Ahmed M . Gad | British University in Egypt (BUE) (original) (raw)
Papers by Ahmed M . Gad
Frontiers in Applied Mathematics and Statistics, Feb 24, 2023
Introduction: Longitudinal individual response profiles could exhibit a mixture of two or more ph... more Introduction: Longitudinal individual response profiles could exhibit a mixture of two or more phases of increase or decrease in trend throughout the followup period, with one or more unknown transition points (changepoints). The detection and estimation of these changepoints is crucial. Most of the proposed statistical methods for detecting and estimating changepoints in literature rely on distributional assumptions that may not hold. In this case, a good alternative is to use a robust approach; the quantile regression model. There are methods in the literature to deal with quantile regression models with a changepoint. These methods ignore the within-subject dependence of longitudinal data. Methods: We propose a mixed e ects quantile regression model with changepoints to account for dependence structure in the longitudinal data. Fixed e ects parameters, in addition to the location of the changepoint, are estimated using the profile estimation method. The stochastic approximation EM algorithm is proposed to estimate the fixed e ects parameters exploiting the link between an asymmetric Laplace distribution and the quantile regression. In addition, the location of the changepoint is estimated using the usual optimization methods. Results and discussion: A simulation study shows that the proposed estimation and inferential procedures perform reasonably well in finite samples. The practical use of the proposed model is illustrated using COVID-data. The data focus on the e ect of global economic and health factors on the monthly death rate due to COVID-from April to th April. the results show a positive e ect on the monthly number of patients with COVID-in intensive care units (ICUs) for both. th and. th quantiles of new monthly deaths per million. The stringency index, hospital beds, and diabetes prevalence have no significant e ect on both. th and. th quantiles of new monthly deaths per million.
International journal of statistics and applications, 2013
Longitudinal studies are very common in public health and medical sciences. Missing values are no... more Longitudinal studies are very common in public health and medical sciences. Missing values are not uncommon with longitudinal studies. Ignoring the missing values in the analysis of longitudinal data leads to biased estimates. Valid inference about longitudinal data must incorporate the missing data model into the analysis. Several approaches have been proposed to obtain valid inference in the presence of missing values. One of these approaches is the imputation techniques. Imputation techniques range from single imputation (the missing value is imputed by a single observation) to multip le imputation, where the missing value is imputed by a fixed number of observations. In this article we propose a new imputation strategy to handle missing values in longitudinal data. The new strategy depends on imputing the missing values with donors from the observed values. The donors represent quantiles of the observed data. This imputation strategy is applicable if the missing data mechanism is missing not at random. The proposed technique is applied to a real data set of antidepressant clinical trial. A lso, a simulation study is conducted to evaluate the proposed strategy.
We introduce a new continuous distribution called the Burr XII-Burr XII distribution. Some of its... more We introduce a new continuous distribution called the Burr XII-Burr XII distribution. Some of its properties are derived. The method of maximum likelihood is used to estimate the unknown parameters. An application is provided with details to illustrate the importance of the new. The new model provides adequate fits as compared to other related models with smallest values for A-IC, B-IC, CA-IC and HQ-IC. Characterization results are presented based on two truncated moments, hazard function as well as based on the conditional expectation.
International journal of statistics and applications, 2013
Longitudinal studies are very common in public health and medical sciences. Missing values are no... more Longitudinal studies are very common in public health and medical sciences. Missing values are not uncommon with longitudinal studies. Ignoring the missing values in the analysis of longitudinal data leads to biased estimates. Valid inference about longitudinal data must incorporate the missing data model into the analysis. Several approaches have been proposed to obtain valid inference in the presence of missing values. One of these approaches is the imputation techniques. Imputation techniques range from single imputation (the missing value is imputed by a single observation) to multiple imputation, where the missing value is imputed by a fixed number of observations. In this article we propose a new imputation strategy to handle missing values in longitudinal data. The new strategy depends on imputing the missing values with donors from the observed values. The donors represent quantiles of the observed data. This imputation strategy is applicable if the missing data mechanism is...
