A robust Spearman correlation coefficient permutation test.

In this work, we show that Spearman's correlation coefficient test about H0:ρs=0 found in most statistical software is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the sample size is small. There is common misconception that the tests about ρs=0 are robust to deviations from bivariate normality. However, we found under certain scenarios violation of the bivariate normality assumption has severe effects on type I error control for the common tests. To address this issue, we developed a robust permutation test for testing the hypothesis H0:ρs=0 based on an appropriately studentized statistic. We will show that the test is asymptotically valid in general settings. This was demonstrated by a comprehensive set of simulation studies, where the proposed test exhibits robust type I error control, even when the sample size is small. We also demonstrated the application of this test in two real world examples.

The generalized sigmoidal quantile function.

In this note we introduce a new smooth nonparametric quantile function estimator based on a newly defined generalized expectile function and termed the sigmoidal quantile function estimator. We also introduce a hybrid quantile function estimator, which combines the optimal properties of the classic kernel quantile function estimator with our new generalized sigmoidal quantile function estimator. The generalized sigmoidal quantile function can estimate quantiles beyond the range of the data, which is important for certain applications given smaller sample sizes. This property of extrapolation is illustrated in order to improve standard bootstrap smoothing resampling methods.

A Characterization of Most(More) Powerful Test Statistics with Simple Nonparametric Applications.

Data-driven most powerful tests are statistical hypothesis decision-making tools that deliver the greatest power against a fixed null hypothesis among all corresponding data-based tests of a given size. When the underlying data distributions are known, the likelihood ratio principle can be applied to conduct most powerful tests. Reversing this notion, we consider the following questions. (a) Assuming a test statistic, say T, is given, how can we transform T to improve the power of the test? (b) Can T be used to generate the most powerful test? (c) How does one compare test statistics with respect to an attribute of the desired most powerful decision-making procedure? To examine these questions, we propose one-to-one mapping of the term "most powerful" to the distribution properties of a given test statistic via matching characterization. This form of characterization has practical applicability and aligns well with the general principle of sufficiency. Findings indicate that to improve a given test, we can employ relevant ancillary statistics that do not have changes in their distributions with respect to tested hypotheses. As an example, the present method is illustrated by modifying the usual t-test under nonparametric settings. Numerical studies based on generated data and a real-data set confirm that the proposed approach can be useful in practice.

Inferential procedures based on the weighted Pearson correlation coefficient test statistic.

In this note, we evaluated the type I error control of the commonly used t-test found in most statistical software packages for testing the hypothesis on H0:ρ=0 vs. H1:ρ>0 based on the sample weighted Pearson correlation coefficient. We found the type I error rate is severely inflated in general cases, even under bivariate normality. To address this issue, we derived the large sample variance of the weighted Pearson correlation. Based on this result, we proposed an asymptotic test and a set of studentized permutation tests. A comprehensive set of simulation studies with a range of sample sizes and a variety of underlying distributions were conducted. The studentized permutation test based on Fisher's Z statistic was shown to robustly control the type I error even in the small sample and non-normality settings. The method was demonstrated with an example data of country-level preterm birth rates.

Leveraging homologous hypotheses for increased efficiency in tumor growth curve testing.

In this note, we present an innovative approach called "homologous hypothesis tests" that focuses on cross-sectional comparisons of average tumor volumes at different time-points. By leveraging the correlation structure between time-points, our method enables highly efficient per time-point comparisons, providing inferences that are highly efficient as compared to those obtained from a standard two-sample t test. The key advantage of this approach lies in its user-friendliness and accessibility, as it can be easily employed by the broader scientific community through standard statistical software packages.

Leveraging Homologous Hypotheses for Increased Efficiency in Tumor Growth Curve Testing.

In this note, we present an innovative approach called "homologous hypothesis tests" that focuses on cross-sectional comparisons of average tumor volumes at different time-points. By leveraging the correlation structure between time-points, our method enables highly efficient per time-point comparisons, providing inferences that are highly efficient as compared to those obtained from a standard two-sample t-test. The key advantage of this approach lies in its user-friendliness and accessibility, as it can be easily employed by the broader scientific community through standard statistical software packages.

