Determining predictors of mortality in HIV positive people in South Africa, 2003 to 2009: a mixed methods approach incorporating unobserved variables

A thesis submitted to the School of Public Health, Faculty of Health Sciences, University of the Witwatersrand, in fulfilment of the requirements for the degree Of Doctor of Philosophy. 02 April 2018.Background The largest proportion of HIV-infected people resides in Southern Africa. In South Africa, the government has taken the lead in the provision of free HIV treatment with a high coverage rate. Provision of free antiretroviral treatment has led to a decline in mortality rates and an increase in life expectancy. However, a significant number of people with HIV continue to die despite the availability of free treatment. A large proportion of studies have concentrated on using quantitative methods of analysis. Very few have used mixed methods that combine quantitative time-to-event frailty models and qualitative methods in assessing risk factors for mortality in HIV-infected individuals. However, use of such mixed methods approach could provide insights that may lead to an improvement in patient care and management. Aim To determine mortality risk factors in HIV-infected people through incorporating unobserved variables using a mixed methods approach in which quantitative findings are explained by the qualitative. Methods To critically review statistical methods used for assessing risk factors for mortality in HIV-infected people between the years 2002 and 2011. We conducted a literature review on the design of studies, how data were analysed and whether suitable statistical methods were utilised in assessing mortality risk factors in HIV-infected people in the period 2002-2011. Only publications written in English and listed in Pubmed/Medline were considered. In this review, papers using time-to-event techniques were regarded as appropriate. Data were split into two equal periods allowing for the comparison of the statistical methods over time. To compare the different time-to-event methods, we ran 1,000 simulations of parametric clustered data using parameters derived from an HIV study that was conducted in South Africa by the Perinatal HIV Research Unit (PHRU). Data for 5, 10 and 20 clusters of size 50 and 100 were simulated. Survival and censoring times were derived from a Weibull distribution. The minimum of survival and censoring times was taken as the study time. Using the simulated data, we compared the following time-to-event methods: Cox proportional hazards regression, shared Gamma frailty with Weibull and exponential baseline hazards (frequentist models), and the Bayesian integrated nested Laplace approximation (INLA) with Weibull baseline hazard. Parameter estimates, standard errors and their fit statistics were averaged over 1,000 simulations. Similarly, means and standard deviations from INLA were averaged (over the 1,000 simulations). Frequentist models were compared using the -2 loglikelihood fit statistics while all the four models were compared using the mean square error (MSE). Additionally, we simulated semiparametric clustered frailty models (using gamma and log-normal frailties) including INLA, h-likelihood, penalized likelihood and penalised partial likelihood estimations. Parameter estimates and their standard errors were presented graphically and compared using the MSE. To assess mortality risk factors in HIV-infected people in South Africa in different settings, factors associated with mortality in HIV-infected people were assessed by INLA survival frailty model using cohort data of HIV-infected people from South Africa. Two thirds were from Soweto (urban) and the rest from Mpumalanga (rural). Findings were evaluated by site. Mixed methods were used to evaluate risk factors for mortality by combining the best fitting model applied to retrospective data and qualitative analysis on prospective data. In order to explain the unobserved frailty modelling results, we conducted a qualitative study that enrolled 20 participants who had confirmed knowing a person that had died as a result of HIV. Participants were recruited from the Zazi VCT in PHRU and were interviewed using a semi-structured interview guide. The aim of the qualitative study was to attempt to explain the unobserved factors influencing mortality in HIV-infected individuals using perceived reasons for death given by the participants. These were later used to complement the potential reasons for death as identified in the frailty modelling (quantitative) results. Results In the critical review, 189 studies met the inclusion criteria that included prospective (69%) and retrospective (30%) studies. Of the 189 studies, 91 were published in the period 2002-2006 and 98 in 2007-2011. Cox regression analysis with frailty was used in only 7 studies (~4%); of which 6 were published between the years 2007- 2011. The simulation study showed that the shared frailty models performed better than Cox-PH. Within the shared frailty models, the Gamma frailty model with a Weibull baseline performed better than the Gamma frailty model with an exponential baseline. The MSE showed that in general, the Bayesian INLA had better results. In the semiparametric simulations, results were similar but INLA had a slightly better fit with consistently lower MSE values relative to both gamma and log-normal frailty models. The random effects estimate for INLA, whose method is slightly different, had lower MSE values consistently relative to the other methods. In the HIV cohort study, 6,690 participants were enrolled with majority being female (78%) and most participants residing in an urban area (67%). Rural participants were older (36 years; IQR: 31-44) and with a higher mortality rate (11/100 person years). Among those residing in rural areas, HAART treatment for between six and twelve months (HR: 0.2, 95% CI: 0.1-0.4) and more than 12 months (HR: 0.1, 95% CI: 0.1- 0.2) was protective relative to not being on treatment. Being on HAART treatment for greater than twelve months was protective in the urban participants (HR: 0.35, 95%CI: 0.27-0.46). Significant heterogeneity, assessed by frailty variance, was high in rural participants and lower in the urban. Since the frailty modelling results suggested that the unobserved variables had a significant effect on mortality in HIV-infected individuals, a qualitative study was conducted to explore the potential causes of death. In the qualitative study, participants perceived that mortality in HIV-infected individuals may have been influenced by engagement in risky sexual behaviour such as multiple sexual partnerships, negative attitude by healthcare workers towards HIV-infected people, believing in the healing power of religion, traditional medicine, food security and social support structure. Conclusions The study found that Cox proportional hazards regression with frailty is not commonly used in research on mortality in HIV-infected individuals as it is used in other fields of health research. Additionally, use of the more complex semiparametric frailty models was even lower in this population. From simulations, we found that frailty survival models provided a better fit in modelling mortality due to their ability to account for unobserved variables especially the Bayesian INLA. As the unobserved variables are complex to explain using only quantitative modelling techniques, qualitative analysis of perceived causes of death was explored. Unobserved variables affecting mortality were explored through qualitative analysis of perceived reasons provided by bereaved participants. This mixed methods approach optimised data by using a quantitative approach followed by a qualitative one that complemented each other. Use of optimal methods in assessing morbidity and mortality in HIV-infected patients may improve patient care and management in South Africa and other countries. Key words: HIV, Mortality, Rural, Urban, unmeasured variables, HAART, FrailtyLG201