In linear models, the ordinary least squares (OLS) estimators of parameters have always turned ou... more In linear models, the ordinary least squares (OLS) estimators of parameters have always turned out to be the best linear unbiased estimators. However, if the data contain outliers, this may affect the least-squares estimates. So, an alternative approach; the so-called robust regression methods, is needed to obtain a better fit of the model or more precise estimates of parameters. In this article, various robust regression methods have been reviewed. The focus is on the presence of outliers in the y-direction (response direction). Comparison of the properties of these methods is done through a simulation study. The comparison's criteria were the efficiency and breakdown point. Also, the methods are applied to a real data set.
International Journal on Advanced Science, Engineering and Information Technology, 2021
When researchers are interested in measuring social phenomena that cannot be measured using a sin... more When researchers are interested in measuring social phenomena that cannot be measured using a single variable, the appropriate statistical tool to be used is a latent variable model. A number of manifest variables is used to define the latent phenomenon. The manifest variables may be incomplete due to different forms of non-response that may or may not be random. In such cases, especially when the missingness is nonignorable, it is inevitable to include a missingness mechanism in the model to obtain valid estimates for parameters. In social surveys, categorical items can be considered the most common type of variable. We thus propose a latent class model where two categorical latent variables are defined; one represents the latent phenomenon of interest, and another represents a respondent's propensity to respond to survey items. All manifest items are considered to be categorical. The proposed model incorporates a missingness mechanism that accounts for forms of missingness that may not be random by allowing the latent response propensity class to depend on the latent phenomenon under consideration, given a set of covariates. The Expectation-Maximization (EM) algorithm is used for estimating the proposed model. The proposed model is used to analyze data from 2014 Egyptian Demographic and Health Survey (EDHS14). Missing data is artificially created in order to study results under the three types of missingness: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR).
Journal of University of Shanghai for Science and Technology, 2021
In this paper, we will review the methods that used to handle longitudinal data in the case of ma... more In this paper, we will review the methods that used to handle longitudinal data in the case of marginal models when inferences about the population average are the primary focus [1] or when future applications of the results require the expectation of the response as a function of the current covariates [7]. We will review the generalized estimating equations method (GEE), quadratic inference functions (QIF), generalized quasi likelihood (GQL) and the generalized method of moments (GMM). These methods will be reviewed by discussing its advantages and disadvantages in more details.
American Journal of Applied Mathematics and Statistics, 2016
In longitudinal studies data are collected for the same set of units for two or more occasions. T... more In longitudinal studies data are collected for the same set of units for two or more occasions. This is in contrast to cross-sectional studies where a single outcome is measured for each individual. Some intended measurements might not be available for some units resulting in a missing data setting. When the probability of missing depends on the missing values, missing mechanism is termed nonrandom. One common type of the missing patterns is the dropout where the missing values never followed by an observed value. In nonrandom dropout, missing data mechanism must be included in the analysis to get unbiased estimates. The parametric fractional imputation method is proposed to handle the missingness problem in longitudinal studies and to get unbiased estimates in the presence of nonrandom dropout mechanism. Also, in this setting the jackknife replication method is used to find the standard errors for the fractionally imputed estimates. Finally, the proposed method is applied to a real...
Communications in Mathematical Biology and Neuroscience, 2022
Diagnostic tests are used to determine the presence or absence of a disease. Diagnostic accuracy ... more Diagnostic tests are used to determine the presence or absence of a disease. Diagnostic accuracy is the main tool to evaluate a test. Four accuracy measures are used to evaluate how well the results of the test under evaluation (index test) agree with the outcome of the reference test (gold standard). These measures are sensitivity, specificity, positive predictive value and negative predictive value. Some subjects are only measured by a subset of tests which result in missing values. This leads to biased results. The mechanism of missing data could be missing completely at random (MCA), missing at random (MAR), or missing not at random (MNAR). Various methods such as the completecase analysis (CCA) and the maximum likelihood (ML) method are used to handle missing data. Also, imputation methods could be used. The article aims to use a multiple imputation approach to evaluate binary diagnostic tests with missing data under the MCAR mechanism. The proposed approach is applied to a real data set. Also, a simulation study is conducted to evaluate the performance of the proposed approach.
