The Birnbaum–Saunders distribution is commonly used to model lifetime data, particularly in reliability analysis. However, when multicollinearity exists among the predictor variables in the log Birnbaum–Saunders regression model, the maximum likelihood estimator (MLE) may yield biased and inefficient parameter estimates. To lessen the effect of multicollinearity, the study proposed the use of ridge regression instead of maximum likelihood estimation. We discussed the choice of the ridge parameters. We conducted a simulation study and a real-life application to evaluate the performance of the ridge regression estimator under different levels of multicollinearity. Furthermore, a SafeML-based predictive analysis confirms the superior generalization performance of the proposed ridge estimators compared to MLE under multicollinearity. We have compared the ridge regression results with those obtained from MLE and demonstrated the superiority of ridge regression in terms of lower MSE. The results imply that, in the presence of multicollinearity, ridge regression estimator provides more accurate and robust parameter estimations.

The use of Almon technique is encouraged for estimation of the distributed lag model (DLM) to avoid some serious problems associated with the direct application of the ordinary least squares (OLS) method. In Almon technique, the OLS procedure is applied on the transformed regressors which may be correlated themselves. To tackle this issue, the use of ordinary ridge regression estimator (ORRE) combined with the Almon technique has been considered as an alternative approach in the literature. However, the ORRE may be sensitive to outliers in the y-direction and thus, its use combined with the Almon technique may raise doubts on the estimated lag coefficients. The present work addresses this issue and suggests an alternative estimation method for the DLM, which is robust in the presence of multicollinearity and outliers. The performance of the proposed estimator has been evaluated through an extensive Monte Carlo simulation study and empirical findings are presented using the mean squared error criterion. The results reveal an attractive performance of the proposed estimator in the presence of outliers.

Growth reference values about mid-upper arm circumference (MUAC) are vital for assessing children's nutritional status. However, Pakistan lacks these reference values and growth charts. This study aims to develop these for children aged 6–60 months and compare them with global standards. The data were acquired from the 2018 National Nutrition Survey of Pakistan, which was conducted by the United Nations Children's Fund (UNICEF) during 2018–2019. The final study cohort comprised 57 285 children, with 51% being boys. Percentile values and charts for MUAC-for-age were developed using generalised additive models for location, scale and shape with the Box–Cox power exponential distribution. The mean MUAC was 14.21 cm (±2.07 cm) and 14.13 cm (±2.12 cm) for the boys and girls, respectively. At 60 months of age, the P3 and P97 percentiles for girls were slightly higher than those for boys. The median percentiles of Pakistani children were smaller than the World Health Organisation 2007 standards and with international references. We observed disparities in MUAC-for-age growth references among Pakistani children compared to global standards, highlighting regional, age and gender variations. This underscores the need for developing countries like Pakistan to establish their growth references.

A common problem that we encounter in linear regression models is that the error variances are not the same for all the observations, that is, there is an issue of heteroscedasticity. To avoid the adverse effects of this issue on the estimates obtained by the ordinary least squares, it is a usual practice to use the estimated weighted least squares (EWLS) method or to use some adaptive methods, especially when the form of heteroscedasticity is unknown. The current article proposes a novel Bayesian version of the EWLS estimator. The performance of the proposed estimator has been evaluated in terms of its efficiency using the Monte Carlo simulations. An example has also been included for the demonstration.

In the current article, we develop the Aslam-Ahmad estimator i.e. the modified Liu-ridge-type estimator as proposed by Aslam and Ahmad [Aslam M, Ahmad S. The modified Liu-ridge-type estimator: a new class of biased estimators to address multicollinearity. Commun Statist Simul Comput. 2022] for the Cox proportional hazards regression model. It is common to use the maximum partial likelihood approach for the parameter estimation of the Cox proportional hazards model. However, when there is considerable multicollinearity among the regressors, this estimator is unable to give stable estimates for the unknown regression coefficients. To vanquish the problem, the literature suggests many alternative biased estimators. Following this, we propose to tailor the Aslam-Ahmad estimator for the Cox proportional hazards model and define its properties. The performance of the proposed estimator with the available estimators has been evaluated by the Monte Carlo simulations using the scalar mean squared error criterion. A numerical example has also been provided for the illustration.

