Box-Cox Transformation Model Research Articles

Bayesian analysis of Box-Cox transformation model for multi-state progression-free survival data

Bayesian analysis of Box-Cox transformation model for multi-state progression-free survival data

Equivalence Tests Before the End of Follow-up Under Box–Cox Transformation Model

Equivalence Tests Before the End of Follow-up Under Box–Cox Transformation Model

Equivalence tests under the non mixture and mixture cure fraction models

In this article, we propose equivalence tests for the difference of two survival functions in the presence of cure fraction. We consider both the non mixture cure model (NMCM) and mixture cure model (MCM). We first demonstrate that the existing tests can be used to test equivalence of two improper survival functions under the class of log transformation (LT) and Box-Cox transformation (BCT) NMCM. For the MCM, a logistic regression model is assumed for the probability of being uncured and the class of LT or BCT models are used to describe the distribution of event time for the uncured subjects. Under the MCM, we consider testing separately the null hypothesis of identical cure rate and that of equivalence of two survival functions of the uncured subjects. We also develop a Wald statistic for simultaneously testing whether or not both the maximal difference between cure rates and that between two short-term survival functions fall within some equivalence margins. Simulation results indicate that the proposed tests have a satisfactory size and an adequate power in finite sample.

Age- and sex-related changes in vertebral trabecular bone architecture in Neolithic and Mediaeval populations from Poland.

This paper investigates trabecular bone ontogenetic changes in two different Polish populations, one prehistoric and the other historical. The studied populations are from the Brześć Kujawski region in Kujawy (north-central Poland), one from the Neolithic Period (4500-4000 BC) and one from the Middle Ages (twelfth-sixteenth centuries AD), in total 62 vertebral specimens (32 males, 30 females). Eight morphometric parameters acquired from microCT scan images were analysed. Two-way ANOVA after Box-Cox transformation and multifactorial regression model were calculated. A significant decrease in percentage bone volume fraction (BV/TV; [%]) with age at death was observed in the studied sample; Tb.N (trabecular number) was also significantly decreased with age; trabecular separation (Tb.Sp) increased with advancing age; connectivity density (Conn.D) was negatively correlated with biological age and higher in the Neolithic population. These data are found to be compatible with data from the current biomedical literature, while no loss of horizontal trabeculae was recorded as would be expected based on modern osteoporosis.

Surface Water Quality Assessment through Remote Sensing Based on the Box–Cox Transformation and Linear Regression

A methodology to estimate surface water quality using remote sensing is presented based on Landsat satellite imagery and in situ measurements taken every six months at four separate sampling locations in a tropical reservoir from 2015 to 2019. The remote sensing methodology uses the Box–Cox transformation model to normalize data on three water quality parameters: total organic carbon (TOC), total dissolved solids (TDS), and chlorophyll a (Chl-a). After the Box–Cox transformation, a mathematical model was generated for every parameter using multiple linear regression to correlate normalized data and spectral reflectance from Landsat 8 imagery. Then, significant testing was conducted to discard spectral bands that did not show a statistically significant response (α = 0.05) from the different water quality models. The r2 values achieved for TOC, TDS, and Chl-a water quality models after the band discrimination process were found 0.926, 0.875, and 0.810, respectively, achieving a fair fitting to real water quality data measurements. Finally, a comparison between estimated and measured water quality values not previously used for model development was carried out to validate these models. In this validation process, a good fit of 98% and 93% was obtained for TDS and TOC, respectively, whereas an acceptable fit of 81% was obtained for Chl-a. This study proposes an interesting alternative for ordered and standardized steps applied to generate mathematical models for the estimation of TOC, TDS, and Chl-a based on water quality parameters measured in the field and using satellite images.

On the Use of the Power Transformation Models to Improve the Temperature Time Series

The aim of this paper is to select an appropriate ARIMA model for the time series after transforming the original responses. Box-Cox and Yeo-Johnson power transformation models were used on the response variables of two time series datasets of average temperatures and then diagnosed and built the appropriate ARIMA models for each time-series. The authors treat the results of the model fitting as a package in an attempt to decide and choose the best model by diagnosing the effect of the data transformation on the response normality, significant of estimated model parameters, forecastability and the behavior of the residuals. The authors conclude that the Yeo-Johnson model was more flexible in smoothing the data and contributedto accessing a simple model with good forecastability.