Applied mathematical sciences, 2016
Longitudinal data differs from other types of data as we take more than one observation from ever... more Longitudinal data differs from other types of data as we take more than one observation from every subject at different occasion or under different conditions. The response variable may be continuous, categorical or count. In this article the focus is on count response. The Poisson distribution is the most suitable discrete distribution for count data. Missing values are not uncommon in longitudinal data setting. Possibility of having missing data makes all traditional methods give biased and inconsistent estimates. Â The missing data mechanism is missing completely at random (MCAR), missing at random (MAR), or missing not at random (MNAR). This article compares different methods of analysis for longitudinal count data in the presence of missing values. The aim is to compare the efficiency of these methods. The relative bias and relative efficiency is used as criteria of comparison. Simulation studies are used to compare different methods. This is done under different settings such ...
Universal journal of public health, Aug 1, 2022
Multilevel survival models can be applied where the data have the hierarchical nature. Three comm... more Multilevel survival models can be applied where the data have the hierarchical nature. Three common models are used in this case. They are the discrete time survival models with mixed effects, the Cox proportional hazard model with mixed effects and the Weibull survival model with mixed effects. The Egyptian Demographic Health Survey (EDHS 2014) data target 21,762 ever-married women aged 15-49. This article aims to determine the factors that may affect the time from the last birth of a woman to the first use of contraceptives. Due to the hierarchical nature of EDHS data, multilevel survival analysis is employed. The above three models are applied to EDHS 2014 data. The Weibull survival model with mixed effects proved to be the best model to fit the survival time. Moreover, it is found that only 25% of the sampled women have not used contraceptives until almost one year from their last birth. In addition, attaining higher education, increasing the age at first sex and breastfeeding contribute to the more efficient use of contraceptives. In addition, the article recommends enhancing family planning campaigns which have a powerful impact on the behavior of women in Egypt for the optimal use of contraceptives.
The longitudinal individual response profiles could exhibit a mixture of two or more phases of i... more The longitudinal individual response profiles could exhibit a mixture of two or more phases of increase or decrease in trend throughout the follow up period, with one or more unknown transition points usually referred to as breakpoints or change points. The existence of such unknown point disturbs the sample characteristics, so the detection and estimation of these points is crucial. Most of the proposed statistical methods in literature, for detecting and estimating change points, assume distributional assumption that may not hold. A good alternative in this case is to use a robust approach which is the quantile regression model. There are trials in the literature to deal with quantile regression models with a change point. These trials ignore the within subject dependence of longitudinal data. In this paper we propose a mixed effect quantile regression model with a change point to account for dependence structure in the longitudinal data. Fixed effect parameters, in addition to t...
Multilevel survival models can be applied where the data have hierarchical nature. Three common m... more Multilevel survival models can be applied where the data have hierarchical nature. Three common models are used in this case. They are the discrete time survival models with mixed effects, the Cox proportional hazard model with mixed effects and the Weibull survival model with mixed effects. The Egyptian Demographic Health Survey (EDHS 2014) data targets 21,762 ever-married women aged 15-49. This article aims to determine the factors that may affect the time from the last birth of a woman to the first use of contraceptives. Due to the hierarchical nature of EDHS data, multilevel survival analysis is employed. The above three models are applied to EDHS 2014 data. The Weibull survival model with mixed effects proved to be the best model to fit the survival time. Moreover, it is found that only 25% of the sampled women have not used contraceptives until almost one year from their last birth. In addition, attaining higher education, increasing the age at first sex and breastfeeding contribute to more efficient use of contraceptives. In addition, the article recommends enhancing family planning campaigns which have powerful impact on the behavior of women in Egypt for the optimal use of contraceptives.
