Research

24 pages, 2245 KiB

Open AccessCommunication

Formulas, Algorithms and Examples for Binomial Distributed Data Confidence Interval Calculation: Excess Risk, Relative Risk and Odds Ratio

by Lorentz Jäntschi

Mathematics 2021, 9(19), 2506; https://doi.org/10.3390/math9192506 - 07 Oct 2021

Cited by 11 | Viewed by 2456

Abstract

Medical studies often involve a comparison between two outcomes, each collected from a sample. The probability associated with, and confidence in the result of the study is of most importance, since one may argue that having been wrong with a percent could be [...] Read more.

Medical studies often involve a comparison between two outcomes, each collected from a sample. The probability associated with, and confidence in the result of the study is of most importance, since one may argue that having been wrong with a percent could be what killed a patient. Sampling is usually done from a finite and discrete population and it follows a Bernoulli trial, leading to a contingency of two binomially distributed samples (better known as

2 \times 2

contingency table). Current guidelines recommend reporting relative measures of association (such as the relative risk and odds ratio) in conjunction with absolute measures of association (which include risk difference or excess risk). Because the distribution is discrete, the evaluation of the exact confidence interval for either of those measures of association is a mathematical challenge. Some alternate scenarios were analyzed (continuous vs. discrete; hypergeometric vs. binomial), and in the main case—bivariate binomial experiment—a strategy for providing exact p-values and confidence intervals is proposed. Algorithms implementing the strategy are given. Full article

(This article belongs to the Special Issue Applied Medical Statistics: Theory, Computation, Applicability)

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17 pages, 478 KiB

Open AccessArticle

Incorporating a New Summary Statistic into the Min–Max Approach: A Min–Max–Median, Min–Max–IQR Combination of Biomarkers for Maximising the Youden Index

by Rocío Aznar-Gimeno, Luis M. Esteban, Gerardo Sanz, Rafael del-Hoyo-Alonso and Ricardo Savirón-Cornudella

Mathematics 2021, 9(19), 2497; https://doi.org/10.3390/math9192497 - 05 Oct 2021

Cited by 4 | Viewed by 2210

Abstract

Linearly combining multiple biomarkers is a common practice that can provide a better diagnostic performance. When the number of biomarkers is sufficiently high, a computational burden problem arises. Liu et al. proposed a distribution-free approach (min–max approach) that linearly combines the minimum and [...] Read more.

Linearly combining multiple biomarkers is a common practice that can provide a better diagnostic performance. When the number of biomarkers is sufficiently high, a computational burden problem arises. Liu et al. proposed a distribution-free approach (min–max approach) that linearly combines the minimum and maximum values of the biomarkers, involving only a single coefficient search. However, the combination of minimum and maximum biomarkers alone may not be sufficient in terms of discrimination. In this paper, we propose a new approach that extends that of Liu et al. by incorporating a new summary statistic, specifically, the median or interquartile range (min–max–median and min–max–IQR approaches) in order to find the optimal combination that maximises the Youden index. Although this approach is more computationally intensive than the one proposed by Liu et al, it includes more information and the number of parameters to be estimated remains reasonable. We compare the performance of the proposed approaches (min–max–median and min–max–IQR) with the min–max approach and logistic regression. For this purpose, a wide range of different simulated data scenarios were explored. We also apply the approaches to two real datasets (Duchenne Muscular Dystrophy and Small for Gestational Age). Full article

(This article belongs to the Special Issue Applied Medical Statistics: Theory, Computation, Applicability)

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14 pages, 399 KiB

Open AccessArticle

An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data

by Diego I. Gallardo, Mário de Castro and Héctor W. Gómez

Mathematics 2021, 9(15), 1815; https://doi.org/10.3390/math9151815 - 31 Jul 2021

Cited by 5 | Viewed by 1759

Abstract

A cure rate model under the competing risks setup is proposed. For the number of competing causes related to the occurrence of the event of interest, we posit the one-parameter Bell distribution, which accommodates overdispersed counts. The model is parameterized in the cure [...] Read more.

A cure rate model under the competing risks setup is proposed. For the number of competing causes related to the occurrence of the event of interest, we posit the one-parameter Bell distribution, which accommodates overdispersed counts. The model is parameterized in the cure rate, which is linked to covariates. Parameter estimation is based on the maximum likelihood method. Estimates are computed via the EM algorithm. In order to compare different models, a selection criterion for non-nested models is implemented. Results from simulation studies indicate that the estimation method and the model selection criterion have a good performance. A dataset on melanoma is analyzed using the proposed model as well as some models from the literature. Full article

(This article belongs to the Special Issue Applied Medical Statistics: Theory, Computation, Applicability)

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11 pages, 284 KiB

Open AccessArticle

Use of Bayesian Markov Chain Monte Carlo Methods to Model Kuwait Medical Genetic Center Data: An Application to Down Syndrome and Mental Retardation

by Reem Aljarallah and Samer A Kharroubi

Mathematics 2021, 9(3), 248; https://doi.org/10.3390/math9030248 - 27 Jan 2021

Cited by 2 | Viewed by 2363

Abstract

Logit, probit and complementary log-log models are the most widely used models when binary dependent variables are available. Conventionally, these models have been frequentists. This paper aims to demonstrate how such models can be implemented relatively quickly and easily from a Bayesian framework [...] Read more.

