Bootstrap Calibration Research Articles

Prediction Intervals for Overdispersed Poisson Data and Their Application in Medical and Pre-Clinical Quality Control.

In pre-clinical and medical quality control, it is of interest to assess the stability of the process under monitoring or to validate a current observation using historical control data. Classically, this is done by the application of historical control limits (HCL) graphically displayed in control charts. In many applications, HCL are applied to count data, for example, the number of revertant colonies (Ames assay) or the number of relapses per multiple sclerosis patient. Count data may be overdispersed, can be heavily right-skewed and clusters may differ in cluster size or other baseline quantities (e.g., number of petri dishes per control group or different length of monitoring times per patient). Based on the quasi-Poisson assumption or the negative-binomial distribution, we propose prediction intervals for overdispersed count data to be used as HCL. Variable baseline quantities are accounted for by offsets. Furthermore, we provide a bootstrap calibration algorithm that accounts for the skewed distribution and achieves equal tail probabilities. Comprehensive Monte-Carlo simulations assessing the coverage probabilities of eight different methods for HCL calculation reveal, that the bootstrap calibrated prediction intervals control the type-1-error best. Heuristics traditionally used in control charts (e.g., the limits in Shewhart c- or u-charts or the mean ± 2 SD) fail to control a pre-specified coverage probability. The application of HCL is demonstrated based on data from the Ames assay and for numbers of relapses of multiple sclerosis patients. The proposed prediction intervals and the algorithm for bootstrap calibration are publicly available via the R package predint.

A consistent test of equality of distributions for Hilbert-valued random elements

Two independent random elements taking values in a separable Hilbert space are considered. The aim is to develop a test with bootstrap calibration to check whether they have the same distribution or not. A transformation of both random elements into a new separable Hilbert space is considered so that the equality of expectations of the transformed random elements is equivalent to the equality of distributions. Thus, a bootstrap test procedure to check the equality of means can be used in order to solve the original problem. It will be shown that both the asymptotic and bootstrap approaches proposed are asymptotically correct and consistent. The results can be applied, for example, in functional data analysis. In practice, the test can be solved with simple operations in the original space without applying the mentioned transformation, which is used only to guarantee the theoretical results. Empirical results and comparisons with related methods support and complement the theory.

Empirical likelihood inference for monotone index model

This paper proposes an empirical likelihood inference method for monotone index models. We construct the empirical likelihood function based on a modified score function developed by Balabdaoui et al. (Scand J Stat 46:517–544, 2019), where the monotone link function is estimated by isotonic regression. It is shown that the empirical likelihood ratio statistic converges to a weighted chi-squared distribution. We suggest inference procedures based on an adjusted empirical likelihood statistic that is asymptotically pivotal, and a bootstrap calibration with recentering. A simulation study illustrates usefulness of the proposed inference methods.

Stratified incomplete local simplex tests for curvature of nonparametric multiple regression

Principled nonparametric tests for regression curvature in $\mathbb{R}^{d}$ are often statistically and computationally challenging. This paper introduces the stratified incomplete local simplex (SILS) tests for joint concavity of nonparametric multiple regression. The SILS tests with suitable bootstrap calibration are shown to achieve simultaneous guarantees on dimension-free computational complexity, polynomial decay of the uniform error-in-size, and power consistency for general (global and local) alternatives. To establish these results, a general theory for incomplete $U$-processes with stratified random sparse weights is developed. Novel technical ingredients include maximal inequalities for the supremum of multiple incomplete $U$-processes.

Assessing the Most Vulnerable Subgroup to Type II Diabetes Associated with Statin Usage: Evidence from Electronic Health Record Data

ABSTRACT There have been increased concerns that the use of statins, one of the most commonly prescribed drugs for treating coronary artery disease, is potentially associated with the increased risk of new-onset Type II diabetes (T2D). Nevertheless, to date, there is no robust evidence supporting as to whether and what kind of populations are indeed vulnerable for developing T2D after taking statins. In this case study, leveraging the biobank and electronic health record data in the Partner Health System, we introduce a new data analysis pipeline and a novel statistical methodology that address existing limitations by (i) designing a rigorous causal framework that systematically examines the causal effects of statin usage on T2D risk in observational data, (ii) uncovering which patient subgroup is most vulnerable for developing T2D after taking statins, and (iii) assessing the replicability and statistical significance of the most vulnerable subgroup via a bootstrap calibration procedure. Our proposed approach delivers asymptotically sharp confidence intervals and debiased estimate for the treatment effect of the most vulnerable subgroup in the presence of high-dimensional covariates. With our proposed approach, we find that females with high T2D genetic risk are at the highest risk of developing T2D due to statin usage. Supplementary materials for this article are available online.

