dignity of the included findings was determined by subsequent imaging and, if required, additional histopathology. The impact of the outcome on the clinical management was also reported. Results: A total of 842 FDG-PET/CT reports of 244 metastatic cutaneous melanoma patients were reviewed. Sixty indeterminate findings were included. Almost half of all indeterminate findings were lymph nodes, lung nodules and cerebral lesions. In total, 43.3% of all included findings proved to be malignant. 81% of all malignant lesions were metastases of cutaneous melanoma, while 19% of all malignant lesions could be attributed to other primary malignancies, such as lung, breast, thyroid and colorectal cancers. Malignant findings influenced clinical management in 60% of the cases. Conclusion: Indeterminate findings on FDG-PET/CT in metastatic cutaneous melanoma patients should be further investigated. Almost one out of every two indeterminate findings on FDG-PET/CT is malignant. The majority of the findings are melanoma manifestations, however, in a significant percentage, other primary tumors are found. Upon verification, patient management is changed in most cases

Predictive Value of Baseline FDG-PET/CT for the Durable Response to Immune Checkpoint Inhibition in NSCLC Patients Using the Morphological and Metabolic Features of Primary Tumors

Objectives: We aimed to investigate the predictive value of baseline 2-deoxy-2-[18F]fluoro-D-glucose positron emission tomography/computed tomography (FDG-PET/CT) for durable responses to immune checkpoint inhibitors (ICIs) by linking the morphological and metabolic features of primary tumors (PTs) in nonsmall cell lung cancer (NSCLC) patients. Methods: For the purpose of this single-center study, the imaging data of the patients with a first diagnosis of NSCLC and an available baseline FDG-PET/CT between 2020 and 2021 were retrospectively assessed. The baseline characteristics were collected based on clinical reports and interdisciplinary tumor board documentation. The metabolic (such as standardized uptake value SUV maximum and mean (SUVmax, SUV mean), metabolic tumor volume (MTV), total lesion glycolysis (TLG)) and morphological (such as volume, morphology, margin, and presence of lymphangiosis through imaging) features of all the PTs were retrospectively assessed using FDG-PET/CT. Overall survival (OS), progression-free survival (PFS), clinical benefit (CB) and mortality rate were used as endpoints to define the long-term response to therapy. A backward, stepwise logistic regression analysis was performed in order to define the best model for predicting lasting responses to treatment. Statistical significance was assumed at p max, mean, MTV, and TLG were respectively 10.1 ± 6.0, 6.1 ± 3.5, 13.5 ± 30.7, and 71.4 ± 247.7. The median volume of PT ± SD was 13.7 ± 30.7 cm3. The PTs were most frequently solid (86.4%) with irregular margins (76.8%). Furthermore, in one out of five cases, the morphological evidence of lymphangiosis was seen through imaging (n = 25). The median follow-up ± SD was 18.93 ± 6.98 months. The median values ± SD of OS and PFS were, respectively, 14.80 ± 8.68 months and 14.03 ± 9.02 months. Age, PT volume, SUVmax, TLG, the presence of lymphangiosis features through imaging, and clinical stage IV were very strong long-term outcome predictors of patients treated with ICIs, while no significant outcome predictors could be found for the cohort with no ICI treatment. The optimal cut-off values were determined for PT volume (26.94 cm3) and SUVmax (15.05). Finally, 58% of NSCLC patients treated with ICIs had a CB vs. 78.7% of patients in the cohort with no ICI treatment. However, almost all patients treated with ICIs and with disease progression over time died (mortality in the case of disease progression 95% vs. 62.5% in the cohort without ICIs). Conclusion: Baseline FDG-PET/CT could be used to predict a durable response to ICIs in NSCLC patients. Age, clinical stage IV, lymphangiosis features through imaging, PT volume (thus PT MTV due to a previously demonstrated linear correlation), PT SUVmax, and TLG were very strong long-term outcome predictors. Our results highlight the importance of linking clinical data, as much as morphological features, to the metabolic parameters of primary tumors in a multivariate outcome-predicting model using baseline FDG-PET/CT