Exact inference around ordinal measures of association is often not exact.

In this paper, we build upon the work of DiCiccio and Romano (2017) by extending their permutation test approach, based on the Pearson correlation coefficient in the continuous case, to ordinal measures of association. We investigate commonly used ordinal measures such as the Spearman correlation, Kendall's tau-b, and gamma, which are widely implemented in commercial and open-source software packages for exact testing routines based on generalized hypergeometric probabilities. Similar to DiCiccio and Romano's method, we apply studentization to correct the test statistic, which yields asymptotically valid inference for testing no ordinal association. We present a comprehensive theoretical framework for our approach, followed by a simulation study. Furthermore, we use toy examples to highlight the differences between the exact tests and the asymptotically valid tests. Our findings align with those of DiCiccio and Romano, indicating that exact permutation tests based on ordinal measures of association are often not exact, whereas the asymptotically correct tests perform well for moderate to large sample sizes.

The Sign Test, Paired Data, and Asymmetric Dependence: A Cautionary Tale.

In the paired data setting, the sign test is often described in statistical textbooks as a test for comparing differences between the medians of two marginal distributions. There is an implicit assumption that the median of the differences is equivalent to the difference of the medians when employing the sign test in this fashion. We demonstrate however that given asymmetry in the bivariate distribution of the paired data, there are often scenarios where the median of the differences is not equal to the difference of the medians. Further, we show that these scenarios will lead to a false interpretation of the sign test for its intended use in the paired data setting. We illustrate the false-interpretation concept via theory, a simulation study, and through a real-world example based on breast cancer RNA sequencing data obtained from the Cancer Genome Atlas (TCGA).

Phase IIa Study of SurVaxM Plus Adjuvant Temozolomide for Newly Diagnosed Glioblastoma.

PURPOSE: Despite intensive treatment with surgery, radiation therapy, temozolomide (TMZ) chemotherapy, and tumor-treating fields, mortality of newly diagnosed glioblastoma (nGBM) remains very high. SurVaxM is a peptide vaccine conjugate that has been shown to activate the immune system against its target molecule survivin, which is highly expressed by glioblastoma cells. We conducted a phase IIa, open-label, multicenter trial evaluating the safety, immunologic effects, and survival of patients with nGBM receiving SurVaxM plus adjuvant TMZ following surgery and chemoradiation (ClinicalTrials.gov identifier: NCT02455557). METHODS: Sixty-four patients with resected nGBM were enrolled including 38 men and 26 women, in the age range of 20-82 years. Following craniotomy and fractionated radiation therapy with concurrent TMZ, patients received four doses of SurVaxM (500 µg once every 2 weeks) in Montanide ISA-51 plus sargramostim (granulocyte macrophage colony-stimulating factor) subcutaneously. Patients subsequently received adjuvant TMZ and maintenance SurVaxM concurrently until progression. Progression-free survival (PFS) and overall survival (OS) were reported. Immunologic responses to SurVaxM were assessed. RESULTS: SurVaxM plus TMZ was well tolerated with no serious adverse events attributable to SurVaxM. Of the 63 patients who were evaluable for outcome, 60 (95.2%) remained progression-free 6 months after diagnosis (prespecified primary end point). Median PFS was 11.4 months and median OS was 25.9 months measured from first dose of SurVaxM. SurVaxM produced survivin-specific CD8+ T cells and antibody/immunoglobulin G titers. Apparent clinical benefit of SurVaxM was observed in both methylated and unmethylated patients. CONCLUSION: SurVaxM appeared to be safe and well tolerated. The combination represents a promising therapy for nGBM. For patients with nGBM treated in this manner, PFS may be an acceptable surrogate for OS. A large randomized clinical trial of SurVaxM for nGBM is in progress.

A generalized BLUE approach for combining location and scale information in a meta-analysis.

