Pairwise fitting of piecewise mixed models for the joint modeling of multivariate longitudinal outcomes, in a randomized crossover trial.

Many statistical models have been proposed in the literature for the analysis of longitudinal data. One may propose to model two or more correlated longitudinal processes simultaneously, with a goal of understanding their association over time. Joint modeling is then required to carefully study the association structure among the outcomes as well as drawing joint inferences about the different outcomes. In this study, we sought to model the associations among six nutrition outcomes while circumventing the computational challenge posed by their clustered and high-dimensional nature. We analyzed data from a 2 × $\times$ 2 randomized crossover trial conducted in Kenya, to compare the effect of high-dose and low-dose iodine in household salt on systolic blood pressure (SBP) and diastolic blood pressure (DBP) in women of reproductive age and their household matching pair of school-aged children. Two additional outcomes, namely, urinary iodine concentration (UIC) in women and children were measured repeatedly to monitor the amount of iodine excreted through urine. We extended the model proposed by Mwangi et al. (2021, Communications in Statistics: Case Studies, Data Analysis and Applications, 7(3), 413-431) allowing flexible piecewise joint models for six outcomes to depend on separate random effects, which are themselves correlated. This entailed fitting 15 bivariate general linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We analyzed the outcomes separately and jointly using piecewise linear mixed-effects (PLME) model and further validated the results using current state-of-the-art Jones and Kenward methodology (JKME model) used for analyzing randomized crossover trials. The results indicate that high-dose iodine in salt significantly reduced blood pressure (BP) compared to low-dose iodine in salt. Estimates for the random effects and residual error components showed that SBP and DBP had strong positive correlation, with effect of the random slope indicating that significantly related outcomes are strongly associated in their evolution. There was a moderately strong inverse relationship between evolutions of UIC and BP both in women and children. These findings confirmed the original hypothesis that high-dose iodine salt has significant lowering effect on BP. We further sought to evaluate the performance of our proposed PLME model against the widely used JKME model, within the multivariate joint modeling framework through a simulation study mimicking a 2 × 2 $2\times 2$ crossover design. From our findings, the multivariate joint PLME model performed exceptionally well both in estimation of random-effects matrix (G) and Hessian matrix (H), allowing satisfactory model convergence during estimation. It allowed a more complex fit to the data with both random intercepts and slopes effects compared to the multivariate joint JKME model that allowed for random intercepts only. When a hierarchical viewpoint is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive definite. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters. The key highlight in this evaluation shows that multivariate joint JKME model is a powerful tool especially while fitting mixed models with random intercepts only, in crossover design settings. Addition of random slopes may lead to model complexities in most cases, resulting in unsatisfactory model convergence during estimation. To circumvent convergence pitfalls, extention of JKME model to PLME model allows a more flexible fit to the data (generated from crossover design settings), especially in the multivariate joint modeling framework.

Modelling trends of CD4 counts for patients on antiretroviral therapy (ART): a comprehensive health care clinic in Nairobi, Kenya.

BACKGROUND: In resource-limited settings, changes in CD4 counts constitute an important component in patient monitoring and evaluation of treatment response as these patients do not have access to routine viral load testing. In this study, we quantified trends on CD4 counts in patients on highly active antiretroviral therapy (HAART) in a comprehensive health care clinic in Kenya between 2011 and 2017. We evaluated the rate of change in CD4 cell count in response to antiretroviral treatment. We further assessed factors that influenced time to treatment change focusing on baseline characteristics of the patients and different initial drug regimens used. This was a retrospective study involving 432 naïve HIV patients that had at least two CD4 count measurements for the period. The relationship between CD4 cell count and time was modeled using a semi parametric mixed effects model while the Cox proportional hazards model was used to assess factors associated with the first regimen change. RESULTS: Majority of the patients were females and the average CD4 count at start of treatment was 362.1 [Formula: see text]. The CD4 count measurements increased nonlinearly over time and these trends were similar regardless of the treatment regimen administered to the patients. The change of logarithm CD4 cell count rises fast for in the first 450 days of antiretroviral initiation. The average time to first regimen change was 2142 days. Tenoforvir (TDF) based regimens had a lower drug substitution(aHR 0.2682, 95% CI:0.08263- 0.8706) compared to Zidovudine(AZT). CONCLUSION: The backbone used was found to be associated with regimen changes among the patients with fewer switches being observed, with the use of TDF when compared to AZT. There was however no significant difference between TDF and AZT in terms of the rate of change in logarithm CD4 count over time.

