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Equal-bin-width histogram versus equal-bin-count histogram.

ABSTRACT: The histogram has all its bin widths equal to some non-random number arbitrary set by an analyst (EBWH). In the result, particular bin counts are random variables. This paper presents also a histogram that is constructed in a converse manner. Bin counts are all equal to some non-random number arbitrary set by an analyst (EBCH). In the result, particular bin widths are random variables. The first goal of the paper is a choose of constant bin width (of bin numbers k) in the EBWH, which maximize the similarity measure in the Monte Carlo simulation. The second goal is a choose of constant bin count in the EBCH, which maximize the similarity measure in the Monte Carlo simulation. The third goal is to present similarity measures between empirical and theoretical data. The fourth goal is the comparative analysis of two histogram methods by means of the frequency formula. The first additional goal is a tip how to proceed in EBCH when modulo(n,k)≠0. The second additional goal is the software in the form of a Mathcad file with the implementation of EBWH and EBCH.

SUBMITTER: Sulewski P

PROVIDER: S-EPMC9041617 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature

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Equal-bin-width histogram versus equal-bin-count histogram.

Sulewski Piotr P

Journal of applied statistics 20200626 12

The histogram has all its bin widths equal to some non-random number arbitrary set by an analyst (EBWH). In the result, particular bin counts are random variables. This paper presents also a histogram that is constructed in a converse manner. Bin counts are all equal to some non-random number arbitrary set by an analyst (EBCH). In the result, particular bin widths are random variables. The first goal of the paper is a choose of constant bin width (of bin numbers <i>k</i>) in the EBWH, which maxi ...[more]

PMID: 35706612

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Project description:BackgroundIdiopathic Pulmonary Fibrosis (IPF) represents a chronic lung disease with unpredictable course.MethodsWe aimed to investigate prognostic performance of complete blood count parameters in IPF. Treatment-naïve patients with IPF were retrospectively enrolled from two independent cohorts (derivation and validation) and split into subgroups (high and low) based on median baseline monocyte count and red cell distribution width (RDW).ResultsOverall, 489 patients (derivation cohort: 300, validation cohort: 189) were analyzed. In the derivation cohort, patients with monocyte count ≥ 0.60 K/μL had significantly lower median FVC%pred [75.0, (95% CI 71.3-76.7) vs. 80.9, (95% CI 77.5-83.1), (P = 0.01)] and DLCO%pred [47.5, (95% CI 44.3-52.3) vs. 53.0, (95% CI 48.0-56.7), (P = 0.02)] than patients with monocyte count < 0.60 K/μL. Patients with RDW ≥ 14.1% had significantly lower median FVC%pred [75.5, (95% CI 71.2-79.2) vs. 78.3, (95% CI 76.0-81.0), (P = 0.04)] and DLCO%pred [45.4, (95% CI 43.3-50.5) vs. 53.0, (95% CI 50.8-56.8), (P = 0.008)] than patients with RDW < 14.1%. Cut-off thresholds from the derivation cohort were applied to the validation cohort with similar discriminatory value, as indicated by significant differences in median DLCO%pred between patients with high vs. low monocyte count [37.8, (95% CI 35.5-41.1) vs. 45.5, (95% CI 41.9-49.4), (P < 0.001)] and RDW [37.9, (95% CI 33.4-40.7) vs. 44.4, (95% CI 41.5-48.9), (P < 0.001)]. Patients with high monocyte count and RDW of the validation cohort exhibited a trend towards lower median FVC%pred (P = 0.09) and significantly lower median FVC%pred (P = 0.001), respectively. Kaplan-Meier analysis in the derivation cohort demonstrated higher all-cause mortality in patients with high (≥ 0.60 K/μL) vs. low monocyte count (< 0.60 K/μL) [HR 2.05, (95% CI 1.19-3.53), (P = 0.01)].ConclusionsIncreased monocyte count and RDW may represent negative prognostic biomarkers in patients with IPF.

Project description:BackgroundSepsis is an organ dysfunction caused by a dysregulated host response to infection. Early detection is fundamental to improving the patient outcome. Laboratory medicine can play a crucial role by providing biomarkers whose alteration can be detected before the onset of clinical signs and symptoms. In particular, the relevance of monocyte distribution width (MDW) as a sepsis biomarker has emerged in the previous decade. However, despite encouraging results, MDW has poor sensitivity and positive predictive value when compared to other biomarkers.ObjectiveThis study aims to investigate the use of machine learning (ML) to overcome the limitations mentioned earlier by combining different parameters and therefore improving sepsis detection. However, making ML models function in clinical practice may be problematic, as their performance may suffer when deployed in contexts other than the research environment. In fact, even widely used commercially available models have been demonstrated to generalize poorly in out-of-distribution scenarios.MethodsIn this multicentric study, we developed ML models whose intended use is the early detection of sepsis on the basis of MDW and complete blood count parameters. In total, data from 6 patient cohorts (encompassing 5344 patients) collected at 5 different Italian hospitals were used to train and externally validate ML models. The models were trained on a patient cohort encompassing patients enrolled at the emergency department, and it was externally validated on 5 different cohorts encompassing patients enrolled at both the emergency department and the intensive care unit. The cohorts were selected to exhibit a variety of data distribution shifts compared to the training set, including label, covariate, and missing data shifts, enabling a conservative validation of the developed models. To improve generalizability and robustness to different types of distribution shifts, the developed ML models combine traditional methodologies with advanced techniques inspired by controllable artificial intelligence (AI), namely cautious classification, which gives the ML models the ability to abstain from making predictions, and explainable AI, which provides health operators with useful information about the models' functioning.ResultsThe developed models achieved good performance on the internal validation (area under the receiver operating characteristic curve between 0.91 and 0.98), as well as consistent generalization performance across the external validation datasets (area under the receiver operating characteristic curve between 0.75 and 0.95), outperforming baseline biomarkers and state-of-the-art ML models for sepsis detection. Controllable AI techniques were further able to improve performance and were used to derive an interpretable set of diagnostic rules.ConclusionsOur findings demonstrate how controllable AI approaches based on complete blood count and MDW may be used for the early detection of sepsis while also demonstrating how the proposed methodology can be used to develop ML models that are more resistant to different types of data distribution shifts.

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Equal-bin-width histogram versus equal-bin-count histogram.

Publications

Equal-bin-width histogram versus equal-bin-count histogram.

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