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Modeling repairable system failure with repair history and covariates

Samira Ehsani, Jayanthi Arasan, Noor Akma Ibrahim

Sains Malaysiana, 2013;42:981-987.

In this paper, we extended a repairable system model under general repair that is based on repair history, to incorporate covariates. We calculated the bias, standard error and RMSE of the parameter estimates of this model at different sample sizes using simulated data. We applied the model to a real demonstration data and tested for existence of time trend, repair and covariate effects. Following that we also conducted a coverage probability study on the Wald confidence interval estimates. Finally we conducted hypothesis testing for the parameters of the model.The results indicated that the estimation procedure is working well for the proposed model but the Wald interval should be applied with much caution.
Approximate bayesian estimates of weibull parameters with Lindley’s method

Chris Bambey Guure, Noor Akma Ibrahim

Sains Malaysiana, 2014;43:1433-1437.

One of the most important lifetime distributions that is used for modelling and analysing data in clinical, life sciences and engineering is the Weibull distribution. The main objective of this paper was to determine the best estimator for the two-parameter Weibull distribution. The methods under consideration are the frequentist maximum likelihood estimator, least square regression estimator and the Bayesian estimator by using two loss functions, which are squared error and linear exponential. Lindley approximation is used to obtain the Bayes estimates. Comparisons are made through simulation study to determine the performance of these methods. Based on the results obtained from this simulation study the Bayesian approach used in estimating the Weibull parameters under linear exponential loss function is found to be superior as compared to the conventional maximum likelihood and least squared methods.
Generating correlated discrete ordinal data using R and SAS IML

Ibrahim NA, Suliadi S

Comput Methods Programs Biomed, 2011 Dec;104(3):e122-32.
PMID: 21764167 DOI: 10.1016/j.cmpb.2011.06.003

Correlated ordinal data are common in many areas of research. The data may arise from longitudinal studies in biology, medical, or clinical fields. The prominent characteristic of these data is that the within-subject observations are correlated, whilst between-subject observations are independent. Many methods have been proposed to analyze correlated ordinal data. One way to evaluate the performance of a proposed model or the performance of small or moderate size data sets is through simulation studies. It is thus important to provide a tool for generating correlated ordinal data to be used in simulation studies. In this paper, we describe a macro program on how to generate correlated ordinal data based on R language and SAS IML.
Fulltext Turnbull versus Kaplan-Meier estimators of cure rate estimation using interval censored data

Bader Ahmad Aljawadi, Mohd Rizam Abu Bakar, Noor Akma

Pertanika Journal of Science & Technology, 2012;20(2):243-255.
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This study deals with the analysis of the cure rate estimation based on the Bounded Cumulative Hazard (BCH) model using interval censored data, given that the exact distribution of the data set is unknown. Thus, the non-parametric estimation methods are employed by means of the EM algorithm. The Turnbull and Kaplan Meier estimators were proposed to estimate the survival function, even though the Kaplan Meier estimator faces some restrictions in term of interval survival data. A comparison of the cure rate estimation based on the two estimators was done through a simulation study.
Fulltext Bootstrapping the confidence intervals of R2 MAD for samples from contaminated standard logistic distribution

Fauziah Maarof, Lim, Fong Peng, Noor Akma Ibrahim

Pertanika Journal of Science & Technology, 2010;18(1):-.
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This paper investigates the confidence intervals of R2 MAD, the coefficient of determination based on
median absolute deviation in the presence of outliers. Bootstrap bias-corrected accelerated (BCa)
confidence intervals, known to have higher degree of correctness, are constructed for the mean and standard deviation of R2 MAD for samples generated from contaminated standard logistic distribution. The results indicate that by increasing the sample size and percentage of contaminants in the samples, and perturbing the location and scale of the distribution affect the lengths of the confidence intervals. The results obtained can also be used to verify the bound of R2 MAD.
Fulltext Bayesian inference of the Weibull model based on interval-censored survival data

Guure CB, Ibrahim NA, Adam MB

Comput Math Methods Med, 2013;2013:849520.
PMID: 23476718 DOI: 10.1155/2013/849520