Factor copula models for right-censored clustered survival data.

In this article we extend the factor copula model to deal with right-censored event time data grouped in clusters. The new methodology allows for clusters to have variable sizes ranging from small to large and intracluster dependence to be flexibly modeled by any parametric family of bivariate copulas, thus encompassing a wide range of dependence structures. Incorporation of covariates (possibly time dependent) in the margins is also supported. Three estimation procedures are proposed: both one- and two-stage parametric and a two-stage semiparametric method where marginal survival functions are estimated by using a Cox proportional hazards model. We prove that the estimators are consistent and asymptotically normally distributed, and assess their finite sample behavior with simulation studies. Furthermore, we illustrate the proposed methods on a data set containing the time to first insemination after calving in dairy cattle clustered in herds of different sizes.

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.

Shelf-life dating of shelf-stable strawberry juice based on survival analysis of consumer acceptance information.

BACKGROUND: Accurate shelf-life dating of food products is crucial for consumers and industries. Therefore, in this study we applied a science-based approach for shelf-life assessment, including accelerated shelf-life testing (ASLT), acceptability testing and the screening of analytical attributes for fast shelf-life predictions. Shelf-stable strawberry juice was selected as a case study. RESULTS: Ambient storage (20 °C) had no effect on the aroma-based acceptance of strawberry juice. The colour-based acceptability decreased during storage under ambient and accelerated (28-42 °C) conditions. The application of survival analysis showed that the colour-based shelf-life was reached in the early stages of storage (≤11 weeks) and that the shelf-life was shortened at higher temperatures. None of the selected attributes (a* and ΔE* value, anthocyanin and ascorbic acid content) is an ideal analytical marker for shelf-life predictions in the investigated temperature range (20-42 °C). Nevertheless, an overall analytical cut-off value over the whole temperature range can be selected. CONCLUSIONS: Colour changes of strawberry juice during storage are shelf-life limiting. Combining ASLT with acceptability testing allowed to gain faster insight into the change in colour-based acceptability and to perform shelf-life predictions relying on scientific data. An analytical marker is a convenient tool for shelf-life predictions in the context of ASLT. © 2017 Society of Chemical Industry.

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 the modeling of marginal 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).

Efficacy of a hydroactive colloid gel versus historical controls for the prevention of radiotherapy-induced moist desquamation in breast cancer patients.

PURPOSE: Radiotherapy-induced moist desquamation (RIMD) is a complication that can affect patients' quality of life and jeopardize radiotherapy outcomes. The curative use of a hydroactive colloid gel has previously been shown effective in the management of RIMD in breast cancer patients. This study aimed at investigating the efficacy of this same gel but in the prevention of RIMD. METHODS: A group of breast cancer patients who applied the hydroactive gel from start to end of post-lumpectomy radiotherapy (Preventive Hydrogel group) were compared with two groups of matched historical controls: a group applying a dexpanthenol cream throughout their therapy and a group applying first the dexpanthenol cream then, after 11-14 fractions of radiotherapy, the hydroactive gel (Curative Hydrogel group). All patients received identical fractionation regimen. The clinical outcomes were the incidence and time to onset of RIMD. KEY RESULTS: After 25 fractions of radiotherapy (50 Gy), patients in the Preventive Hydrogel group (N = 202) developed RIMD significantly less frequently and later than patients in the Dexpanthenol group (N = 131; incidence = 7% vs 35% respectively, odds ratios = 7.27; probability of RIMD-free survival after 50 Gy = 0.88 vs 0.62). There were no significant differences between the Preventive and the Curative Hydrogel group (N = 87). CONCLUSIONS: These findings confirm our previous results: applying the hydroactive colloid gel, rather than dexpanthenol, delayed the onset and reduced the incidence of RIMD in breast cancer patients. However, applying the hydrogel preventively offered no statistically significant advantages over applying it curatively.

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.

Modeling Outcomes of First-Line Antiretroviral Therapy and Rate of CD4 Counts Change among a Cohort of HIV/AIDS Patients in Ethiopia: A Retrospective Cohort Study.