Prediction intervals for all of M future observations based on linear random effects models

In many pharmaceutical and biomedical applications such as assay validation, assessment of historical control data, or the detection of anti‐drug antibodies, the calculation and interpretation of prediction intervals (PI) is of interest. The present study provides two novel methods for the calculation of prediction intervals based on linear random effects models and restricted maximum likelihood (REML) estimation. Unlike other REML‐based PI found in the literature, both intervals reflect the uncertainty related with the estimation of the prediction variance. The first PI is based on Satterthwaite approximation. For the other PI, a bootstrap calibration approach that we will callquantile‐calibrationwas used. Due to the calibration process this PI can be easily computed for more than one future observation and based on balanced and unbalanced data as well. In order to compare the coverage probabilities of the proposed PI with those of four intervals found in the literature, Monte Carlo simulations were run for two relatively complex random effects models and a broad range of parameter settings. The quantile‐calibrated PI was implemented in the statistical software R and is available in the predint package.

A Hybrid Approach for the Dynamic Instability Analysis of Single-Layer Latticed Domes with Uncertainties

Currently, there is no unified criterion to evaluate the failure of single-layer latticed domes, and an accurate nonlinear time-history analysis (NTHA) is generally required; however, this does not consider the uncertainties found in practice. The seismic instability of domes subjected to earthquake ground motions has not been thoroughly investigated. In this paper, a new approach is developed to automatically capture the instability points in the incremental dynamic analysis (IDA) of single-layer lattice domes by integrating different efficient and robust methods. First, a seismic fragility analysis with instability parameters is performed using the bootstrap calibration method for the perfect dome. Second, based on the Sobol sequence, the quasi-Monte Carlo (QMC) sampling method is used to efficiently calculate the failure probability of the dome with uncertain parameters, in which the truncated distributions of random parameters are considered. Third, the maximum entropy principle (MEP) method is used to improve the computational efficiency in the analyses of structures with uncertainties. Last, the uncertain interval of the domes is determined based on the IDA method. The proposed method has been used to investigate the instability of single-layer lattice domes with uncertain parameters. The results show that it can determine the probability of structural failure with high efficiency and reliability. Additionally, the limitations of the proposed method for parallel computation are discussed.

Testing similarity between first-order intensities of spatial point processes. A comparative study

Testing whether two spatial point processes have the same spatial distribution is an important task that can be addressed from different perspectives. A Kolmogorov-Smirnov test with asymptotic calibration and a Cramer von Mises type test with bootstrap calibration have recently been developed to compare the first-order intensity of two observed patterns. Motivated by common practice in epidemiological studies, we introduce a regression test based on the relative risk function with two alternative bootstrap calibrations. This paper compares the performance of these nonparametric tests through both an intensive simulation study, and the application to wildfire and crime data. The three tests provide good calibrations of the null hypothesis for simulated Poisson and non-Poisson spatial point processes, but the Cramer von Mises and regression tests outperform the cost-efficient Kolmogorov-Smirnov test in terms of power. In the real data analysis we have seen that the Kolmogorov-Smirnov test does not detect differences between spatial point patterns when dealing with sparse data. In view of these results, it would be preferable using the Cramer von Mises or regression tests despite their higher computational demand.

Possible Association of Periodontal Disease and Macular Degeneration: A Case-Control Study.

Oral pathogens have been identified in bioptic specimens from Age-Related Macular Degeneration (ARMD) patients, and alveolar bone loss has been related to ARMD. Therefore, the possible association between ARMD and periodontal disease was investigated in the present case-control study, evaluating clinical and radiographic periodontal parameters, primarily, in cases vs. controls and, secondarily, in relation to ARMD risk factors, in cases, to highlight a possible pathogenic link between the disorders. Forty ARMD cases and 40 non-ARMD controls, matched for age (±3 years) and gender and homogeneous for ARMD risk factors, therefore comparable, underwent full-mouth periodontal charting, panoramic radiograph, and medical data, including ARMD risk factors, collection. Statistical analysis was conducted using the language R. Comparisons between groups were made using both traditional t-tests and Yuen’s test with bootstrap calibration. Enrolled subjects were ≥55 years old, and 50 females and 30 males were equally distributed among the two groups. No statistically significant difference was found in clinical and radiographic periodontal parameters in cases vs. controls. In the case group, no differences were found when relating the periodontal parameters to ARMD risk factors, except for Clinical Attachment Level values that were statistically significantly higher in hypertensive ARMD subjects. A possible association between periodontal disease and ARMD may be hypothesized in hypertensive ARMD subjects, with hypertension as a possible pathogenic link between the disorders.

