Statistical Modeling of Acute HIV Infection from a Cohort of High-risk Individuals in South Africa = Ukufakwa kwamamodeli Ezibalomininingo Ekuthelelekeni Kwesikhashana nge-HIV Eqoqweni labantu Abasengcupheni Enkulu eNingizimu Afrika.

Abstract

In this dissertation, longitudinal data modeling approaches to analyze data on CD4 cell counts measured repeatedly in HIV-infected patients enrolled in the Centre for the AIDS Programme of Research in South Africa are investigated. Longitudinal data, or repeated measurement data, is a specific form of multilevel data. In longitudinal studies, repeated observations are made on an individual on one or more outcomes, including covariates information at a baseline and over time. Mixedeffects models have become popular for modeling longitudinal data. This statistical procedure also permits the estimation of variability in hierarchically structured data and examines the impacts of factors at different levels. Since longitudinal studies are often faced with the incompleteness of the data due to partially observed subjects, the mixed-effects model is by its very nature able to deal with unbalanced data of this nature. Therefore, the study adopts the mixed-effects model and identifies whether specific clinical and sociodemographic factors present in the data influenced CD4 count in a cohort of HIV-infected patients. Since it is of great interest for a biomedical analyst or an investigator to correctly model the CD4 cell count or disease biomarkers of a patient in the presence of covariates or factors determining the disease progression over time, the Poisson regression approach, which explain variability in counts, is considered. The Poisson generalized mixed-effects models can be an appropriate choice for repeated count data. However, this model is not realistic because of the restriction that the mean and variance are equal. Therefore, the Poisson mixed-effects model is replaced by the negative binomial mixed-effects model. The later model effectively managed over-dispersion of the longitudinal data. We evaluate and compare the proposed models and their application to model CD4 cell counts of HIV-infected patients recruited in the study data set. The results reveal that the negative binomial mixedeffects model has appropriate properties and outperforms the Poisson mixed-effects model in terms of handling the over-dispersion of the data. Multiple imputation techniques are also used to handle missing values in the dataset to validate parameter estimates in modeling the negative binomial mixed-effects model by assuming a missing at random missingness.

To illustrate the full conditional distribution of the repeated outcome, a quantile mixed-effects model is employed. This gives greater inclusive statistical modeling than conventional ordinary mixed models. Quantile regression offers an invaluable tool to discern effects that would be missed by other conventional regression models, which are solely based on modeling conditional mean. The quantile regression model that assumes asymmetric Laplace distribution for the error term was applied to longitudinal CD4 count data. The exact maximum likelihood estimation of the covariate effects and variance-covariance elements in the quantile mixed-effects model was implemented using the Stochastic Approximation Expectation-Maximization algorithm. In the model, multiple random effects are also incorporated to consider the correlation among the observations. Thus, we obtain robust parameter estimates for various conditional distribution positions that communicate an inclusive and more complete picture of the effects. Furthermore, to get more insights into the functional relationship between the response variable and the covariates, the generalized additive mixed-effects models, such as the additive negative binomial mixed-effects model, a versatile model used to better understand and analyze complex nonlinear trajectories in an overdispersed longitudinal data, is applied. Following the additive negative binomial mixed-effects model, an attempt to fit additive quantile mixed-effects model, an efficient and flexible framework for nonparametric as well as parametric longitudinal forms of data analysis focused on features of the outcome beyond its central tendency, was made. The response variable at hand is a CD4 count of HIV-infected patients as a function of Highly Active Antiretroviral Therapy initiation and other relevant baseline characteristics of the patients. Thus, even though this is a biostatistics methodological dissertation research, some interesting clinical and sociodemographic findings are also discussed. Discussion and conclusion of the results from the proposed models with a suggestion of possible further research avenues completed the study.