Journal of Data Science, 2021
Missing values are not uncommon in longitudinal data studies. Missingness could be due to withdra... more Missing values are not uncommon in longitudinal data studies. Missingness could be due to withdrawal from the study (dropout) or intermittent. The missing data mechanism is termed non-ignorable if the probability of missingness depends on the unobserved (missing) observations. This paper presents a model for continuous longitudinal data with non-ignorable non-monotone missing values. Two separate models, for the response and missingness, are assumed. The response is modeled as multivariate normal whereas the binomial model for missingness process. Parameters in the adopted model are estimated using the stochastic EM algorithm. The proposed model (approach) is then applied to an example from the International Breast Cancer Study Group.
Journal of Data Science, 2021
Longitudinal data analysis had been widely developed in the past three decades. Longitudinal data... more Longitudinal data analysis had been widely developed in the past three decades. Longitudinal data are common in many fields such as public health, medicine, biological and social sciences. Longitudinal data have special nature as the individual may be observed during a long period of time. Hence, missing values are common in longitudinal data. The presence of missing values leads to biased results and complicates the analysis. The missing values have two patterns: intermittent and dropout. The missing data mechanisms are missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). The appropriate analysis relies heavily on the assumed mechanism and pattern. The parametric fractional imputation is developed to handle longitudinal data with intermittent missing pattern. The maximum likelihood estimates are obtained and the Jackkife method is used to obtain the standard errors of the parameters estimates. Finally a simulation study is conducted to validate the proposed approach. Also, the proposed approach is applied to a real data.
Measurements made on several outcomes for the same unit, implying multivariate longitudinal data,... more Measurements made on several outcomes for the same unit, implying multivariate longitudinal data, are very likely to be correlated. Therefore, fitting such a data structure can be quite challenging due to the high dimensioned correlations exist within and between outcomes over time. Moreover, an additional challenge is encountered in longitudinal studies due to premature withdrawal of the subjects from the study resulting in incomplete (missing) data. Incomplete data is more problematic when missing data mechanism is related to the unobserved outcomes implying what so-called non-ignorable missing data or missing not at random (MNAR). Obtaining valid estimation under non-ignorable assumption requires that the missing-data mechanism be modeled as a part of the estimation process. The multiple continuous outcome-based data model is introduced via the Gaussian multivariate linear mixed models while the missing-data mechanism is linked to the data model via the selection model such that ...
American Journal of Applied Mathematics and Statistics, 2020
Radio channel signals are heavily used tool in telecommunications. A suitable probability distrib... more Radio channel signals are heavily used tool in telecommunications. A suitable probability distribution is needed to model signals. Many probability distributions have been introduced for this purpose. The α-μ probability distribution is a general channel signal fading model that encompasses many applied important distributions as a special case. This distribution is also known as generalized gamma, Stacy distribution. This distribution is used to describe the fading mobile radio signal under a general diffuse scattering. The main advantage of this probability distribution is that it is flexible and mathematically tractable. Also, many other distributions can be considered as a special case of α-μ probability distribution. In this article we discuss the model parameters' estimation. Two new maximum likelihood (ML) and Psi-inverse (PI) estimators for the α-μ channel signal fading distribution have been proposed. Simulation study is finally conducted to evaluate the performance of ...
International Journal of Statistical Distributions and Applications, 2017
Journal of Data Science, Jul 12, 2021
American Journal of Applied Mathematics and Statistics, 2013
Longitudinal studies represent one of the principal research strategies employed in medical and s... more Longitudinal studies represent one of the principal research strategies employed in medical and social research. These studies are the most appropriate for studying individual change over time. The prematurely withdrawal of some subjects from the study (dropout) is termed nonrandom when the probability of missingness depends on the missing value. Nonrandom dropout is common phenomenon associated with longitudinal data and it complicates statistical inference. The shared parameter model is used to fit longitudinal data in the presence of nonrandom dropout. The stochastic EM algorithm is developed to obtain the model parameter estimates. Also, parameter estimates of the dropout model have been obtained. Standard errors of estimates have been calculated using the developed Monte Carlo method. The proposed approach performance is evaluated through a simulation study. Also, the proposed approach is applied to a real data set.