Random Effect Models in the Statistical Analysis of Human Fecundability Data: Application to artificial insemination with sperm from donor.

The main aim of this dissertation is to explore methodological approaches to correlated binary data and to assess their suitability for the analysis of data on human fertility. The dataset concerns a study of Artificial Insemination by Donor (AID). AID represents an unusual research opportunity to study both male and female fecundability simultaneously. In each attempt to conceive, artificial insemination is carried out in consecutive ovulatory cycles until conception or change of treatment. The probability of conception may differ between women, so that the data are discrete time survival data with censoring and between-subject heterogeneity. There is also potential heterogeneity between donors. Non-systematic allocation of the donor to recipient ensures that the same woman receives semen from several donors, This added heterogeneity as well as other cycle dependent covariates have to be taken into account. The analysis must also take account of covariates, most of them time-varying. Our dataset have a crossed hierarchical structure due to the presence of both, female and male factors. The rather complicated "design" calls for unit specific regression models. These models are presented as well as their lack of tractability except in some rather specific cases. The motivation for choosing Gaussian random effects in unit specific regression models is discussed. We demonstrate the use of an approximate inference method (Penalized Quasi Likelihood). This method is shown to be a useful and practical way of carrying out preliminary data analysis. Finally a Bayesian procedure (Gibbs sampling) provides validation and more accurate results despite the intensive computation it needs. The main substantive finding of the analysis is the unexpectedly pronounced heterogeneity of donor fecundability, even after inclusion of conventional measures of sperm quality into the model. These measures were shown to be predictive at the donor level but not at the level of individual donation