BACKGROUND: Antiretroviral therapy has shown to be effective in reducing morbidity and mortality in patients infected with HIV for the past couples of decades. However, there remains a need to better understand the characteristics of long-term treatment outcomes in resource poor settings. The main aim of this study was to determine and compare the long-term response of patients on nevirapine and efavirenz based first line antiretroviral therapy regimen in Ethiopia. METHODS: Hospital based retrospective cohort study was conducted from January 2009 to December 2013 at University hospital located in Northwest Ethiopia. Human subject research approval for this study was received from University of Gondar Research Ethics Committee and the medical director of the hospital. Cox-proportional hazards model was used to assess the effect of baseline covariates on composite outcome and a semi-parametric mixed effect model was used to investigate CD4 counts response to treatments. RESULTS: A total of 2386 HIV/AIDS naive patients were included in this study. Nearly one-in-four patients experienced the events, of which death, lost to follow up, treatment substitution and discontinuation of Non-Nucleoside Reverse Transcriptase Inhibitors(NNRTI) accounted: 99 (26.8%), 122 (33.0%), 137 (37.0%) and 12 (3.2%), respectively. The hazard of composite outcome on nevirapine compared with efavirenz was 1.02(95%CI: 0.52-1.99) with p-value = 0.96. Similarly, the hazard of composite outcome on tenofovir and stavudine compared with zidovudine were 1.87 (95%CI: 1.52-2.32), p-value < 0.0001 and 1.72(95% CI: 1.22-2.32), p-value = 0.002, respectively. The rate of CD4 increase in response to treatment was high during the first 10 months and stabilized later. CONCLUSIONS: This study revealed that treatment responses were comparable whether nevirapine or efavirenz was chosen to initiate antiretroviral therapy for HIV/AIDS patients in Ethiopia. There was significant difference on risk of composite outcome between patients who were initiated with Tenofovir containing ART regimen compared with zidovudine after controlling for NNRTI drug combinations.

A combined gamma frailty and normal random-effects model for repeated, overdispersed time-to-event data.

This paper presents, extends, and studies a model for repeated, overdispersed time-to-event outcomes, subject to censoring. Building upon work by Molenberghs, Verbeke, and Demétrio (2007) and Molenberghs et al. (2010), gamma and normal random effects are included in a Weibull model, to account for overdispersion and between-subject effects, respectively. Unlike these authors, censoring is allowed for, and two estimation methods are presented. The partial marginalization approach to full maximum likelihood of Molenberghs et al. (2010) is contrasted with pseudo-likelihood estimation. A limited simulation study is conducted to examine the relative merits of these estimation methods. The modeling framework is employed to analyze data on recurrent asthma attacks in children on the one hand and on survival in cancer patients on the other.

Retrospective study of radiotherapy-induced skin reactions in breast cancer patients: reduced incidence of moist desquamation with a hydroactive colloid gel versus dexpanthenol.

PURPOSE: Dermatitis is a very frequent and distressing side effect of radiation therapy that may necessitate a treatment interruption when evolving towards more severe forms such as moist desquamation (MD). The aim of this study was to compare the efficacy of two topical agents, a dexpanthenol cream vs a hydroactive colloid gel combining absorbing and moisturising properties, in preventing MD in breast cancer patients. METHODS: This retrospective study compared two successive groups of breast cancer patients undergoing radiotherapy after breast-sparing surgery between 2008 and 2012. A group of 267 patients applied a 5% dexpanthenol cream on the irradiated zone throughout the course of their radiotherapy. Another group of 216 patients applied first the dexpanthenol cream then replaced it by the hydroactive colloid gel after 11-14 days of radiotherapy. Radiation treatment (total dose, technique, and equipment) was the same for the two groups. The clinical outcomes were the occurrence and time to onset of moist desquamation. KEY RESULTS: The overall incidence of MD was significantly lower in patients who applied the hydroactive colloid gel (16%) than in those who applied the dexpanthenol cream (32%, odds-ratio = 0.35). Also, MD occurred significantly later with the hydroactive colloid gel than with the dexpanthenol cream (hazard ratio = 0.39). CONCLUSIONS: Compared with the dexpanthenol cream, the hydroactive colloid gel significantly reduced the risk of developing MD in patients undergoing radiotherapy for breast cancer. These promising results warrant further research on the efficacy of hydroactive colloid gels in managing radiation dermatitis.