Frontiers in Applied Mathematics and Statistics, Feb 24, 2023
Introduction: Longitudinal individual response profiles could exhibit a mixture of two or more ph... more Introduction: Longitudinal individual response profiles could exhibit a mixture of two or more phases of increase or decrease in trend throughout the followup period, with one or more unknown transition points (changepoints). The detection and estimation of these changepoints is crucial. Most of the proposed statistical methods for detecting and estimating changepoints in literature rely on distributional assumptions that may not hold. In this case, a good alternative is to use a robust approach; the quantile regression model. There are methods in the literature to deal with quantile regression models with a changepoint. These methods ignore the within-subject dependence of longitudinal data. Methods: We propose a mixed e ects quantile regression model with changepoints to account for dependence structure in the longitudinal data. Fixed e ects parameters, in addition to the location of the changepoint, are estimated using the profile estimation method. The stochastic approximation EM algorithm is proposed to estimate the fixed e ects parameters exploiting the link between an asymmetric Laplace distribution and the quantile regression. In addition, the location of the changepoint is estimated using the usual optimization methods. Results and discussion: A simulation study shows that the proposed estimation and inferential procedures perform reasonably well in finite samples. The practical use of the proposed model is illustrated using COVID-data. The data focus on the e ect of global economic and health factors on the monthly death rate due to COVID-from April to th April. the results show a positive e ect on the monthly number of patients with COVID-in intensive care units (ICUs) for both. th and. th quantiles of new monthly deaths per million. The stringency index, hospital beds, and diabetes prevalence have no significant e ect on both. th and. th quantiles of new monthly deaths per million.
International journal of statistics and applications, 2013
Longitudinal studies are very common in public health and medical sciences. Missing values are no... more Longitudinal studies are very common in public health and medical sciences. Missing values are not uncommon with longitudinal studies. Ignoring the missing values in the analysis of longitudinal data leads to biased estimates. Valid inference about longitudinal data must incorporate the missing data model into the analysis. Several approaches have been proposed to obtain valid inference in the presence of missing values. One of these approaches is the imputation techniques. Imputation techniques range from single imputation (the missing value is imputed by a single observation) to multip le imputation, where the missing value is imputed by a fixed number of observations. In this article we propose a new imputation strategy to handle missing values in longitudinal data. The new strategy depends on imputing the missing values with donors from the observed values. The donors represent quantiles of the observed data. This imputation strategy is applicable if the missing data mechanism is missing not at random. The proposed technique is applied to a real data set of antidepressant clinical trial. A lso, a simulation study is conducted to evaluate the proposed strategy.
We introduce a new continuous distribution called the Burr XII-Burr XII distribution. Some of its... more We introduce a new continuous distribution called the Burr XII-Burr XII distribution. Some of its properties are derived. The method of maximum likelihood is used to estimate the unknown parameters. An application is provided with details to illustrate the importance of the new. The new model provides adequate fits as compared to other related models with smallest values for A-IC, B-IC, CA-IC and HQ-IC. Characterization results are presented based on two truncated moments, hazard function as well as based on the conditional expectation.
International journal of statistics and applications, 2013
Longitudinal studies are very common in public health and medical sciences. Missing values are no... more Longitudinal studies are very common in public health and medical sciences. Missing values are not uncommon with longitudinal studies. Ignoring the missing values in the analysis of longitudinal data leads to biased estimates. Valid inference about longitudinal data must incorporate the missing data model into the analysis. Several approaches have been proposed to obtain valid inference in the presence of missing values. One of these approaches is the imputation techniques. Imputation techniques range from single imputation (the missing value is imputed by a single observation) to multiple imputation, where the missing value is imputed by a fixed number of observations. In this article we propose a new imputation strategy to handle missing values in longitudinal data. The new strategy depends on imputing the missing values with donors from the observed values. The donors represent quantiles of the observed data. This imputation strategy is applicable if the missing data mechanism is...