A nomogram to predict cadmium-induced renal tubular dysfunction

Cadmium-induced renal dysfunction varies between individuals. It would be valuable to figure out those susceptible individuals or predict the risk of cadmium induced renal dysfunction. In the present study, we used a nomogram model to identify high-risk of cadmium-induced renal tubular dysfunction. 342 subjects living in low and moderately cadmium polluted areas were included in this study. The daily cadmium intake from food (FCd) was estimated using food survey. The cadmium in blood (BCd) and urine (UCd) were detected by using flame atomic absorption spectrometry. Urinary β2Microglobulin (UBMG) was chosen as indicator of renal dysfunction. Logistic regression was used to select the independent risk factors for renal dysfunction. Bootstrap self-sampling and calibration curves were performed to quantify our modeling strategy. Age, sex, BCd and TCd were used to construct the nomogam in total population; age, BCd and TCd were adopted in women; age and BCd were used in men. The internal validation showed the C-index was 0.76 (95% 47 confidence interval (CI): 0.71–0.82) in total population, 0.74 (95% CI: 0.69–0.79) in men and 0.78 (95% CI: 0.72–0.84) in women. The area under the curve of the nomogram was 0.77 (95% CI: 0.71–0.83) in total population, 0.82(95% CI: 0.74–0.90) in women and 0.74(95% CI: 0.66–0.82) in men. Nomogram may be a rapid and simple risk assessment tool for predicting high-risk of renal tubular dysfunction in subjects exposed cadmium.

Improving coverage probabilities for parametric tolerance intervals via bootstrap calibration.

Statistical tolerance intervals are commonly employed in biomedical and pharmaceutical research, such as in lifetime analysis, the assessment of biosimilarity of branded and generic versions of biopharmaceutical drugs, and in quality control of drug products to ensure that a specified proportion of the products are covered within established acceptance limits. Exact two-sided parametric tolerance intervals are only available for the normal distribution, while exact one-sided parametric tolerance limits are available for a limited number of distributions. Approximations to two-sided parametric tolerance intervals often use the Bonferroni correction on the one-sided tolerance interval calculation; however, this often incurs a higher coverage probability than the nominal level. Recently, the usage of a bootstrap calibration has been demonstrated as a way to improve coverage probabilities of tolerance intervals for very specific and complex distributional settings. We present a focused treatment on using a single-layer bootstrap calibration to improve the coverage probabilities of two-sided parametric tolerance intervals. Simulation results clearly demonstrate the improved coverage probabilities towards the nominal level over the uncalibrated setting. Applications to medical data for various parametric distributions also highlight the utility of constructing these calibrated tolerance intervals.

Fire seasonality identification with multimodality tests

Understanding the role of vegetation fires in the Earth system is an important environmental problem. Although fire occurrence is influenced by natural factors, human activity related to land use and management has altered the temporal patterns of fire in several regions of the world. Hence, for a better insight into fires regimes it is of special interest to analyze where human activity has altered fire seasonality. For doing so, multimodality tests are a useful tool for determining the number of annual fire peaks. The periodicity of fires and their complex distributional features motivate the use of nonparametric circular statistics. The unsatisfactory performance of previous circular nonparametric proposals for testing multimodality justifies the introduction of a new approach, considering an adapted version of the excess mass statistic, jointly with a bootstrap calibration algorithm. A systematic application of the test on the Russia–Kazakhstan area is presented in order to determine how many fire peaks can be identified in this region. A False Discovery Rate correction, accounting for the spatial dependence of the data, is also required.

