A Regularization Method for Approximating the Inverse Laplace Transform

A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace transform as finite sum

Identifying Malaria Hotspots Regions in Ghana Using Bayesian Spatial and Spatiotemporal Models

Background:Malaria remains a significant public health concern in Ghana,with varying risk levels across different geographical areas.Malaria affects millions of people each year and imposes a substantial burden on the health care system and population.Accurate risk estimation and mapping are crucial for effectively allocating resources and implementing targeted interventions to identify regions with disease hotspots.This study aimed to identify regions exhibiting elevated malaria risk so that public health interventions can be implemented,and to identify malaria risk predictors that can be controlled as part of public health interventions for malaria control.Methods:The data on laboratory-confirmed malaria cases from 2015 to 2021 were obtained from the Ghana Health Service and Ghana Statistical Service.We studied the spatial and spatiotemporal patterns of the relative risk of malaria using Bayesian spatial and spatiotemporal models.The malaria risk for each region was mapped to visually identify regions with malaria hotspots.Clustering and heterogeneity of disease risks were established using correlated and uncorrelated structures via the conditional autoregressive and Gaussian models,respectively.Parameter estimates from the marginal posterior distribution were estimated within the Integrated Nested Laplace Approximation using the R software.Results:The spatial model indicated an increased risk of malaria in the North East,Bono East,Ahafo,Central,Upper West,Brong Ahafo,Ashanti,and Eastern regions.The spatiotemporal model results highlighted an elevated malaria risk in the North East,Upper West,Upper East,Savannah,Bono East,Central,Bono,and Ahafo regions.Both spatial and spatiotemporal models identified the North East,Upper West,Bono East,Central,and Ahafo Regions as hotspots for malaria risk.Substantial variations in risk were evident across regions(H=104.9,P<0.001).Although climatic and economic factors influenced malaria infection,statistical significance was not established.Conclusions:Malaria risk was clustered and varied among regions in Ghana.There are many regions in Ghana that are hotspots for malaria risk,and climate and economic factors have no significant influence on malaria risk.This study could provide information on malaria transmission patterns in Ghana,and contribute to enhance the effectiveness of malaria control strategies.

Joint modeling of longitudinal proportional measurements and survival time with a cure fraction

In cancer clinical trials and other medical studies, both longitudinal measurements and data on a time to an event(survival time) are often collected from the same patients. Joint analyses of these data would improve the efficiency of the statistical inferences. We propose a new joint model for the longitudinal proportional measurements which are restricted in a finite interval and survival times with a potential cure fraction. A penalized joint likelihood is derived based on the Laplace approximation and a semiparametric procedure based on this likelihood is developed to estimate the parameters in the joint model. A simulation study is performed to evaluate the statistical properties of the proposed procedures. The proposed model is applied to data from a clinical trial on early breast cancer.