Multi-state models for the analysis of time-to-treatment modification among HIV patients under highly active antiretroviral therapy in Southwest Ethiopia

Background Highly active antiretroviral therapy (HAART) has shown a dramatic change in controlling the burden of HIV/AIDS. However, the new challenge of HAART is to allow long-term sustainability. Toxicities, comorbidity, pregnancy, and treatment failure, among others, would result in frequent initial HAART regimen change. The aim of this study was to evaluate the durability of first line antiretroviral therapy and to assess the causes of initial highly active antiretroviral therapeutic regimen changes among patients on HAART. Methods A Hospital based retrospective study was conducted from January 2007 to August 2013 at Jimma University Hospital, Southwest Ethiopia. Data on the prescribed ARV along with start date, switching date, and reason for change was collected. The primary outcome was defined as the time-to-treatment change. We adopted a multi-state survival modeling approach assuming each treatment regimen as state. We estimate the transition probability of patients to move from one regimen to another. Result A total of 1284 ART naive patients were included in the study. Almost half of the patients (41.2%) changed their treatment during follow up for various reasons; 442 (34.4%) changed once and 86 (6.69%) changed more than once. Toxicity was the most common reason for treatment changes accounting for 48.94% of the changes, followed by comorbidity (New TB) 14.31%. The HAART combinations that were robust to treatment changes were tenofovir (TDF) + lamivudine (3TC)+ efavirenz (EFV), tenofovir + lamivudine (3TC) + nevirapine (NVP) and zidovudine (AZT) + lamivudine (3TC) + nevirapine (NVP) with 3.6%, 4.5% and 11% treatment changes, respectively. Conclusion Moving away from drugs with poor safety profiles, such as stavudine(d4T), could reduce modification rates and this would improve regimen tolerability, while preserving future treatment options

Flexible modeling based on copulas in nonparametric median regression

Consider the model Y = m(X) + epsilon, where m(.) = med(Y|.) is unknown but smooth. It is often assumed that epsilon and X are independent. However, in practice this assumption is violated in many cases. In this paper we propose modeling the dependence between epsilon and X by means of a copula model, i.e.. (epsilon, X) similar to C-theta(F-epsilon(.), F-X(.)), where C-theta is a copula function depending on an unknown parameter theta, and F-epsilon and F-X are the marginals of epsilon and X. Since many parametric copula families contain the independent copula as a special case, the so-obtained regression model is more flexible than the 'classical' regression model. We estimate the parameter theta via a pseudo-likelihood method and prove the asymptotic normality of the estimator, based on delicate empirical process theory. We also study the estimation of the conditional distribution of Y given X. The procedure is illustrated by means of a simulation study, and the method is applied to data on food expenditures in households. (C) 2008 Elsevier Inc. All rights reserved

A conditional Koziol-Green model under dependent censoring

In this paper we extend the conditional Koziol-Green model of Veraverbeke, N. and Cadarso Suárez, C. [2000. Estimation of the conditional distribution in a conditional Koziol-Green model. Test 9, 97-122] to also accommodate dependent censoring and in this way introduce a model with two different types of informative censoring. We derive in this model a copula-graphic estimator for the conditional distribution of the lifetime and establish an exponential bound and an almost sure asymptotic representation which serve as starting points for an almost sure consistency and an asymptotic normality result. Afterwards we apply this estimator to a real data set about the survival of Atlantic halibut.

Flexible modeling based on copulas in nonparametric median regression

Consider the model Y = m(X ) + ε, where m(·) = med(Y|·) is unknown but smooth. It is often assumed that ε and X are independent. However, in practice this assumption is in many cases violated. In this paper we propose to model the dependence between ε and X by means of a copula model, i.e. (ε,X)∼Cθ(Fε (·), FX(·)), where Cθ is a copula function depending on an unknown parameter θ, and Fε and FX are the marginals of ε and X . Since many parametric copula families contain the independent copula as a special case, the so-obtained regression model is more flexible than the ‘classical’ regression model. We estimate the parameter θ via a pseudo-likelihood method and prove the asymptotic normality of the estimator, based on delicate empirical process theory. We also study the estimation of the conditional distribution of Y given X . The procedure is illustrated by means of a simulation study, and the method is applied to data on food expenditures in households

Investigating the correlation structure of quadrivariate udder infection times through hierarchical Archimedean copulas

The correlation structure imposed on multivariate time to event data is often of a simple nature, such as in the shared frailty model where pairwise correlations between event times in a cluster are all the same. In modeling the infection times of the four udder quarters clustered within the cow, more complex correlation structures are possibly required, and if so, such more complex correlation structures give more insight in the infection process. In this article, we will choose a marginal approach to study more complex correlation structures, therefore leaving themodeling ofmarginal distributions unaffected by the association parameters. The dependency of failure times will be induced through copula functions. The methods are shown for (mixtures of) the Clayton copula, but can be generalized to mixtures of Archimedean copulas for which the nesting conditions are met (McNeil in J Stat Comput Simul 6:567-581, 2008; Hofert in Comput Stat Data Anal 55:57-70, 2011)

A general frailty model to accommodate individual heterogeneity in the acquisition of multiple infections: An application to bivariate current status data

The analysis of multivariate time-to-event (TTE) data can become complicated due to the presence of clustering, leading to dependence between multiple event times. For a long time, (conditional) frailty models and (marginal) copula models have been used to analyze clustered TTE data. In this article, we propose a general frailty model employing a copula function between the frailty terms to construct flexible (bivariate) frailty distributions with the application to current status data. The model has the advantage to impose a less restrictive correlation structure among latent frailty variables as compared to traditional frailty models. Specifically, our model uses a copula function to join the marginal distributions of the frailty vector. In this article, we considered different copula functions, and we relied on marginal gamma distributions due to their mathematical convenience. Based on a simulation study, our novel model outperformed the commonly used additive correlated gamma frailty model, especially in the case of a negative association between the frailties. At the end of the article, the new methodology is illustrated on real-life data applications entailing bivariate serological survey data.status: publishe