Iqoqa Kule dizetheshini izindlelasu zokulinganisela imininingo eziyilongitudinal modeling approaches ukuhlaziya imininingo yezibalo zamasosha e-CD4 count ezikalwa ngokuphindaphindeka ezigulini ezitheleleke nge-HIV ezibhalise eSikhungweni soHlelo Lokucwaninga nge-AIDS eNingizimu Afrika kuyaphenywa. Imininingo enqumile, noma imininingo ekalwa ngokuphindelela, iwuhlobo oluqondile lwemininingo emazingeni ahlukene. Ocwaningweni olunqumile, ukubheka okuphindwayo kwenziwa kumuntu oyedwa emphumeleni owodwa noma engaphezulu, okufaka ulwazi lwamakhovariyenti njengesisekelo nangokuhamba kwesikhathi. Amamodeli anemithelela exubile aseyathandeka ekuhambiselaneni nemininingo yemodeli enqumile. Inqubo yezibalomininingo iphinde ivumele ukuqagula ukuguquguquka emininingweni enomumo onokugibelana iphinde ihlole imithelela yezimo emazingeni ehlukene. Njengoba ucwaningo olunqumile luvame ukubhekana nokungaphothulwa kwemininingo ngenxa yabantu ababhekwe ingxenye, imodeli enomthelelangxube ngokomumo wayo iyakwazi ukubhekana nemininingo engabhalansile eyilolu hlobo bese luhlonza izimo zokokusebenza kwengqondo nomumoqoqobantu emphakathini emininingweni ethinta i-CD4 count eqoqweni leziguli ezitheleleke nge-HIV. Njengoba kunentshisekelo enkulu ukuba umhlaziyi wezempilokwelapha noma umphenyi enze imodeli ngendlela ukubalwa kwamasosha i-CD4 count noma amabhayomakha esifo esigulini ebukhoneni bamakhovariyenti noma izimo ezihlonza ukuqhubeka kwesifo ngokuhamba kwesikhathi, indlelasu yokunqandeka kwesifo ngokukaPoisson, okuchaza ukuguquguquka ngokubalwa, kuyabhekwa. Amamodeli kaPoisson abekwe eceleni anemithelela exubile angaba wukukhetha okuyikho kwemininingo yokubala kokuphindelela. Kodwa, le modeli ayivezi okuyikho ngenxa yokuvimbeleka ukuthi imini nevariyenti kuyalingana. Ngakho-ke, imodeli kaPoisson enemithelelangxube imelwe yimodeli enemithelelangxube yebhayinomiyali engeyinhle. Imodeli yakamuva ilawula ngempumelelo yokusabalalisa kakhulu imininingo enqumile. Sihlaziya siphinde siqhathanise namamodeli aphakanyisiwe nokusetshenziswa kwayo ekubaleni amasosha omzimba i-CD4 cell count yeziguli ezitheleleke nge-HIV abafakwe ekubambeni iqhaza emininingweni yocwaningo. Imiphumela iveza ukuthi imodeli yemithelelangxube yebhayinomiyali engeyinhle enezakhiwomumo eyiwo nesebenza yedlule ekaPoisson nemodeli enomthelelangxube ngokwemigomo yokubheka ukusabalalisa ngokweqile imininingo. Amasu amaningi emvezabubi asetshenziselwa ukubhekana nezimo ezingabonakali kwisethi yemininingo ehlaziya iziqagulo zamapharamitha ekufakweni kwemodeli enemithelelangxube yebhayinomiyali ngokuthatha ngokuthi kunokungatholakali okungahleliwe. Ukukhombisa ukusabalalisa okugcwele okunemibandela komphumela ophindaphindekile, imodeli enemithelelangxube iyasetshenziswa. Lokhu kuveza ukufaka imodeli yezibalomininingo ezifaka konke okunamamodeli ajwayelekile ayingxube. Ukuncipha kwekhwantayli kunika ithuluzi elingenamsebenzi ukuhlonza imithelela ebingetholwe amamodeli ejwayelekile okuncipha, agxile kuphela kwimini encike ekufakweni kwemodeli. Imodeli yokuncipha kwekhwantayli evuma ukusabalalisa i-Laplace etshekile yetemu elingene ngephutha kwasetshenziswa emininingweni yokubala i-CD4. Ukuqagula okuyikho okuphezulu kwemithelela yamakhovariyenti nezakhi zekhovariyensi-variyensi kwimodeli enemithelelangxube yekhwantayli eyaqaliswa ukusebenza kusetshenziswa i-algorithimu i- Stochastic Approximation Expectation-Maximization. Kwimodeli, imithelela engahlelekile emininingo iphinde yafakwa ukuze kubhekwane nokuxhumana kokuqashelwayo. Ngakho-ke, sithola ukuqagula amapharamitha okunzulu ngemumo yokusabalalisa okunemigomo eyehlukahlukene okunika isithombe esifaka konke nesiphelele semithelela. Ngaphezu kwalokho, ukuthola imibono eyongeziwe ngobudlelwane obusebenzayo phakathi kwevariyebhuli yempendulo namakhovariyethi, amamodeli anemithelelangxube eyongezwayo, njengemodeli yemithelela exubile engemihle yebhayinomiyali eyongezwayo, imodeli enguqunguqu isetshenziselwe ukuqonda kangcono ngemodeli yokuhlaziya izinkombakusasa ezingenamigoqo ezinkimbi emininingweni engumumokuqonda ohlakazwe kakhulu, iyasetshenziswa. Uma kulandelwa imodeli enemithelelangxube yebhayinomiyali engeyinhle eyongezwayo, ukuze kuhambelane nomzamo wokufaka imodeli enemithelelangxube ayikhwayintali eyongezwayo, uhlaka oluguqulekayo nolusebenza ngendlela yezindlela ezingahambelani nepharamethrikhi kanjalo nepharamethrikhi engumumokuqonda wokuhlaziya imininingo okugxile ezicini zomphumela owedlula injwayelosenzo ewumongo, nakho kwenziwa. Ivariyebhuli yempendulo esebenzayo yisibalo samasosha omzimba i-CD4 ezigulini ezitheleleke nge-HIV njengomzamokuziqamba Wengxubekwelapha Ethithibalisa igciwane leSandulela Ngculazi Esebenza Kakhulu kanye nezinye izici eziyisisekelo eziyiso zeziguli. Ngakho-ke nakuba lena kuyidizetheshini yocwaningo lwendlelakwenza yocwaningo kwezibalomininingokuphila, kuphinde kwadingidwa okutholakele kwezempilongqondo nakwisifundomumoqoqobantu emphakathini. Ukudingida nokuphothulwe yimiphumela yamamodeli aphakanyisiwe ngesiphakamiso sezindlela zokukwenza ucwaningo oluqhubekayo ukuphothula ucwaningo.