Bootstrap tuning in Gaussian ordered model selection

The paper focuses on the problem of model selection in linear Gaussian regression with unknown possibly inhomogeneous noise. For a given family of linear estimators $\{\widetilde{\boldsymbol{{\theta}}}_{m},m\in\mathscr{M}\}$, ordered by their variance, we offer a new “smallest accepted” approach motivated by Lepski’s device and the multiple testing idea. The procedure selects the smallest model which satisfies the acceptance rule based on comparison with all larger models. The method is completely data-driven and does not use any prior information about the variance structure of the noise: its parameters are adjusted to the underlying possibly heterogeneous noise by the so-called “propagation condition” using a wild bootstrap method. The validity of the bootstrap calibration is proved for finite samples with an explicit error bound. We provide a comprehensive theoretical study of the method, describe in details the set of possible values of the selected model $\widehat{m}\in\mathscr{M}$ and establish some oracle error bounds for the corresponding estimator $\widehat{\boldsymbol{{\theta}}}=\widetilde{\boldsymbol{{\theta}}}_{\widehat{m}}$.

Abstract P2-07-12: A prognostic prediction nomogram (PDIDC) for breast Paget's disease with infiltrating ductal carcinoma patients: A SEER cohort analysis

Abstract Purpose The aim of the study was to develop a specific nomogram for prediction of prognosis for breast Paget's disease with infiltrating ductal carcinoma (PD-IDC) patients. Patients and Methods Patients data were obtained by the Surveillance, Epidemiology, and End Results (SEER) program (N=2502). Study outcome was Breast Cancer Specific Survival (BCSS). Cox proportional hazards model was applied to identify risk factors and develop predictive model. For internal validation, discrimination was calculated with the concordance index (C-index) using the bootstrap method and calibration assessed. Results NPI classification, skin symptom, tumor site and age showed significant association with BCSS(table.1)and were used to build the PDIDC nomogram and to calculate risk score. PDIDC nomogram's C-index (0.791, 95%CI 0.783-0.818) showed better discrimination power than NPI classification (0.691, 95%CI, 0.650-0.735, P= 0.000) and AJCC staging (0.718, 95%CI, 0.695-0.741, P=0.000). Patients were divided into high-risk (1882/2502, 75.21%) and low-risk (620/2502, 24.78%) subgroups with the optimal cut-off of risk scores (4.28). The total BCSS of low-risk subgroup was 77.8% (95%CI 74.4%-81.4%) vs. 31.1% (95%CI 19.4-49.8) of high-risk group (P=0.000). Bootstrap internal validation demonstrated an average C-index of 0.739 (95% CI, 0.692-0.746). The nomogram calibration was validated to be accurate in predicting 5-year and 10-year survival. Variable finally selected for risk predicted model.PredictorHazard RatioP Value95% CINPI classification Good1 Moderate2.170.0001.51-3.14Poor7.260.0004.96-10.63Skin symptom Without1 With1.760.0001.34-2.32Tumor site Centrally located1 Non-centrally located1.250.0421.07-1.56Age*1.010.0001.01-1.03* Continuous variable. Conclusion Utilizing NPI classification, skin symptom, tumor site and age, we developed the PDIDC nomogram to predict the 5-year and 10-year BCSS of breast PD-IDC patients. Citation Format: Tan L, Chen K, Jiang WG, You N, Wang Y, Sanders A, Liang G, Liu Z, Ling Y, Zhong W, Tian Z, Gong C. A prognostic prediction nomogram (PDIDC) for breast Paget's disease with infiltrating ductal carcinoma patients: A SEER cohort analysis [abstract]. In: Proceedings of the 2018 San Antonio Breast Cancer Symposium; 2018 Dec 4-8; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2019;79(4 Suppl):Abstract nr P2-07-12.

Hypofractionated stereotactic radiotherapy for oligometastatic patients: developing of a response predictive model.

Treatment of oligometastatic patients is a current challenge in radiation oncology. Aim of this study is to define a dose-response relationship for hypofractionated radiotherapy of oligometastases. Retrospective analysis of metastases treated by hypofractionated stereotactic radiotherapy was performed. Delivered dose was calculated both as biological effective dose (BED10), and as ratio between BED10 and the logarithm of metastasis volume (BED10 logVolume Ratio, BVR). Two dose-response models were defined by logistic regression. The fitted outcome was the Metastases Complete Response (MCR). Performances of the models were assessed by area under the receiver operating curve (AUC) and by bootstrap calibration of original data. BED10 and BVR impact on survival outcomes has been evaluated. Fifty-three patients with 79 metastases were analyzed. AUC and calibration of BVR-based logistic model showed better accuracy in predicting MCR with respect to BED10-based model. No significant difference between the two ROCs was observed (De Long test p value > 0.05), but significant discordance in calibration resulted in the BED10 model (p value < 0.05 in Hosmer-Lemeshow Goodness of fit test). BVR returned also better results in multivariate analyses for survival outcomes. The ratio between BED10 and the logarithm of metastasis volume (BVR), as a corrective factor for fitting the probability of metastases response to stereotactic radiotherapy, could be a tool for evaluating and prescribing treatments for oligometastatic disease. BVR can be useful for producing more reliable survival statistics too.