In systematic reviews and meta-analyses, one is interested in combining information from a variety of sources in order to obtain unbiased and efficient pooled estimates of the mean treatment effect compared to a control group along with the corresponding standard errors and confidence intervals, particularly when the source data is unavailable. However, in many studies the mean and standard deviation are not reported in lieu of other descriptive measures such as the median and quartiles. In this note we provide a theoretically optimal best linear unbiased estimator (BLUE) strategy for combining different types of summary information in order to pool results and estimate the overall treatment effect and the corresponding confidence intervals. Our approach is less biased and much more flexible than past attempts at solving this problem and can accommodate combining a variety of summary information across studies. We show that confidence intervals based on our methods have the appropriate coverage probabilities. Our proposed methods are theoretically justified and verified by simulation studies. The BLUE method is illustrated via a real data application.

A semi-parametric bootstrap-based best linear unbiased estimator of location under symmetry.

In this note we provide a novel semi-parametric best linear unbiased estimator (BLUE) of location and its corresponding variance estimator under the assumption the random variate is generated from a symmetric location-scale family of distributions. The approach follows in a two-stage fashion and is based on the exact bootstrap estimate of the covariance matrix of the order statistic. We generalize our approach to add a robustness component in order to derive a trimmed BLUE of location under a semi-parametric symmetry assumption.

First-In-Human Computer-Optimized Endobronchial Ultrasound-Guided Interstitial Photodynamic Therapy for Patients With Extrabronchial or Endobronchial Obstructing Malignancies.

Objective: Patients with inoperable extrabronchial or endobronchial tumors who are not candidates for curative radiotherapy have dire prognoses with no effective long-term treatment options. To reveal that our computer-optimized interstitial photodynamic therapy (I-PDT) is safe and potentially effective in the treatment of patients with inoperable extra or endobronchial malignancies inducing central airway obstructions. Methods: High-spatial resolution computer simulations were used to personalize the light dose rate and dose for each tumor. Endobronchial ultrasound with a transbronchial needle was used to place the optical fibers within the tumor according to an individualized plan. The primary and secondary end points were safety and overall survival, respectively. An exploratory end point evaluated changes in immune markers. Results: Eight patients received I-PDT with planning, and five of these received additional external beam PDT. Two additional patients received external beam PDT. The treatment was declared safe. Three of 10 patients are alive at 26.3, 12, and 8.3 months, respectively, after I-PDT. The treatments were able to deliver a prescribed light dose rate and dose to 87% to 100% and 18% to 92% of the tumor volumes, respectively. A marked increase in the proportion of monocytic myeloid-derived suppressor cells expressing programmed death-ligand 1 was measured in four of seven patients. Conclusions: Image-guided light dosimetry for I-PDT with linear endobronchial ultrasound transbronchial needle is safe and potentially beneficial in increasing overall survival of patients. I-PDT has a positive effect on the immune response including an increase in the proportion of programmed death-ligand 1-expressing monocytic myeloid-derived suppressor cells.

Exact unconditional inference for analyzing contingency tables in finite populations.

With recent developments in computer power the application of exact inferential methods has become more feasible which has resulted in increasing popularity of these approaches. However, there is a lack of such methodology for populations with more complex structure, such as finite populations. When a small sample is drawn from a finite population, the number of individuals with a specific characteristic of interest follows hypergeometric distribution. In order to test for the comparison of two proportions in finite populations we develop an exact unconditional test. We utilize the information gained from the sample to restrict our search for the maximum p-value. Our proposed test has power equal to its competitors while maintains the pre-specified nominal significance level.

A Presurgical-Window Intervention Trial of Isothiocyanate-Rich Broccoli Sprout Extract in Patients with Breast Cancer.