Data Study Group Final Report: Roche

Data Study Groups are week-long events at The Alan Turing Institute bringing together some of the country’s top talent from data science, artificial intelligence, and wider fields, to analyse real-world data science challenges. Roche: Personalised lung cancer treatment modelling using electronic health records and genomics Cancer immunotherapy (CIT) is a promising new type of cancer treatment that uses the patient’s own immune system to fight cancer cells. CIT drugs work to stop the cancer cells from turning off the immune system’s T-cells by inhibiting the PD-L1 produced by the tumour cells (PD-L1 is a protein that binds to PD-1 receptors on T-cells and prevents the immune system from attacking the cancer cells). CIT is currently being used to treat patients with non-small cell lung cancer (NSCLC) for whom chemotherapy or other drugs have failed. CIT is also be-ing used as part of the first-line treatment in patients with advanced NSCLC (aNSCLC - stage III and higher). Theoretically, patients with high PD-L1 ex-pression levels are more likely to respond well to CIT; however, in practice, patient outcomes vary considerably. In this data study group, we investigated different approaches for predicting survival time for patients treated with CIT as first line of treatment, using both electronic health records and tumour genomic data. We also investigated the causal effects of CIT vs other oncology treatments, and studied treatment heterogeneity. The results contribute to identifying patients who are most likely to benefit from CIT

Testing the Correlation for Clustered Categorical and Censored Discrete Time‐to‐Event Data When Covariates Are Measured without/with Errors

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/92373/1/1541-0420.00004.pd

Modeling Consideration Sets and Brand Choice Using Artificial Neural Networks

The concept of consideration sets makes brand choice a two-step process. House-holds first construct a consideration set which not necessarily includes all available brands and conditional on this set they make a final choice. In this paper we put forward a parametric econometric model for this two-step process, where we take into account that consideration sets usually are not observed. It turns out that our model is an artificial neural network, where the consideration set corresponds with the hidden layer. We discuss representation, parameter estimation and inference.We illustrate our model for the choice between six detergent brands and show that the model improves upon a one-step multinomial logit model, in terms of fit and out-of-sample forecasting.brand choice;consideration set;artificial neural network

Divergent Effects of Factors on Crash Severity under Autonomous and Conventional Driving Modes Using a Hierarchical Bayesian Approach

Influencing factors on crash severity involved with autonomous vehicles (AVs) have been paid increasing attention. However, there is a lack of comparative analyses of those factors between AVs and human-driven vehicles. To fill this research gap, the study aims to explore the divergent effects of factors on crash severity under autonomous and conventional (i.e., human-driven) driving modes. This study obtained 180 publicly available autonomous vehicle crash data, and 39 explanatory variables were extracted from three categories, including environment, roads, and vehicles. Then, a hierarchical Bayesian approach was applied to analyze the impacting factors on crash severity (i.e., injury or no injury) under both driving modes with considering unobserved heterogeneities. The results showed that some influencing factors affected both driving modes, but their degrees were different. For example, daily visitors\u27 flowrate had a greater impact on the crash severity under the conventional driving mode. More influencing factors only had significant impacts on one of the driving modes. For example, in the autonomous driving mode, mixed land use increased the severity of crashes, while daytime had the opposite effects. This study could contribute to specifying more appropriate policies to reduce the crash severity of both autonomous and human-driven vehicles especially in mixed traffic conditions

A review of R-packages for random-intercept probit regression in small clusters

Generalized Linear Mixed Models (GLMMs) are widely used to model clustered categorical outcomes. To tackle the intractable integration over the random effects distributions, several approximation approaches have been developed for likelihood-based inference. As these seldom yield satisfactory results when analyzing binary outcomes from small clusters, estimation within the Structural Equation Modeling (SEM) framework is proposed as an alternative. We compare the performance of R-packages for random-intercept probit regression relying on: the Laplace approximation, adaptive Gaussian quadrature (AGQ), Penalized Quasi-Likelihood (PQL), an MCMC-implementation, and integrated nested Laplace approximation within the GLMM-framework, and a robust diagonally weighted least squares estimation within the SEM-framework. In terms of bias for the fixed and random effect estimators, SEM usually performs best for cluster size two, while AGQ prevails in terms of precision (mainly because of SEM's robust standard errors). As the cluster size increases, however, AGQ becomes the best choice for both bias and precision