Asian Journal of Probability and Statistics

Aim: “This study Analytical Hierarchy Process (AHP) Model for Malaria Control” was aimed at using analytical hierarchy process model to prioritize alternative strategies for malaria control.

Place and the Duration of the Study: The study was carried out in Bauchi State, Nigeria from May, 2017 to June, 2019.

Methodology: The study used primary and secondary data. The secondary data were the identified alternatives strategies for malaria control and the criteria for evaluating these strategies obtained from malaria control journals and World Health Organization report. The criteria and malaria control strategies were used as input for developing a 9-point scale used in a questionnaire to obtained responses from the Experts in scoring the pairwise comparison of the criteria and the alternatives. Analytical hierarchy process (AHP) model was used to develop the pairwise comparison matrices from the Experts opinions. Computations were carried out with the help of computer software, business performance management Singapore (BPMSG-AHP ONLINE).

Results:The result of the analysis shows that the use of insecticide treated nets was ranked the best strategy for malaria control (AHP score 0.348). Based on the findings of this paper, it is recommended that the use of treated mosquito net should be given much attention in controlling malaria in Nigeria.

Conclusion:We therefore conclude that in a multi -criteria decision making situation, AHP is a powerful tool to assists decision makers.

Aim: The aim of this study is to evaluate the agreement between three routinely used non-surgical management techniques for large periapical lesions namely the treatments with Calcium hydroxide, Mineralo-Trioxide Aggregate and Bio-dentine.

Methods: Data was collected from 60 patients at the Department of Restorative Dentistry, Faculty of Dental Sciences, University of Peradeniya. The variables age, gender and area of the infected                 region before and after the treatment and the treatment type were considered. Two homoscedastic               and heteroscedastic Mixed-effects models were fitted and the agreement between three                     treatments were assessed using Concordance Correlation Coefficient (CCC) and Total Deviation Index (TDI).

Results: CCC value calculated for treatment types 1 & 2, 1 & 3 and 2 & 3 are (0.905, 0.909, 0.874) for homoscedastic model and (0.989, 0.990, 0.975) for heteroscedastic model. Further, corresponding TDI values for homoscedastic and heteroscedastic models are (3.148, 4.390, 1.647) and (2.963, 4.388, 1.457) respectively.

Conclusions: Since all the CCC values are close to 1 and TDI values are low, there is a strong agreement between all three treatments and hence they be used interchangeably. Moreover, the agreement between Treatments with Calcium hydroxide and Bio-dentine is higher compared to the agreements between the other treatments. (i.e., Calcium hydroxide with Mineralo-Trioxide Aggregate and Biodentine with Mineralo-Trioxide Aggregate).

An arbitrary non-smooth functional is estimated using a nonparametric set-up. Exploratory data analysis methods are relied on to come up with the functional form for the sample to allow both robustness and optimality to be achieved. An infinite number of parameters are involved and thus the Hilbert sample space is a natural choice. An important step in understanding this problem is the normal means problem, . The basic difficulty of estimating  as defined can be traced back to the non differentiability of the absolute value function, at the origin. Accordingly, constructing an optimal estimator is not easy partly due to the nonexistence of an unbiased estimate of the absolute value function. Therefore, best polynomial approximation was used to smooth the singularity at the origin and then an unbiased estimator for every term in the expansion constructed by use of Hermite polynomials when the averages are bounded by a given constant M > 0 say. The expansion of the Gaussian density function in terms of Hermite polynomials gives a clear and almost accurate estimate that admits cumulant generating function; the Saddle point approximation. Additional precision is obtained by using a higher order Taylor series expansion about the mean resulting in Edgeworth expansion techniques.

Aim: To propose an updated algorithm with an extra step added to the Newton-type algorithm used in robust rank based non-parametric regression for minimizing the dispersion function associated with Wilcoxon scores in order to account for the effect of covariates.

Methodology: The proposed accelerated failure time approach is aimed at incorporating right random censoring in survival data sets for low to moderate levels of censoring. The existing Newton algorithm is modified to account for the effect of one or more covariates. This is done by first applying Mantel scores to residuals obtained from a regression model, and second by minimizing the dispersion function of these scored residuals. Diagnostic check of the model fit is performed by observing the distribution of the residuals and suitable Bent scores are considered in the case of skewed residuals. To demonstrate the efficacy of this method, a simulation study is conducted to compare the power of this method under three different scenarios: non-proportional hazard, proportional and constant hazard, and proportional but non-constant hazard.

Results: In most situations, this method yielded reasonable estimates of power for detecting an association of the covariate with the response as compared to popular parametric and semi-parametric approaches. The estimates of the regression coefficient obtained from this method were evaluated and were found to have low bias, low mean square error, and adequate coverage. In a real-life example pertaining to pancreatic cancer study, the proposed method performed admirably well and provided a more realistic interpretation about the effect of covariates (age and Karnofsky score) compared to a standard parametric (lognormal) model.

Conclusion: In situations where there is no clear best parametric fit for time-to-event data with moderate level of censoring, the proposed method provides a robust alternative to obtain regression coefficients (both adjusted and unadjusted) with a performance comparable to that of a proportional hazards model.

This paper examines the exchange rate volatility with GARCH-type model of the daily exchange rate return series from January 2012 – August 2016 for Naira/Chinese Yuan, Naira/India Rupees, Naira/Spain Euro, Naira/UK Pounds and Naira/US Dollar returns. The studies compare estimates of variants of GARCH (1, 1), EGARCH (1, 1), TGARCH (1,1) and GJR-GARCH (1,1) models. The result from all models indict presence of volatility in the five currencies and equally indicate that most of the asymmetric models rejected the existence of a leverage effect except for models with volatility break. For GARCH (1, 1), GJR-GARCH (1, 1,) EGARCH (1,1) and TGARCH (1, 1), it was observed that India have the best exchange rate with the highest log-likelihood (Log L) and the lowest AIC and BIC followed by USA, China, Spain and United Kingdom respectively. The four models was later compared for the exchange rates of the five countries under consideration i.e. China, India, Spain, UK and USA  to select the best fitted model for each country and it was discovered that GJR-GARCH (1,1) is the best fitted model for all the countries followed by GARCH (1,1), TGARCH (1,1) and EGARCH (1,1) in that order.