Purpose: Quality assurance for stereotactic body radiation treatment requires that isocentric verification be ensured during gantry rotation at various angles. This study examined statistical parameters on Winston-Lutz tests to distinguish the deviation of angles from isocenter during gantry rotation using machine learning. Method: The Varian TrueBeam linac was aligned with the marked lines on the Ruby phantom. Eight images were captured while the gantry was rotating at a 45° shift. The statistical features were derived from IsoCheck EPID software. The decision tree model was applied to these Winston-Lutz tests to cluster data into two groups: precise and error angles. Results: At 90° and 270° angles, the gantry exhibits isocentric stability compared to other angles. In these angles, the most statistical features were inside the range. Most variations were observed at 0° and 180° angles. In most tests, the angles 45°, 135°, 225°, and 315° showed reasonable performance and with less variation. Conclusion: The comprehensive statistical analyses for gantry rotation of angles assists expert radiotherapists in determining the contribution of each feature that highly affects gantry movement at specific angles. Misalignment between radiation isocenter and imaging isocenter, tuning of the beam at each angle, or a slight change in the position of the Ruby phantom can further improve the inaccuracy that causes the most variations. Better precision can effectively increase patient safety and quality during cancer treatment.

AIM:Growth reference values about mid-upper arm circumference (MUAC) are vital for assessing children's nutritional status. However, Pakistan lacks these reference values and growth charts. This study aims to develop these for children aged 6-60 months and compare them with global standards. METHODS:The data were acquired from the 2018 National Nutrition Survey of Pakistan, which was conducted by the United Nations Children's Fund (UNICEF) during 2018-2019. The final study cohort comprised 57 285 children, with 51% being boys. Percentile values and charts for MUAC-for-age were developed using generalised additive models for location, scale and shape with the Box-Cox power exponential distribution. RESULTS:The mean MUAC was 14.21 cm (±2.07 cm) and 14.13 cm (±2.12 cm) for the boys and girls, respectively. At 60 months of age, the P3 and P97 percentiles for girls were slightly higher than those for boys. The median percentiles of Pakistani children were smaller than the World Health Organisation 2007 standards and with international references. CONCLUSION:We observed disparities in MUAC-for-age growth references among Pakistani children compared to global standards, highlighting regional, age and gender variations. This underscores the need for developing countries like Pakistan to establish their growth references.

AbstractThe ongoing pandemic of COVID-19 has changed every aspect of life. Most of the people who become a victim of COVID-19 experience mild to moderate symptoms, but some people may become seriously ill. This illness, sometimes, may lead to a very painful death. The Fréchet distribution is one of the flexible distribution for survival time. Hence, in this article, the recovery time of COVID-19 patients is modeled by a new Fréchet-exponential (FE) distribution, and the parameters of the distribution are estimated in the classical and Bayesian paradigms. Since the Bayes estimators using informative priors are not in the closed form, the Lindley and Tierney–Kadane approximation methods are used for their evaluation. The results obtained through simulation studies and the COVID-19 data set assess the superiority of the Bayes estimators over the classical estimators in terms of minimum risks. Mathematically and graphically, it is shown that our proposed model appropriately fits the data set. The minimum values of Akaike information criterion, Bayesian information criterion, corrected Akaike information criterion, and Hannan-Quinn information criterion proves that the FE distribution better fit than the competitors’ distribution for the data set about the recovery time of COVID-19 patients.

The failure of electric feeders is a common problem in the summer season in Pakistan. In this article, one of the troubling aspects of the electric power system of Pakistan (Multan city) has been studied. The time lapses between the breakdown of electric feeders of the city have been modeled by suggesting an inverse Rayleigh-exponential distribution. The parameters of the distribution are estimated in both the frequentist and Bayesian paradigms. Since the Bayes estimators under informative priors are not attained in the closed form, this paper provides a comparative analysis of the Bayes estimators under Lindley and Tierney–Kadane approximation methods. The simulation study and the real-life data set assessed the validity of the model and the superiority of the Bayes estimators over the maximum likelihood estimators.

The use of Almon technique is very common for the estimation of distributed lag model (DLM) to encounter the problems stemming due to direct application of the ordinary least squares (OLS) method to this model. However, the Almon estimator may suffer from the problem of multicollinearity as the constructed regressors in the Almon technique may be plagued with considerable degree of multicollinearity. To address this issue, the use of Almon-ridge estimator (ARE) has been considered as an alternative method for the estimation of DLM by many authors. In addition, the DLM may also face the problem of heteroscedasticity that may result in inconsistent covariance matrix estimator of ARE, leading to invalid testing inference about parameters of the DLM. In the present article, we propose to use the robust covariance matrix estimators of ARE for providing valid inference about parameters of the DLM taking multicollinearity and heteroscedasticity into account. These covariance estimators are used to construct confidence intervals, t- and F-tests. The performance of these confidence intervals and tests is evaluated empirically through the Monte Carlo simulations. The simulation results reveal an attractive performance of the proposed covariance matrix estimators.