SCOPE: Dietary isothiocyanates (ITCs) from cruciferous vegetables have shown potent anti-breast cancer activities in preclinical models, but their anticancer effects in vivo in breast cancer patients remain elusive. A proof-of-principle, presurgical window of opportunity trial is conducted to assess the anticancer effects of dietary ITCs in breast cancer patients. METHODS AND RESULTS: Thirty postmenopausal breast cancer patients are randomly assigned to receive ITC-rich broccoli sprout extract (BSE) (200 µmol ITC per day) or a placebo for 2 weeks. Expression of biomarkers related to ITCs functions are measured in breast cancer tissue specimens at pre- and post-interventions using immunohistochemistry staining. First morning urine samples are collected at both timepoints for proteomic analysis. Overall, the study shows high compliance (100%) and low toxicity (no grade 4 adverse event). Trends of increase in cleaved caspase 3 and tumor-infiltrating lymphocytes (TILs) and trends of decrease in Ki-67 and nuclear to cytoplasm ratio of estrogen receptor (ER)-α are observed in the BSE arm only, consistent with the significantly altered signaling pathways identified in urinary proteomic analysis. CONCLUSIONS: Anticancer activities of ITCs are observed in breast cancer patients, supporting the potential beneficial roles of ITC-containing cruciferous vegetables in breast cancer prognosis.

Understanding Drug Sensitivity and Tackling Resistance in Cancer.

Decades of research into the molecular mechanisms of cancer and the development of novel therapeutics have yielded a number of remarkable successes. However, our ability to broadly assign effective, rationally targeted therapies in a personalized manner remains elusive for many patients, and drug resistance persists as a major problem. This is in part due to the well-documented heterogeneity of cancer, including the diversity of tumor cell lineages and cell states, the spectrum of somatic mutations, the complexity of microenvironments, and immune-suppressive features and immune repertoires, which collectively require numerous different therapeutic approaches. Here, we describe a framework to understand the types and biological causes of resistance, providing translational opportunities to tackle drug resistance by rational therapeutic strategies.

Practical and robust test for comparing binomial proportions in the randomized phase II setting.

The one-arm, non-randomized, one/two-stage phase II designs have been a mainstay in oncology trials for evaluating response rates or similar variants (i.e., tests about single proportions). With the goal of screening new therapies that have the potential to move into a randomized phase III trial or a subsequent randomized phase II trial, all while maintaining a logistically feasible sample size. However, since the implementation of the Food and Drug Administration's Fast Track Designation, there has been a trend toward randomized phase II clinical trials as a source of stronger evidence for those seeking fast-track approvals. While there are many single- and multi-stage randomized designs for evaluating proportions in this phase II setting, there still exist limitations in terms of sample size (which directly impacts cost and study duration) or operating characteristics (ex. maintained type I error). In this article, we propose a new test for comparing two binomial proportions, which is a modification across existing methods (the standard z-test and Jung's test). This approach is contrasted with existing methods via numeric evaluation and further contrasted using a real-world oncology trial. The proposed method demonstrates improvements in efficiency and robustness against deviations from design assumptions. When applied to the existing trial, significant savings with respect to cost and time are illustrated. Our proposed test for comparing binomial proportions provides an efficient and robust alternative in the randomized phase II oncology setting, especially when the control arm has a high rate.

Phase Ib/II Study of Cetuximab plus Pembrolizumab in Patients with Advanced RAS Wild-Type Colorectal Cancer.

PURPOSE: We evaluated the antitumor efficacy of cetuximab in combination with pembrolizumab in patients with RAS wild-type (RASwt), metastatic colorectal adenocarcinoma (mCRC). PATIENTS AND METHODS: In this phase Ib/II study, cetuximab was combined with pembrolizumab in patients with RASwt mCRC with ≥ one prior line of therapy for advanced disease. We analyzed baseline on-treatment tumor tissues for changes in the tumor microenvironment (TME), using flow cytometry and multispectral immunofluorescence. RESULTS: Forty-four patients were evaluable for efficacy. The study was negative for the primary efficacy endpoint [overall response rate: 2.6%, 6-month progression-free survival (PFS): 31%; P = 0.52]. Median PFS was 4.1 months [95% confidence interval (CI): 3.9-5.5 months]. No increase in adverse effects was identified. We observed favorable immunomodulation with 47% increase in the number of intratumoral CTLs posttreatment (P = 0.035). These changes were more pronounced in patients with tumor shrinkage (P = 0.05). The TME was characterized by high numbers of TIM3+ and CTLA4+ cells; there were few activated OX40+ cells. PD-L1 expression was higher in pretreatment tumor cells from metastatic sites versus primary tumor samples (P < 0.05). Higher numbers of PD-L1+ tumor cells at baseline were associated with tumor shrinkage (P = 0.04). Analysis of immune populations in the blood demonstrated decreases in PD-1+ memory effector cells (P = 0.04) and granulocytic myeloid-derived suppressor cells (P = 0.03), with simultaneous increases in CD4+/CTLA4+ cells (P = 0.01). CONCLUSIONS: The combination of cetuximab and pembrolizumab is inactive in patients with RASwt mCRC, despite its partial local immunologic efficacy. Further development of immuno-oncology combinations with enhanced efficacy and/or targeting additional or alternative immune checkpoints merits investigation.