Logit, probit and complementary log-log models are the most widely used models when binary dependent variables are available. Conventionally, these models have been frequentists. This paper aims to demonstrate how such models can be implemented relatively quickly and easily from a Bayesian framework using Gibbs sampling Markov chain Monte Carlo simulation methods in WinBUGS. We focus on the modeling and prediction of Down syndrome (DS) and Mental retardation (MR) data from an observational study at Kuwait Medical Genetic Center over a 30-year time period between 1979 and 2009. Modeling algorithms were used in two distinct ways; firstly, using three different methods at the disease level, including logistic, probit and cloglog models, and, secondly, using bivariate logistic regression to study the association between the two diseases in question. The models are compared in terms of their predictive ability via R², adjusted R², root mean square error (RMSE) and Bayesian Deviance Information Criterion (DIC). In the univariate analysis, the logistic model performed best, with

R^{2}

(0.1145), adjusted

R^{2}

(0.114), RMSE (0.3074) and DIC (7435.98) for DS, and

R^{2}

(0.0626), adjusted

R^{2}

(0.0621), RMSE (0.4676) and DIC (23120) for MR. In the bivariate case, results revealed that 7 and 8 out of the 10 selected covariates were significantly associated with DS and MR respectively, whilst none were associated with the interaction between the two outcomes. Bayesian methods are more flexible in handling complex non-standard models as well as they allow model fit and complexity to be assessed straightforwardly for non-nested hierarchical models. Full article

(This article belongs to the Special Issue Applied Medical Statistics: Theory, Computation, Applicability)

17 pages, 3394 KiB

Open AccessArticle

Wavelet Transform-Statistical Time Features-Based Methodology for Epileptic Seizure Prediction Using Electrocardiogram Signals

by Andrea V. Perez-Sanchez, Carlos A. Perez-Ramirez, Martin Valtierra-Rodriguez, Aurelio Dominguez-Gonzalez and Juan P. Amezquita-Sanchez

Mathematics 2020, 8(12), 2125; https://doi.org/10.3390/math8122125 - 27 Nov 2020

Cited by 9 | Viewed by 2620

Abstract

Epilepsy is a brain disorder that affects about 50 million persons around the world and is characterized by generating recurrent seizures, which can put patients in permanent because of falls, drowning, burns, and prolonged seizures that they can suffer. Hence, it is of [...] Read more.

Epilepsy is a brain disorder that affects about 50 million persons around the world and is characterized by generating recurrent seizures, which can put patients in permanent because of falls, drowning, burns, and prolonged seizures that they can suffer. Hence, it is of vital importance to propose a methodology with the capability of predicting a seizure with several minutes before the onset, allowing that the patients take their precautions against injuries. In this regard, a methodology based on the wavelet packet transform (WPT), statistical time features (STFs), and a decision tree classifier (DTC) for predicting an epileptic seizure using electrocardiogram (ECG) signals is presented. Seventeen STFs were analyzed to measure changes in the properties of ECG signals and find characteristics capable of differentiating between healthy and 15 min prior to seizure signals. The effectiveness of the proposed methodology for predicting an epileptic event is demonstrated using a database of seven patients with 10 epileptic seizures, which was provided by the Massachusetts Institute of Technology–Beth Israel Hospital (MIT–BIH). The results show that the proposed methodology is capable of predicting an epileptic seizure 15 min before with an accuracy of 100%. Our results suggest that the use of STFs at frequency bands related to heart activity to find parameters for the prediction of epileptic seizures is suitable. Full article

(This article belongs to the Special Issue Applied Medical Statistics: Theory, Computation, Applicability)

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17 pages, 3020 KiB

Open AccessArticle

Receiver Operating Characteristic Prediction for Classification: Performances in Cross-Validation by Example

by Andra Ciocan, Nadim Al Hajjar, Florin Graur, Valentin C. Oprea, Răzvan A. Ciocan and Sorana D. Bolboacă

Mathematics 2020, 8(10), 1741; https://doi.org/10.3390/math8101741 - 10 Oct 2020

Cited by 6 | Viewed by 2577

Abstract

The stability of receiver operating characteristic in context of random split used in development and validation sets, as compared to the full models for three inflammatory ratios (neutrophil-to-lymphocyte (NLR), derived neutrophil-to-lymphocyte (dNLR) and platelet-to-lymphocyte (PLR) ratio) evaluated as predictors for metastasis in patients [...] Read more.