Equivalence tests for the difference of two survival functions under the class of Box–Cox transformation model

Equivalence tests for the difference of two survival functions under the class of Box–Cox transformation model

SPDPOA: Student Psychology Dragonfly Political Optimizer Algorithm-Based Soil Moisture and Heat-Level Prediction for Plant Health Monitoring in Internet of Things

Abstract This article devised an effective Student Psychology-based Dragonfly Political Optimizer (SPDPOA) for predicting heat level and soil moisture to monitor plant health in the Internet of Things (IoT). The developed SPDPOA is modeled by integrating the Student Psychology-based Optimization (SPBO) algorithm, Dragonfly Algorithm (DA) and Political optimizer (PO), respectively. The prediction process is done in the base station (BS), which gathers the IoT nodes’ information through optimal Cluster Head (CH) using Deep Recurrent Neural Network (Deep RNN). Moreover, the CH selection and routing process are established using a developed SPDPOA scheme. The data transformation and feature selection processes are done based on Box-Cox transformation and wrapper model, correspondingly, which helps in the selection of best features. Moreover, the developed SPDPOA scheme attained better performance in Packet Delivery Ratio (PDR), energy and testing accuracy of 0.7232, 0.6342 J and 0.9372, respectively.

Forecasting the incidence of dengue in Bangladesh-Application of time series model.

BackgroundDengue is an alarming public health concern in terms of its preventive and curative measures among people in Bangladesh; moreover, its sudden outbreak created a lot of suffering among people in 2018. Considering the greater burden of disease in larger epidemic years and the difficulty in understanding current and future needs, it is highly needed to address early warning systems to control epidemics from the earliest.ObjectiveThe study objective was to select the most appropriate model for dengue incidence and using the selected model, the authors forecast the future dengue outbreak in Bangladesh.Methods and MaterialsThis study considered a secondary data set of monthly dengue occurrences over the period of January 2008 to January 2020. Initially, the authors found the suitable model from Autoregressive Integrated Moving Average (ARIMA), Error, Trend, Seasonal (ETS) and Trigonometric seasonality, Box‐Cox transformation, ARMA errors, Trend and Seasonal (TBATS) models with the help of selected model selection criteria and finally employing the selected model make forecasting of dengue incidences in Bangladesh.ResultsAmong ARIMA, ETS, and TBATS models, the ARIMA model performs better than others. The Box‐Jenkin's procedure is applicable here and it is found that the best‐selected model to forecast the dengue outbreak in the context of Bangladesh is ARIMA (2,1,2).ConclusionBefore establishing a comprehensive plan for future combating strategies, it is vital to understand the future scenario of dengue occurrence. With this in mind, the authors aimed to select an appropriate model that might predict dengue fever outbreaks in Bangladesh. The findings revealed that dengue fever is expected to become more frequent in the future. The authors believe that the study findings will be helpful to take early initiatives to combat future dengue outbreaks.

A two-way flexible generalized gamma transformation cure rate model.

We propose a two-way flexible cure rate model. The first flexibility is provided by considering a family of Box-Cox transformation cure models that include the commonly used cure models as special cases. The second flexibility is provided by proposing the wider class of generalized gamma distributions to model the associated lifetime. The advantage of this two-way flexibility is that it allows us to carry out tests of hypotheses to select an adequate cure model (within the family of Box-Cox transformation cure models) and a suitable lifetime distribution (within the wider class of generalized gamma distributions) that jointly provides the best fit to a given data. First, we study the maximum likelihood estimation of the generalized gamma Box-Cox transformation (GGBCT) model parameters. Then, we use the flexibility of our proposed model to carry out power studies to demonstrate the power of likelihood ratio test in rejecting mis-specified models. Furthermore, we study the bias and efficiency of the estimators of the cure rates under model mis-specification. Our findings strongly suggest the importance of selecting a correct lifetime distribution and a correct cure rate model, which can be achieved through the proposed two-way flexible model. Finally, we illustrate the applicability of our proposed model using a data from a breast cancer study and show that our model provides a better fit than the existing semiparametric Box-Cox transformation cure model with piecewise exponential approximation to the lifetime distribution.