Nonparametric Interval Estimators for the Coefficient of Variation.

The coefficient of variation (CV) is a widely used scaleless measure of variability in many disciplines. However the inference for the CV is limited to parametric methods or standard bootstrap. In this paper we propose two nonparametric methods aiming to construct confidence intervals for the coefficient of variation. The first one is to apply the empirical likelihood after transforming the original data. The second one is a modified jackknife empirical likelihood method. We also propose bootstrap procedures for calibrating the test statistics. Results from our simulation studies suggest that the proposed methods, particularly the empirical likelihood method with bootstrap calibration, are comparable to existing methods for normal data and yield better coverage probabilities for nonnormal data. We illustrate our methods by applying them to two real-life datasets.

Subgroups from regression trees with adjustment for prognostic effects and postselection inference.

Identification of subgroups with differential treatment effects in randomized trials is attracting much attention. Many methods use regression tree algorithms. This article addresses 2 important questions arising from the subgroups: how to ensure that treatment effects in subgroups are not confounded with effects of prognostic variables and how to determine the statistical significance of treatment effects in the subgroups. We address the first question by selectively including linear prognostic effects in the subgroups in a regression tree model. The second question is more difficult because it falls within the subject of postselection inference. We use a bootstrap technique to calibrate normal-theory t intervals so that their expected coverage probability, averaged over all the subgroups in a fitted model, approximates the desired confidence level. It can also provide simultaneous confidence intervals for all subgroups. The first solution is implemented in the GUIDE algorithm and is applicable to data with missing covariate values, 2 or more treatment arms, and outcomes subject to right censoring. Bootstrap calibration is applicable to any subgroup identification method; it is not restricted to regression tree models. Two real examples are used for illustration: a diabetes trial where the outcomes are completely observed but some covariate values are missing and a breast cancer trial where the outcome is right censored.

Characteristics of new solid nodules detected in incidence screening rounds of low-dose CT lung cancer screening: the NELSON study

PurposeNew nodules after baseline are regularly found in low-dose CT lung cancer screening and have a high lung cancer probability. It is unknown whether morphological and location characteristics can improve...

Approximate confidence and tolerance limits for the discrete Pareto distribution for characterizing extremes in count data

Statistical tolerance intervals for discrete distributions are widely employed for assessing the magnitude of discrete characteristics of interest in applications like quality control, environmental monitoring, and the validation of medical devices. For such data problems, characterizing extreme counts or outliers is also of considerable interest. These applications typically use traditional discrete distributions, like the Poisson, binomial, and negative binomial. The discrete Pareto distribution is an alternative yet flexible model for count data that are heavily right‐skewed. Our contribution is the development of statistical tolerance limits for the discrete Pareto distribution as a strategy for characterizing the extremeness of observed counts in the tail. We discuss the coverage probabilities of our procedure in the broader context of known coverage issues for statistical intervals for discrete distributions. We address this issue by applying a bootstrap calibration to the confidence level of the asymptotic confidence interval for the discrete Pareto distribution's parameter. We illustrate our procedure on a dataset involving cyst formation in mice kidneys.

Establishing of a 1000 V Multi-Decade Inductive Voltage Divider Standard at NIM

A multi-decade 1000-V inductive voltage divider (IVD) was established at the National Institute of Metrology in China. This multi-decade IVD will function as the 1000-V voltage ratio standard at the power frequency in a traceability system. It can provide a wide output ratio ranging from $1\times 10^{-8}$ to 1 with the accuracy better than $0.05~\mu \text{V}$ /V (in-phase and quadrature). Two different winding connection methods are used to achieve their respective effects. A special structure with four independent shieldings is used at first two windings in order to reduce the IVD’s burden. An error compensation method, which is based on the transformer injection, is introduced to improve the output ratio accuracy. An improved bootstrap calibration method with fully equal potential guards on all parts of the circuits at nonzero potential is presented, and a multi-ratio reference transformer with symmetric leakage design is used to calibrate the multi-decade IVD for combinational usage. The expanded uncertainty of the self-calibration is less than $0.02~\mu \text{V}$ /V.