Evaluation of nutritional status is necessary during childhood and the juvenile years when the level of hydration and the adipose tissues experience significant changes. Anthropometric measurements and their derived indices are valid proxies to predict body fat, obesity (general or central) and their associated cardiovascular risks. The dataset under consideration also provides the socio-demographic related information and anthropometric measurement values related to height, weight, body mass index (BMI), waist circumference (WC), hip circumference (HpC), waist-to-hip ratio (WHpR), waist-to-height ratio (WHtR), mid-upper arm circumference (MUAC), neck circumference (NC), and wrist circumference (WrC). Standard procedure was adopted for quantifying the body measurements. The data were consisting of 10,782 children and adolescents aged 2–19 years, belonging four major cities of Pakistan viz. Multan, Lahore, Rawalpindi and Islamabad. This dataset is beneficial to develop anthropometric growth charts which will provide the essential knowledge of growth and nutritional disorders (e.g., stunted, overweight and obesity) of Pakistani children and adolescents. The dataset can also be used by researchers to calculate body surface area (BSA), body frame size (BFS), body shape index (BSI), and tri-ponderal mass index (TMI) of children and adolescents that are also some other reliable indicators of obesity and insulin resistance as well as cardiometabolic risk in children and adults.

Abstract Objective: Neck circumference (NC) is currently used as an embryonic marker of obesity and its associated risks. But its use in clinical evaluations and other epidemiological purposes requires sex and age-specific standardised cut-offs which are still scarce for the Pakistani paediatric population. We therefore developed sex and age-specific growth reference charts for NC for Pakistani children and adolescents aged 2–18 years. Design: Cross-sectional multi-ethnic anthropometric survey (MEAS) study. Setting: Multan, Lahore, Rawalpindi and Islamabad. Participants: The dataset of 10 668 healthy Pakistani children and adolescents aged 2–18 years collected in MEAS were used. Information related to age, sex and NC were taken as study variables. The lambda–mu–sigma (LMS) and quantile regression (QR) methods were applied to develop growth reference charts for NC. Results: The 5th, 10th, 25th, 50th, 75th, 90th and 95th smoothed percentile values of NC were presented. The centile values showed that neck size increased with age in both boys and girls. During 8 and 14 years of age, girls were found to have larger NC than boys. A comparison of NC median (50th) percentile values with references from Iranian and Turkish populations reveals substantially lower NC percentiles in Pakistani children and adolescents compared to their peers in the reference population. Conclusion: The comparative results suggest that the uses of NC references of developed countries are inadequate for Pakistani children. A small variability between empirical centiles and centiles obtained by QR procedure recommends that growth charts should be constructed by QR as an alternative method.

Aim: The aim of this work was to study the acceptability of plans prepared for prostate patients treated by volumetric modulated arc therapy (VMAT) with the vision to evaluate the quality of plans and test pre-treatment quality assurance (QA). Material methods: VMAT plans of 35 patients, planned on the Eclipse Treatment Planning System (Aria 15), were included in the study. Plan acceptability was checked using statistical analysis, which includes homogeneity index, radical and median homogeneity index, coverage and uniformity index. Dose-volume histograms (DVH) of the plans were also studied to check prescribed dose (PD), D-max, D-min, D-5 and D-95. Portal dosimetry was also done by gamma analysis using 3%/3 mm criterion. SD and mean SD error were also calculated and analysed. Results: Statistical analysis showed a mean HI of 1 center dot 054, coverage 0 center dot 959, UI 1 center dot 055, mDHI 0 center dot 962 and rDHI 0 center dot 866. SD of HI, coverage, UI, mDHI and rDHI was 0 center dot 019, 0 center dot 019, 0 center dot 014, 0 center dot 013 and 0 center dot 030, respectively. From the DVHs, mean of D-5, D-95, D-min and D-max was calculated at 6,252 center dot 9, 5,757 center dot 4, 6,413 center dot 3 and 5,657 center dot 7 cGy, respectively, with a prescribed dose of 6,000 cGy. According to gamma analysis, area gamma < 1 was 99 center dot 12% with a tolerance limit of 95%, maximum gamma was 1 center dot 466 with a tolerance limit of 3 center dot 5, average gamma was 0 center dot 388 with a tolerance limit of 0 center dot 5, area gamma > 1 center dot 2 was 0 center dot 242% with a tolerance limit of 0 center dot 5%, maximum dose difference was 0 center dot 6 with a tolerance limit of 1 center dot 0 and average dose difference was 0 center dot 029 with a tolerance limit of 0 center dot 2. Conclusion: All three computations showed the results to be within acceptable limits. VMAT possesses a unique feature of delivering the whole treatment with only two rotations of the gantry. VMAT has an improved efficiency of delivery for equivalent dosimetric quality.