In linear models, the ordinary least squares (OLS) estimators of parameters have always turned ou... more In linear models, the ordinary least squares (OLS) estimators of parameters have always turned out to be the best linear unbiased estimators. However, if the data contain outliers, this may affect the least-squares estimates. So, an alternative approach; the so-called robust regression methods, is needed to obtain a better fit of the model or more precise estimates of parameters. In this article, various robust regression methods have been reviewed. The focus is on the presence of outliers in the y-direction (response direction). Comparison of the properties of these methods is done through a simulation study. The comparison's criteria were the efficiency and breakdown point. Also, the methods are applied to a real data set.
International Journal on Advanced Science, Engineering and Information Technology, 2021
When researchers are interested in measuring social phenomena that cannot be measured using a sin... more When researchers are interested in measuring social phenomena that cannot be measured using a single variable, the appropriate statistical tool to be used is a latent variable model. A number of manifest variables is used to define the latent phenomenon. The manifest variables may be incomplete due to different forms of non-response that may or may not be random. In such cases, especially when the missingness is nonignorable, it is inevitable to include a missingness mechanism in the model to obtain valid estimates for parameters. In social surveys, categorical items can be considered the most common type of variable. We thus propose a latent class model where two categorical latent variables are defined; one represents the latent phenomenon of interest, and another represents a respondent's propensity to respond to survey items. All manifest items are considered to be categorical. The proposed model incorporates a missingness mechanism that accounts for forms of missingness that may not be random by allowing the latent response propensity class to depend on the latent phenomenon under consideration, given a set of covariates. The Expectation-Maximization (EM) algorithm is used for estimating the proposed model. The proposed model is used to analyze data from 2014 Egyptian Demographic and Health Survey (EDHS14). Missing data is artificially created in order to study results under the three types of missingness: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR).
Journal of University of Shanghai for Science and Technology, 2021
In this paper, we will review the methods that used to handle longitudinal data in the case of ma... more In this paper, we will review the methods that used to handle longitudinal data in the case of marginal models when inferences about the population average are the primary focus [1] or when future applications of the results require the expectation of the response as a function of the current covariates [7]. We will review the generalized estimating equations method (GEE), quadratic inference functions (QIF), generalized quasi likelihood (GQL) and the generalized method of moments (GMM). These methods will be reviewed by discussing its advantages and disadvantages in more details.
American Journal of Applied Mathematics and Statistics, 2016
In longitudinal studies data are collected for the same set of units for two or more occasions. T... more In longitudinal studies data are collected for the same set of units for two or more occasions. This is in contrast to cross-sectional studies where a single outcome is measured for each individual. Some intended measurements might not be available for some units resulting in a missing data setting. When the probability of missing depends on the missing values, missing mechanism is termed nonrandom. One common type of the missing patterns is the dropout where the missing values never followed by an observed value. In nonrandom dropout, missing data mechanism must be included in the analysis to get unbiased estimates. The parametric fractional imputation method is proposed to handle the missingness problem in longitudinal studies and to get unbiased estimates in the presence of nonrandom dropout mechanism. Also, in this setting the jackknife replication method is used to find the standard errors for the fractionally imputed estimates. Finally, the proposed method is applied to a real...
Communications in Mathematical Biology and Neuroscience, 2022
Diagnostic tests are used to determine the presence or absence of a disease. Diagnostic accuracy ... more Diagnostic tests are used to determine the presence or absence of a disease. Diagnostic accuracy is the main tool to evaluate a test. Four accuracy measures are used to evaluate how well the results of the test under evaluation (index test) agree with the outcome of the reference test (gold standard). These measures are sensitivity, specificity, positive predictive value and negative predictive value. Some subjects are only measured by a subset of tests which result in missing values. This leads to biased results. The mechanism of missing data could be missing completely at random (MCA), missing at random (MAR), or missing not at random (MNAR). Various methods such as the completecase analysis (CCA) and the maximum likelihood (ML) method are used to handle missing data. Also, imputation methods could be used. The article aims to use a multiple imputation approach to evaluate binary diagnostic tests with missing data under the MCAR mechanism. The proposed approach is applied to a real data set. Also, a simulation study is conducted to evaluate the performance of the proposed approach.