Interval-censored data consist of adjacent inspection times that surround an unknown failure time. We have in this paper reviewed the classical approach which is maximum likelihood in estimating the Weibull parameters with interval-censored data. We have also considered the Bayesian approach in estimating the Weibull parameters with interval-censored data under three loss functions. This study became necessary because of the limited discussion in the literature, if at all, with regard to estimating the Weibull parameters with interval-censored data using Bayesian. A simulation study is carried out to compare the performances of the methods. A real data application is also illustrated. It has been observed from the study that the Bayesian estimator is preferred to the classical maximum likelihood estimator for both the scale and shape parameters.
Review of air pollution and health impacts in Malaysia

Afroz R, Hassan MN, Ibrahim NA

Environ Res, 2003 Jun;92(2):71-7.
PMID: 12854685

In the early days of abundant resources and minimal development pressures, little attention was paid to growing environmental concerns in Malaysia. The haze episodes in Southeast Asia in 1983, 1984, 1991, 1994, and 1997 imposed threats to the environmental management of Malaysia and increased awareness of the environment. As a consequence, the government established Malaysian Air Quality Guidelines, the Air Pollution Index, and the Haze Action Plan to improve air quality. Air quality monitoring is part of the initial strategy in the pollution prevention program in Malaysia. Review of air pollution in Malaysia is based on the reports of the air quality monitoring in several large cities in Malaysia, which cover air pollutants such as Carbon monoxide (CO), Sulphur Dioxide (SO2), Nitrogen Dioxide (NO2), Ozone (O3), and Suspended Particulate Matter (SPM). The results of the monitoring indicate that Suspended Particulate Matter (SPM) and Nitrogen Dioxide (NO2) are the predominant pollutants. Other pollutants such as CO, O(x), SO2, and Pb are also observed in several big cities in Malaysia. The air pollution comes mainly from land transportation, industrial emissions, and open burning sources. Among them, land transportation contributes the most to air pollution. This paper reviews the results of the ambient air quality monitoring and studies related to air pollution and health impacts.
Temporal and spatial mapping of hand, foot and mouth disease in Sarawak, Malaysia

Sham NM, Krishnarajah I, Ibrahim NA, Lye MS

Geospat Health, 2014 May;8(2):503-7.
PMID: 24893027

Hand, foot and mouth disease (HFMD) is endemic in Sarawak, Malaysia. In this study, a geographical information system (GIS) was used to investigate the relationship between the reported HFMD cases and the spatial patterns in 11 districts of Sarawak from 2006 to 2012. Within this 7-years period, the highest number of reported HFMD cases occurred in 2006, followed by 2012, 2008, 2009, 2007, 2010 and 2011, in descending order. However, while there was no significant distribution pattern or clustering in the first part of the study period (2006 to 2011) based on Moran's I statistic, spatial autocorrelation (P = 0.068) was observed in 2012.
Fulltext The beta Burr type X distribution properties with application

Merovci F, Khaleel MA, Ibrahim NA, Shitan M

Springerplus, 2016;5(1):697.
PMID: 27347471 DOI: 10.1186/s40064-016-2271-9

We develop a new continuous distribution called the beta-Burr type X distribution that extends the Burr type X distribution. The properties provide a comprehensive mathematical treatment of this distribution. Further more, various structural properties of the new distribution are derived, that includes moment generating function and the rth moment thus generalizing some results in the literature. We also obtain expressions for the density, moment generating function and rth moment of the order statistics. We consider the maximum likelihood estimation to estimate the parameters. Additionally, the asymptotic confidence intervals for the parameters are derived from the Fisher information matrix. Finally, simulation study is carried at under varying sample size to assess the performance of this model. Illustration the real dataset indicates that this new distribution can serve as a good alternative model to model positive real data in many areas.
Fulltext Joint modelling of longitudinal 3MS scores and the risk of mortality among cognitively impaired individuals