Inference for L-estimators of location using a bootstrap warping approach.

In this note we propose a new semi-parametric bootstrap procedure for hypothesis tests about a statistical function and termed bootstrap warping. This procedure was motivated by empirical likelihood and bootstrap tilting techniques. The procedure is computationally efficient and has a fixed number of parameters. We show that the warping procedure has good type I error control and has monotone power as a function of sample size and shift alternatives.

An Accelerated Life Model Analog for Discrete Survival and Count Data.

BACKGROUND AND OBJECTIVE: Our goal is to provide an overall strategy for utilizing continuous accelerated life models in the discrete setting that provides a unique and flexible modeling approach across a variety of hazard shapes. METHODS: We convert well-known continuous accelerated life distributions into their discrete counterpart and show theoretically that the existing software that currently exists to accommodate, left, right and interval censoring in the continuous case is re-usable in the discrete setting due to the structure of the likelihood equations. RESULTS: We demonstrate across a variety of simulated and real-world data that our modeling approach can accommodate discrete data that may either be approximately symmetric, left-skewed or right skewed, overcoming the limitations of more traditional modeling approaches. CONCLUSIONS: We illustrate both theoretically and through simulations that our approach for accommodating discrete failure time and count data is quite flexible. We demonstrate that the special case of the discrete Weibull model readily can accommodate truly Poisson distributed data and has a great degree of flexibility for non-Poisson distributed data.

Sex Hormones, Insulin, and Insulin-like Growth Factors in Recurrence of High-Stage Endometrial Cancer.

BACKGROUND: The influence of sex hormone and insulin/insulin-like growth factor (IGF) axis signaling on endometrial cancer recurrence is unknown. We evaluated these pathways in a prospective cohort of Gynecologic Oncology Group (GOG)0210 trial endometrial adenocarcinoma patients. METHODS: Stage II-IV patients (N = 816) were included in this study. Pretreatment specimens were tested for tumor mRNA and protein expression of IGF1, IGF2, IGF-binding proteins (IGFBP)-1 and -3, insulin (IR) and IGF-I receptors (IGF1R), phosphorylated IR/IGF1R (pIGF1R/pIR), and estrogen (ER) and progesterone receptors (PR) using qPCR and IHC. Serum concentrations of insulin, IGF-I, IGFBP-3, estradiol, estrone, and sex hormone binding globulin were measured. HRs and 95% confidence intervals (CI) for progression-free survival were calculated from Cox models adjusting for age, stage, and grade. RESULTS: Recurrence occurred in 280 (34%) cases during a median of 4.6 years of follow-up. ER positivity (HR, 0.67; 95% CI, 0.47-0.95), IR positivity (HR, 0.53; 95% CI, 0.29-0.98), and circulating IGF-I (highest vs. lowest quartile: HR, 0.66; 95% CI, 0.47-0.92) were inversely associated with recurrence risk. Circulating estradiol (highest vs. lowest tertile: HR, 1.55; 95% CI, 1.02-2.36) and pIGF1R/pIR positivity (HR, 1.40; 95% CI, 1.02-1.92) were associated with increased recurrence risk. CONCLUSIONS: Circulating estradiol and tumor tissue phosphorylated (activated) IGR1R/IR were independently associated with higher risk of recurrence in patients with endometrial cancer. IMPACT: This study may inform future clinical trials of endocrine-targeted adjuvant therapies in patients with endometrial cancer that could include baseline assessment of serum and tissue biomarkers of estradiol and insulin signaling pathways.