Applied mathematical sciences, 2016
Longitudinal data differs from other types of data as we take more than one observation from ever... more Longitudinal data differs from other types of data as we take more than one observation from every subject at different occasion or under different conditions. The response variable may be continuous, categorical or count. In this article the focus is on count response. The Poisson distribution is the most suitable discrete distribution for count data. Missing values are not uncommon in longitudinal data setting. Possibility of having missing data makes all traditional methods give biased and inconsistent estimates. Â The missing data mechanism is missing completely at random (MCAR), missing at random (MAR), or missing not at random (MNAR). This article compares different methods of analysis for longitudinal count data in the presence of missing values. The aim is to compare the efficiency of these methods. The relative bias and relative efficiency is used as criteria of comparison. Simulation studies are used to compare different methods. This is done under different settings such ...
Universal journal of public health, Aug 1, 2022
Multilevel survival models can be applied where the data have the hierarchical nature. Three comm... more Multilevel survival models can be applied where the data have the hierarchical nature. Three common models are used in this case. They are the discrete time survival models with mixed effects, the Cox proportional hazard model with mixed effects and the Weibull survival model with mixed effects. The Egyptian Demographic Health Survey (EDHS 2014) data target 21,762 ever-married women aged 15-49. This article aims to determine the factors that may affect the time from the last birth of a woman to the first use of contraceptives. Due to the hierarchical nature of EDHS data, multilevel survival analysis is employed. The above three models are applied to EDHS 2014 data. The Weibull survival model with mixed effects proved to be the best model to fit the survival time. Moreover, it is found that only 25% of the sampled women have not used contraceptives until almost one year from their last birth. In addition, attaining higher education, increasing the age at first sex and breastfeeding contribute to the more efficient use of contraceptives. In addition, the article recommends enhancing family planning campaigns which have a powerful impact on the behavior of women in Egypt for the optimal use of contraceptives.
The longitudinal individual response profiles could exhibit a mixture of two or more phases of i... more The longitudinal individual response profiles could exhibit a mixture of two or more phases of increase or decrease in trend throughout the follow up period, with one or more unknown transition points usually referred to as breakpoints or change points. The existence of such unknown point disturbs the sample characteristics, so the detection and estimation of these points is crucial. Most of the proposed statistical methods in literature, for detecting and estimating change points, assume distributional assumption that may not hold. A good alternative in this case is to use a robust approach which is the quantile regression model. There are trials in the literature to deal with quantile regression models with a change point. These trials ignore the within subject dependence of longitudinal data. In this paper we propose a mixed effect quantile regression model with a change point to account for dependence structure in the longitudinal data. Fixed effect parameters, in addition to t...
Multilevel survival models can be applied where the data have hierarchical nature. Three common m... more Multilevel survival models can be applied where the data have hierarchical nature. Three common models are used in this case. They are the discrete time survival models with mixed effects, the Cox proportional hazard model with mixed effects and the Weibull survival model with mixed effects. The Egyptian Demographic Health Survey (EDHS 2014) data targets 21,762 ever-married women aged 15-49. This article aims to determine the factors that may affect the time from the last birth of a woman to the first use of contraceptives. Due to the hierarchical nature of EDHS data, multilevel survival analysis is employed. The above three models are applied to EDHS 2014 data. The Weibull survival model with mixed effects proved to be the best model to fit the survival time. Moreover, it is found that only 25% of the sampled women have not used contraceptives until almost one year from their last birth. In addition, attaining higher education, increasing the age at first sex and breastfeeding contribute to more efficient use of contraceptives. In addition, the article recommends enhancing family planning campaigns which have powerful impact on the behavior of women in Egypt for the optimal use of contraceptives.