Guure CB, Ibrahim NA, Adam MB, Said SM

PLoS One, 2017;12(8):e0182873.
PMID: 28813458 DOI: 10.1371/journal.pone.0182873

BACKGROUND: Modified Mini-Mental State Examination (3MS) is an instrument administered by trained personnel to examine levels of participants' cognitive function. However, the association between changes in scores over time and the risk of death (mortality) is not known. The aims of this study are to examine the association between 3MS scores and mortality via cognitive impairment among older women and to determine individuals' risk of changes in scores to better predict their survival and mortality rates.
METHODS: We propose a Bayesian joint modelling approach to determine mortality due to cognitive impairment via repeated measures of 3MS scores trajectories over a 21-year follow-up period. Data for this study are taken from the Osteoporotic Fracture longitudinal study among women aged 65+ which started in 1986-88.
RESULTS: The standard relative risk model from the analyses with a baseline 3MS score after adjusting for all the significant covariates demonstrates that, every unit decrease in a 3MS score corresponds to a non-significant 1.059 increase risk of mortality with a 95% CI of (0.981, 1.143), while the extended model results in a significant 0.09% increased risk in mortality. The joint modelling approach found a strong association between the 3MS scores and the risk of mortality, such that, every unit decrease in 3MS scores results in a 1.135 (13%) increased risk of death via cognitive impairment with a 95% CI of (1.056, 1.215).
CONCLUSION: It has been demonstrated that a decrease in 3MS results has a significant increase risk of mortality due to cognitive impairment via joint modelling, but insignificant when considered under the standard relative risk approach.
Fulltext Variations and Determinants of Anemia among Reproductive Age Women in Five Sub-Saharan Africa Countries

Nti J, Afagbedzi S, da-Costa Vroom FB, Ibrahim NA, Guure C

Biomed Res Int, 2021;2021:9957160.
PMID: 34395630 DOI: 10.1155/2021/9957160

Background: The Ghana Demographic and Health Survey 2014 report indicates that anemia among women in their reproductive age in the country stood at 42 percent, making it a severe public health problem according to the World Health Organization (WHO) classification. WHO Global Observatory data indicates that some sub-Saharan African countries have been able to reduce the prevalence of anemia among women of reproductive age compared to Ghana in 2016. To inform policy decisions, data from the Demographic and Health Surveys 2014-2018 were analyzed to determine the disparities in the prevalence of anemia and related factors among women of reproductive age in Ghana, Ethiopia, Uganda, Tanzania, and Rwanda.
Methods: This research utilized data from the Demographic and Health Surveys 2014, 2016, 2014-2015, 2015-2016, and 2016 from Ghana, Ethiopia, Rwanda, Tanzania, and Uganda, respectively. Respondents were women aged between 15 and 49 years. Hemoglobin levels were measured by HemoCue hemoglobin meter. 45,299 women data were extracted from the five countries with 4,644, 14,923, 6,680, 13,064, and 5,988 from Ghana, Ethiopia, Rwanda, Tanzania, and Uganda, respectively. Association between anemia and selected predictive variables was assessed using Pearson's chi-square test statistic. Poisson regression with robust standard errors was used to estimate the prevalence rate ratios of developing anemia. The deviance goodness of fit test was employed to test the fit of the Poisson model to the data set.
Results: There was a statistically significant difference in prevalence of 1,962 (42.3%), 3,527 (23.6%), 1,284 (19.3%), 5,857 (44.8%), and 1,898 (31.7%) for Ghana, Ethiopia, Rwanda, Tanzania, and Uganda, respectively, χ 2 = 2,181.86 and p value < 0.001. Parity, pregnancy status, and contraceptives significantly increased the prevalence rate ratio of a woman developing anemia. Women in Ethiopia with a parity of six or more were 58% more likely to develop anemia than those with parity of zero. Tanzanian women who were pregnant had a 14% increased rate ratio of developing anemia. Factors that significantly decreased anemia in this study were wealth index, women's age, and women's highest level of education. Women who were in the higher education category in Ethiopia were 57% less likely to develop anemia. Ugandan women in the richest category of the wealth index were 28% less likely to develop anemia. Rwandan women in the middle category of the wealth index were 20% less likely to develop anemia. Women who were within the 45-49 age category in Ethiopia were 48% less likely to develop anemia.
Conclusion: The individual country governments should encourage the implementation of increasing female enrollment in higher education. Women in their reproductive age should be encouraged to use modern contraceptives to reduce their anemia prevalence.