Objectives: Children from different countries and with different ethnic backgrounds have a distinct pattern of central fat deposition. Therefore, it is essential to develop population-specific percentiles of waist circumference (WC), waist-to-height ratio (WHtR) and waist-to-height ratio exponent (WHtR (exp)) for the evaluation of central obesity. The objective of this study was to develop age-and-gender-specific smoothed WC and WHtR percentile curves for the Pakistani children and adolescents aged 2-18 years. Methods: A cross-sectional data-set from a multi-ethnic anthropometric survey was considered. A sample of 10,668 healthy subjects (boys = 51.92%; and girls = 48.08%), aged 2-18 years was studied. Height (cm) and WC (cm) of each subject was measured under standard procedure and WHtR & WHtR (exp) were calculated. Age-and-gender-specific smoothed curves were obtained using the lambdamu-sigma (LMS) method and compared with percentile curves obtained from different countries. Results: Except few early ages, the WC values increased with age in both sexes. Both boys and girls had approximately similar WC during 6-11 years of age and after age of 11, the boys had larger WC than the girls had. For WHtR, the centile curves showed a continuous decrease by 16 years of age and then increased gradually. WHtR of the girls in various ages were having similar or higher than those of the boys. In comparison of WC 50th and 90th percentiles with other countries, it was found that except few ages, the Pakistani children had larger WC than the other reference populations and the results of WHtR were also comparable to the other nations. Conclusions: We present new reference data of WC, WHtR and WHtR (exp) using a representative sample of the Pakistani children aged 2-18 years. These reference values can be used provisionally for early detection of central obesity and its associated risks in the Pakistani children.

Multicollinearity, a common problem encountered in regression analysis, has many adverse effects on the ordinary least squares estimator. According to the literature, the ridge regression estimator is one of the useful remedies to overcome this problem. The present study is aimed to use the Bayesian approach for ridge regression and to use estimation of biasing parameters in the Bayesian paradigm by incorporating the prior information of the parameters involved. In contrary to the available Bayesian estimators, our proposed estimator permits easy computation of many posterior features of interest in regression to overcome the problem of multicollinearity. The performance of this technique has been compared with the well-known ridge regression estimators by executing an extensive simulation study. The numerical results provided an exceptional performance of the proposed technique using the mean squared error criterion. An example has been used to illustrate the proposed technique.

Different anthropometric parameters have been proposed for assessing central obesity. The diagnostic performance of these anthropometric parameters and their ability to correctly measure central obesity for the professional community, like drivers, is questionable and needs to be assessed. The study aimed to examine the diagnostic performance of anthropometric parameters as indicators of central obesity in drivers as measured by waist circumference (WC) and to determine the best cut-off values for these parameters that would identify obese drivers. Anthropometric measurements from a cross-sectional sample of 197 professional drivers were taken under standard protocol. Receiver operating characteristics (ROC) analysis was used to examine the diagnostic performance and to determine the optimal cut-off point of each anthropometric parameter to identify centrally obese drivers. It was found that WC had a significant positive correlation with all other obesity indicators. The ROC curve analysis indicated that all the parameters analyzed had a good performance, but the waist-to-height ratio (WHtR) had a more predictive value of the area under the curve (AUC). Optimal cut-offs to identify central obesity in drivers were 0.55, 2.06, 0.95, and 25.44 for WHtR, conicity index, waist-to-hip ratio, and body mass index, respectively. These cut-off points for different indicators can be used to detect central obesity for drivers.