Journal of Data Science, 2021
Missing values are not uncommon in longitudinal data studies. Missingness could be due to withdra... more Missing values are not uncommon in longitudinal data studies. Missingness could be due to withdrawal from the study (dropout) or intermittent. The missing data mechanism is termed non-ignorable if the probability of missingness depends on the unobserved (missing) observations. This paper presents a model for continuous longitudinal data with non-ignorable non-monotone missing values. Two separate models, for the response and missingness, are assumed. The response is modeled as multivariate normal whereas the binomial model for missingness process. Parameters in the adopted model are estimated using the stochastic EM algorithm. The proposed model (approach) is then applied to an example from the International Breast Cancer Study Group.
Journal of Data Science, 2021
Longitudinal data analysis had been widely developed in the past three decades. Longitudinal data... more Longitudinal data analysis had been widely developed in the past three decades. Longitudinal data are common in many fields such as public health, medicine, biological and social sciences. Longitudinal data have special nature as the individual may be observed during a long period of time. Hence, missing values are common in longitudinal data. The presence of missing values leads to biased results and complicates the analysis. The missing values have two patterns: intermittent and dropout. The missing data mechanisms are missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). The appropriate analysis relies heavily on the assumed mechanism and pattern. The parametric fractional imputation is developed to handle longitudinal data with intermittent missing pattern. The maximum likelihood estimates are obtained and the Jackkife method is used to obtain the standard errors of the parameters estimates. Finally a simulation study is conducted to validate the proposed approach. Also, the proposed approach is applied to a real data.
Measurements made on several outcomes for the same unit, implying multivariate longitudinal data,... more Measurements made on several outcomes for the same unit, implying multivariate longitudinal data, are very likely to be correlated. Therefore, fitting such a data structure can be quite challenging due to the high dimensioned correlations exist within and between outcomes over time. Moreover, an additional challenge is encountered in longitudinal studies due to premature withdrawal of the subjects from the study resulting in incomplete (missing) data. Incomplete data is more problematic when missing data mechanism is related to the unobserved outcomes implying what so-called non-ignorable missing data or missing not at random (MNAR). Obtaining valid estimation under non-ignorable assumption requires that the missing-data mechanism be modeled as a part of the estimation process. The multiple continuous outcome-based data model is introduced via the Gaussian multivariate linear mixed models while the missing-data mechanism is linked to the data model via the selection model such that ...
American Journal of Applied Mathematics and Statistics, 2020
Radio channel signals are heavily used tool in telecommunications. A suitable probability distrib... more Radio channel signals are heavily used tool in telecommunications. A suitable probability distribution is needed to model signals. Many probability distributions have been introduced for this purpose. The α-μ probability distribution is a general channel signal fading model that encompasses many applied important distributions as a special case. This distribution is also known as generalized gamma, Stacy distribution. This distribution is used to describe the fading mobile radio signal under a general diffuse scattering. The main advantage of this probability distribution is that it is flexible and mathematically tractable. Also, many other distributions can be considered as a special case of α-μ probability distribution. In this article we discuss the model parameters' estimation. Two new maximum likelihood (ML) and Psi-inverse (PI) estimators for the α-μ channel signal fading distribution have been proposed. Simulation study is finally conducted to evaluate the performance of ...
International Journal of Statistical Distributions and Applications, 2017
Journal of Data Science, Jul 12, 2021
American Journal of Applied Mathematics and Statistics, 2013
Longitudinal studies represent one of the principal research strategies employed in medical and s... more Longitudinal studies represent one of the principal research strategies employed in medical and social research. These studies are the most appropriate for studying individual change over time. The prematurely withdrawal of some subjects from the study (dropout) is termed nonrandom when the probability of missingness depends on the missing value. Nonrandom dropout is common phenomenon associated with longitudinal data and it complicates statistical inference. The shared parameter model is used to fit longitudinal data in the presence of nonrandom dropout. The stochastic EM algorithm is developed to obtain the model parameter estimates. Also, parameter estimates of the dropout model have been obtained. Standard errors of estimates have been calculated using the developed Monte Carlo method. The proposed approach performance is evaluated through a simulation study. Also, the proposed approach is applied to a real data set.