Fitting three parameter growth curves using a nonlinear mixed effects modelling approach

A nonlinear mixed modelling approach was applied to model individual tree diameter increment using three nonlinear growth functions for Eucalyptus tree plantations. The objective of the study is to develop a stem radial increment model for two clones of Eucalyptus tree, and compare their growth potential. Three nonlinear growth curves (Gompertz, logistic and asymptotic regression) were fitted to stem radius data. Estimations of parameters were made using the approximate likelihood functions. The estimators obtained from these approximate likelihood function are a combination of least squares estimators for nonlinear mixed effects models and maximum likelihood estimators from linear mixed effects models. The asymptotic regression model with three random effects appears well suited to represent the random effect covariance structure. The heterogeneous variance model that varies with tree age is found to be suitable model that characterize the within tree error variability. Clone has a significant effect on the asymptote of the asymptotic regression curve. The analysis suggests that GU clone on the average has a larger stem radial measurement than the GC clone during the entire juvenile stage

A nonparametric vertical model: An application to discrete time competing risks data with missing failure causes

Discrete time competing risks data continue to arise in social sciences, education etc., where time to failure is usually measured in discrete units. This data may also come with unknown failure causes for some subjects. This occurs against a background of very limited discrete time analysis methods that were developed to handle such data. A number of continuous time missing failure causes models have been proposed over the years. We select one of these continuous time models, the vertical model (Nicolaie et al., 2015), and present it as a nonparametric model that can be applied to discrete time competing risks data with missing failure causes. The proposed model is applied to real data and compared to the MI. It was found that the proposed model compared favorably with the MI method

A mixture model with application to discrete competing risks data

In this paper, we modify the continuous time mixture competing risks model (Larson and Dinse, 1985) to handle discrete competing risks data. The main result of the model is an alternate regression expression for the cumulative incidence function. The structure of the regression expression for the cumulative incidence function under this model, and the proportional hazards assumption for the conditional hazard rates with piece-wise constant baseline conditional hazards, combine to allow for another means to assess the covariate effects on the cumulative incidence function. This benefit comes at some computational costs because the parameters are estimated via an EM algorithm. The proposed model is applied to real data and it is found that it improves the exercise of evaluating the covariate effects on the cumulative incidence function compared to other discrete competing risks models

Modelling CD4 counts before and after HAART for HIV infected patients in KwaZulu-Natal South Africa

Background: This study aims to make use of a longitudinal data modelling approach to analyze data on the number of CD4+cell counts measured repeatedly in HIV-1 Subtype C infected women enrolled in the Acute Infection Study of the Centre for the AIDS Programme of Research in South Africa. Methodology: This study uses data from the CAPRISA 002 Acute Infection Study, which was conducted in South Africa. This cohort study observed N=235 incident HIV-1 positive women whose disease biomarkers were measured repeatedly at least four times on each participant. Results: From the findings of this study, post-HAART initiation, baseline viral load, and the prevalence of obese nutrition status were found to be major significant factors on the prognosis CD4+ count of HIV-infected patients. Conclusion: Effective HAART initiation immediately after HIV exposure is necessary to suppress the increase of viral loads to induce potential ART benefits that accrue over time. The data showed evidence of strong individual-specific effects on the evolution of CD4+ counts. Effective monitoring and modelling of disease biomarkers are essential to help inform methods that can be put in place to suppress viral loads for maximum ART benefits that can be accrued over time at an individual level