An Intelligent Data-Driven Learning Approach to Enhance Online Probabilistic Voltage Stability Margin Prediction

This letter presents a self-adaptive data-driven learning method for enhanced probabilistic prediction of voltage stability margin (VSM). An online probabilistic extreme learning machine (ELM) algorithm based on the power transformation technique is developed. The prediction interval (PI) estimation for VSM is formulated as a Box-Cox transformation (BT) model to take into account uncertainties associated with predictions. The parameters in the transformed model are determined by the maximum likelihood estimator. The proposed PI-based VSM estimation method is applied to power grids with high proliferation of renewable energy generation. It enables to update the prediction model online and adapt to changing operating conditions. Numerical studies along with comparative results demonstrate the efficacy and robustness of the proposed method.

Improvement of the Nonparametric Estimation of Functional Stationary Time Series Using Yeo-Johnson Transformation with Application to Temperature Curves

In this article, Box-Cox and Yeo-Johnson transformation models are applied to two time series datasets of monthly temperature averages to improve the forecast ability. An application algorithm was proposed to transform the positive original responses using the first model and the stationary responses using the second model to improve the nonparametric estimation of the functional time series. The Box-Cox model contributed to improving the results of the nonparametric estimation of the original data, but the results become somewhat confusing after attempting to make the transformed response variable stationary in the mean, while the functional time series predictions were more accurate using the transformed stationary datasets using the Yeo-Johnson model.

Forecasting COVID-19 confirmed cases, deaths and recoveries: Revisiting established time series modeling through novel applications for the USA and Italy.

The novel coronavirus (COVID-19) is an emergent disease that initially had no historical data to guide scientists on predicting/ forecasting its global or national impact over time. The ability to predict the progress of this pandemic has been crucial for decision making aimed at fighting this pandemic and controlling its spread. In this work we considered four different statistical/time series models that are readily available from the ‘forecast’ package in R. We performed novel applications with these models, forecasting the number of infected cases (confirmed cases and similarly the number of deaths and recovery) along with the corresponding 90% prediction interval to estimate uncertainty around pointwise forecasts. Since the future may not repeat the past for this pandemic, no prediction model is certain. However, any prediction tool with acceptable prediction performance (or prediction error) could still be very useful for public-health planning to handle spread of the pandemic, and could policy decision-making and facilitate transition to normality. These four models were applied to publicly available data of the COVID-19 pandemic for both the USA and Italy. We observed that all models reasonably predicted the future numbers of confirmed cases, deaths, and recoveries of COVID-19. However, for the majority of the analyses, the time series model with autoregressive integrated moving average (ARIMA) and cubic smoothing spline models both had smaller prediction errors and narrower prediction intervals, compared to the Holt and Trigonometric Exponential smoothing state space model with Box-Cox transformation (TBATS) models. Therefore, the former two models were preferable to the latter models. Given similarities in performance of the models in the USA and Italy, the corresponding prediction tools can be applied to other countries grappling with the COVID-19 pandemic, and to any pandemics that can occur in future.

Short-term Forecasting Ability of Hybrid Models for BRIC Currencies

This article proposes a new framework to improve short-term forecasting accuracy of exchange rates of BRIC nations, that is, Brazil (USD/BRL), Russia (USD/RUB), India (USD/INR) and China (USD/CNY). The study employs three methodologies for a 42-day forecast: hybrid models based on least square support vector machine, residual hybrid model and automatic hybrid model forecasting using R software. The results show that the proposed residual hybrid model framework, including autoregressive integrated moving average-artificial neural network (ARIMA–ANN)-TBATS, outperformed other models with Brazil and China return series reflecting the best accuracy in ANN model and India and Russia demonstrating the best accuracy in trigonometric seasonal, box-cox transformation, ARIMA residuals, trend and seasonality (TBATS) model. Further, the results indicate that Brazil and China return series follow a non-linear pattern, while India and Russia follow a non-linear complex seasonal pattern. The highest level of forecast accuracy has been observed in China followed by Brazil, India and Russia.

Bayesian analysis of the Box-Cox transformation model based on left-truncated and right-censored data

In this paper, we discuss the inference problem about the Box-Cox transformation model when one faces left-truncated and right-censored data, which often occur in studies, for example, involving the cross-sectional sampling scheme. It is well-known that the Box-Cox transformation model includes many commonly used models as special cases such as the proportional hazards model and the additive hazards model. For inference, a Bayesian estimation approach is proposed and in the method, the piecewise function is used to approximate the baseline hazards function. Also the conditional marginal prior, whose marginal part is free of any constraints, is employed to deal with many computational challenges caused by the constraints on the parameters, and a MCMC sampling procedure is developed. A simulation study is conducted to assess the finite sample performance of the proposed method and indicates that it works well for practical situations. We apply the approach to a set of data arising from a retirement center.