Background: Obesity is a serious public health problem that is growing alarmingly worldwide. The main objective of this study is to examine the current prevalence of overweight and obesity among Pakistani adults and to identify the sociodemographic factors that are associated with overweight and obesity. Methods: Secondary data from a population-based household survey (the Pakistan Panel Household Survey) were used for this study. A total of 10,063 participants (3,916 men and 6,147 women) were included. Overweight and obese individuals were identified using the World Health Organization-recommended cutoffs for body mass index (kg/m(2)). Along with descriptive statistics, the Pearson chi-square test was used to investigate the association among categorical variables. Odds ratios (ORs) along with 95% confidence intervals (CIs) were estimated using univariate logistic regression analysis to evaluate the most significantly associated risk factors for overweight/obesity. Results: The mean age and body mass index of the participants were 38.2 years and 22.9 kg/m(2), respectively. Overall, 22.8% of the participants (23.9% of the women and 21.1% of the men) were overweight, and 5.1% (6.3% of the women and 3.2% of the men) were obese. Sociodemographic factors, such as sex, marital status, and residential area, were significantly associated with body mass index categories. Women (OR, 1.34; 95% CI, 1.23-1.47; P<0.01), ever-married individuals (OR, 1.92; 95% CI, 1.70-2.16; P<0.01), and individuals living in urban areas (OR, 1.23; 95% CI, 1.12-1.35; P<0.01) were more likely to become overweight/obese than their counterparts. Conclusion: We have found the excess weight problem to be quite high in the Pakistani adult population. The government and other health agencies should take initiatives in launching programs about nutritional awareness for adults to prevent obesity.

Objective:Neck circumference (NC) is considered to be an alternative screening method for obesity. The aims were: (1) to examine the correlation between body mass index (BMI) and NC; and (2) to determine diagnostic performance including the best cut-off values of NC for identification of overweight and obese Pakistani children.Methods:The study sample was 7,921 children, aged 5-14 years, by cross-sectional survey carried-out in four major cities of Pakistan. Receiver operating characteristic analysis was used to investigate the diagnostics performance of NC and to determine the optimal cut-off points for identifying children with overweight and obesity.Results:The mean of each anthropometric variable (i.e., height, weight, BMI and NC) increased with age in both sexes. In the whole sample, NC had a strong positive correlation (r=0.61, p<0.01) with BMI. NC optimal cut-off points for identifying overweight and obesity in Pakistani boys ranged between 25.00 to 30.35 cm and the corresponding values for the girls were 24.00 to 31.62 cm. In the prepubertal period, NC cut-off points indicative overweight, in both boys and girls were 26.36 cm and 25.27 cm, respectively; the corresponding values for obesity were 26.78 cm and 25.02 cm. During puberty, the cut-off values for overweight and obesity respectively were 28.32 cm and 28.57 cm in boys and 28.70 cm and 28.82 cm in girls.Conclusion:NC may be used as a simple and widely applicable measure for identification of overweight and obesity with reasonable accuracy in Pakistani children.

BACKGROUND: Assessment of growth and nutritional status is an essential part of clinical evaluation and care in pediatrics. Therefore, we aimed to establish age and gender specific smoothed BMI growth reference charts of Pakistani children and adolescents aged 2-18 years and to compare our LMS median percentile values with WHO 2007 international references and with references from other foreign studies.METHODS: A representative cross-sectional sample of 10,668 healthy Pakistani subjects aged 2 to 18 years was studied. For calculation of BMI (kg/m2), height (cm) and weight (kg) were measured using standard procedures. Age and gender specific smoothed BMI growth reference values and associated charts were obtained using lambda-mu-sigma (LMS) as well as quantile regression (QR) statistical methods.RESULTS: In the sample studied, the mean (±SD) BMI of all subjects was 16.50 (±2.83 kg/m2). Smoothed BMI percentile curves (5th, 10th, 25th, 50th, 75th, 90th and 95th) obtained by using LMS and QR methods, showed that BMI increased with age in both sexes. During pubertal age, girls had larger percentiles than boys. Centile values estimated by the LMS and QR procedure had small variability from the empirical centiles. Comparison of LMS BMI 50th percentile with references from WHO 2007 and data from other countries demonstrated that Pakistani children had substantially lower BMI percentiles than their counterparts in the reference population.CONCLUSIONS: This comprehensive study suggests that WHO 2007 references are not suitable for Pakistani children. The QR method should be considered as an alternative method to develop growth charts.

The ridge regression estimator, one of the commonly used alternatives to the conventional ordinary least squares estimator, avoids the adverse effects in the situations when there exists some considerable degree of multicollinearity among the regressors. There are many software packages available for estimation of ridge regression coefficients. However, most of them display limited methods to estimate the ridge biasing parameters without testing procedures. Our developed package, lmridge can be used to estimate ridge coefficients considering a range of different existing biasing parameters, to test these coefficients with more than 25 ridge related statistics, and to present different graphical displays of these statistics.