The stability of receiver operating characteristic in context of random split used in development and validation sets, as compared to the full models for three inflammatory ratios (neutrophil-to-lymphocyte (NLR), derived neutrophil-to-lymphocyte (dNLR) and platelet-to-lymphocyte (PLR) ratio) evaluated as predictors for metastasis in patients with colorectal cancer, was investigated. Data belonging to patients admitted with the diagnosis of colorectal cancer from January 2014 until September 2019 in a single hospital were used. There were 1688 patients eligible for the study, 418 in the metastatic stage. All investigated inflammatory ratios proved to be significant classification models on both the full models and on cross-validations (AUCs > 0.05). High variability of the cut-off values was observed in the unrestricted and restricted split (full models: 4.255 for NLR, 2.745 for dNLR and 255.56 for PLR; random splits: cut-off from 3.215 to 5.905 for NLR, from 2.625 to 3.575 for dNLR and from 134.67 to 335.9 for PLR), but with no effect on the models characteristics or performances. The investigated biomarkes proved limited value as predictors for metastasis (AUCs < 0.8), with largely sensitivity and specificity (from 33.3% to 79.2% for the full model and 29.1% to 82.7% in the restricted splits). Our results showed that a simple random split of observations, weighting or not the patients with and whithout metastasis, in a ROC analysis assures the performances similar to the full model, if at least 70% of the available population is included in the study. Full article

(This article belongs to the Special Issue Applied Medical Statistics: Theory, Computation, Applicability)

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11 pages, 911 KiB

Open AccessArticle

Definition and Estimation of Covariate Effect Types in the Context of Treatment Effectiveness

by Yasutaka Chiba

Mathematics 2020, 8(10), 1657; https://doi.org/10.3390/math8101657 - 25 Sep 2020

Viewed by 1316

Abstract

In some clinical studies, assessing covariate effect types indicating whether a covariate is predictive and/or prognostic is of interest, in addition to the study endpoint. Recently, for a case with a binary outcome, Chiba (Clinical Trials, 2019; 16: 237–245) proposed the new concept [...] Read more.

In some clinical studies, assessing covariate effect types indicating whether a covariate is predictive and/or prognostic is of interest, in addition to the study endpoint. Recently, for a case with a binary outcome, Chiba (Clinical Trials, 2019; 16: 237–245) proposed the new concept of covariate effect type, which is assessed in terms of four response types, and showed that standard subgroup or regression analysis is applicable only in certain cases. Although this concept could be useful for supplementing conventional standard analysis, its application is limited to cases with a binary outcome. In this article, we aim to generalize Chiba’s concept to continuous and time-to-event outcomes. We define covariate effect types based on four response types. It is difficult to estimate the response types from the observed data without making certain assumptions, so we propose a simple method to estimate them under the assumption of independent potential outcomes. Our approach is illustrated using data from a clinical study with a time-to-event outcome. Full article

(This article belongs to the Special Issue Applied Medical Statistics: Theory, Computation, Applicability)

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17 pages, 2643 KiB

Open AccessArticle

Common Medical and Statistical Problems: The Dilemma of the Sample Size Calculation for Sensitivity and Specificity Estimation

by M. Rosário Oliveira, Ana Subtil and Luzia Gonçalves

Mathematics 2020, 8(8), 1258; https://doi.org/10.3390/math8081258 - 01 Aug 2020

Cited by 1 | Viewed by 2984

Abstract

Sample size calculation in biomedical practice is typically based on the problematic Wald method for a binomial proportion, with potentially dangerous consequences. This work highlights the need of incorporating the concept of conditional probability in sample size determination to avoid reduced sample sizes [...] Read more.

Sample size calculation in biomedical practice is typically based on the problematic Wald method for a binomial proportion, with potentially dangerous consequences. This work highlights the need of incorporating the concept of conditional probability in sample size determination to avoid reduced sample sizes that lead to inadequate confidence intervals. Therefore, new definitions are proposed for coverage probability and expected length of confidence intervals for conditional probabilities, like sensitivity and specificity. The new definitions were used to assess seven confidence interval estimation methods. In order to determine the sample size, two procedures—an optimal one, based on the new definitions, and an approximation—were developed for each estimation method. Our findings confirm the similarity of the approximated sample sizes to the optimal ones. R code is provided to disseminate these methodological advances and translate them into biomedical practice. Full article

(This article belongs to the Special Issue Applied Medical Statistics: Theory, Computation, Applicability)

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