Joint analysis of panel count and interval-censored data using distribution-free frailty analysis.

We propose a joint analysis of recurrent and nonrecurrent event data subject to general types of interval censoring. The proposed analysis allows for general semiparametric models, including the Box-Cox transformation and inverse Box-Cox transformation models for the recurrent and nonrecurrent events, respectively. A frailty variable is used to account for the potential dependence between the recurrent and nonrecurrent event processes, while leaving the distribution of the frailty unspecified. We apply the pseudolikelihood for interval-censored recurrent event data, usually termed as panel count data, and the sufficient likelihood for interval-censored nonrecurrent event data by conditioning on the sufficient statistic for the frailty and using the working assumption of independence over examination times. Large sample theory and a computation procedure for the proposed analysis are established. We illustrate the proposed methodology by a joint analysis of the numbers of occurrences of basal cell carcinoma over time and time to the first recurrence of squamous cell carcinoma based on a skin cancer dataset, as well as a joint analysis of the numbers of adverse events and time to premature withdrawal from study medication based on a scleroderma lung diseasedataset.

Ranking of Univariate Forecasting Techniques for Seasonal Time Series using Analytical Hierarchy Process

The choice of a suitable forecasting method carries noteworthy significance for organisations in adequately accomplishing their business targets. The selection of forecasting method becomes more sophisticated when there is a significant impact of seasonality on the business of an organisation. To deal with the situation of selecting the most relevant forecasting method for seasonal data, this paper proposes a framework using analytical hierarchy process (AHP) to rank various forecasting techniques for long time series. Accuracy measures namely Theil's U, mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE) are used as AHP criteria for performance measurement of various univariate time series methods such as naive + season level trend (SLT), error, trend, seasonal (ETS), seasonal autoregressive moving average (SARIMA), exponential smoothing state space model with Box-Cox transformation (BATS) and trigonometric exponential smoothing state space model with Box-Cox transformation (TBATS) for seasonal data. The proposed framework is validated through real-time data provided by a public sector company in India. Ranking obtained from the developed AHP framework suggests that SARIMA is ranked top amongst all the techniques for short-term forecasting of seasonal data.

Testing economic “genetic pleiotropy” for Box-Cox linear model

Genetic pleiotropy occurs when a single gene influences two or more seemingly unrelated phenotypic traits. It is significant to detect pleiotropy and understand its causes. However, most current statistical methods to discover pleiotropy mainly test the null hypothesis that none of the traits is associated with a variant, which departures from the null to test just one associated trait or k associated traits. Schaid et al. (2016) first proposed a sequential testing framework to analyze pleiotropy based on a linear model and a multivariate normal distribution. In this paper, we analyze the Economic pleiotropy which occurs when an economic action or policy influences two or more economic phenomena. In this paper, we extend the linear model to Box-Cox transformation model and proposed a new decision method. It improves the efficiency of hypothesis test and controls the Type I error. We then apply the method using economic data to multivariate sectoral employments in response to governmental expenditures and provide a quantitative assessment and some insights of different impacts from economic policy.

A class of box-cox transformation models for recurrent event data with a terminal event

In this article, we study a class of Box-Cox transformation models for recurrent event data in the presence of terminal event, which includes the proportional means models as special cases. Estimating equation approaches and the inverse probability weighting technique are used for estimation of the regression parameters. The asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed methods is examined through simulation studies, and an application to a heart failure study is presented to illustrate the proposed method.

Semiparametric estimation of a Box-Cox transformation model with varying coefficients model

This paper considers the estimation of a Box-Cox transformation model with varying coefficient. A two-step approach is proposed in which the first step estimates the varying coefficients nonparametrically for any given parameter $% \alpha $\ in the transformation function. Then a one-dimensional search of $% \alpha $\ has been employed based on some least absolute deviation criterion function. The validity of our estimator does not require independence assumption thus is robust to the conditional heteroscedasticity. A simulation study shows a reasonably well finite sample performance. Additionally, a comprehensive empirical study has been carefully examined.