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Browsing Statistics by Author "Batidzirai, Jesca Mercy."

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    Discrete time-to-event construction for multiple recurrent state transitions.
    (2023) Batidzirai, Jesca Mercy.; Manda, Samuel.; Mwambi, Henry Godwell.
    Recent developments in multi-state models have considered discrete time rather than continuous time in the modeling of transition intensities, whose major drawback lies in the possibility of resulting in biased parameter estimates that arise from issues of handling ties. Discrete-time models have included univariate multilevel models to account for possible dependence among specific pairwise recurrent transitions within the same subject. However, in most cases, there would be several specific pairwise transitions of interest. In such cases, there is a need to model the transitions with the aim of identifying those transitions that are correlated. This provides insight into how the transitions are related to each other. In order to investigate the interdependencies between transitions, the unique contribution of this thesis is to propose a multivariate discrete-time multi-state model with multiple state transitions. In this model, each specific recurrent transition is associated with a random effect to capture possible dependence in the transitions of the same type or different types. The random effects themselves were then modeled by a multivariate normal distribution and model parameters were estimated using maximum likelihood methods with Gaussian quadratures numerical integration. A simulation study was done to evaluate the performance of the proposed model. The model yielded satisfactory results for most fixed effects and random effects estimates. This is noticed by near-zero biases and mean square errors of the average estimates as well as high 95% coverage probabilities of the 95% confidence intervals from 1000 replications. The proposed methodology was applied to marriage formation and dissolution data from KwaZulu-Natal province, South Africa. Five transitions were considered, namely: Never Married to Married, Married to Separated, Married to Widowed, Separated to Married and Widowed to Married. The presence of very small unobserved subject-to subject heterogeneity for each transition and a weak positive correlation between transitions were produced. Statistically, the model produced smaller standard errors compared to those from univariate models, hence it is more precise on estimates. The multivariate modeling of discrete time-to-event models provides a better understanding of the evolution of all transitions simultaneously, thus in addition to covariate effects, giving an assessment of how one transition is associated with the other. Empirical results confirmed well known important socio-demographic predictors of entering and exiting a marriage. Age at sexual debut played a positive critical role in most of the transitions. More educated subjects were associated with a lower likelihood of entering a first marriage, experiencing a marital dissolution as well as remarrying after widowhood. Subjects who had a sexual debut at younger ages were more likely to experience a marital dissolution than those who started late. Age at first marriage had a negative association with marital dissolution. We may, therefore, postulate that existing programs that encourage delay in onset of sexual activity for HIV risk reduction for example, may also have a positive impact on lowering rates of marital dissolution, thus ultimately improving psychological and physical health.
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    Meta-analysis of time to seizure relapse after a post-operative epilepsy surgery.
    (2020) Memela, Smilo Patrick.; Batidzirai, Jesca Mercy.; Mwambi, Henry Godwell.
    Epilepsy is a common disease world-wide whose suggested treatment vary from surgical to non-surgical. Although surgical treatments may be commonly recommended and successful in pharmacoresistant epilepsy for patients with refractory epilepsy, there are some patients who experience a seizure relapse. It is of interest to medical practitioners to determine how long patients survive epilepsy after a successful surgery. Survival analysis methods have been used to model time-to-event data. Hence we attempt to determine the time to a seizure relapse in epilepsy patients after a surgery. However, single study have some limitations, such as lack of accommodation of spatial factors, different research approaches to mention a few. Most of the time, single studies are under-powered to detect the factors of covariates. Meta-analysis methods have been developed to overcome this problem, where a number of studies are amalgamated and a common conclusion is drawn. This thesis aims is to determine the long-term seizure outcome after an epilepsy surgery of refractory epilepsy without focusing on the types of refractory but rather in resective surgery. In the current study a systematic review was done using Google Scholar, Medline, and PubMed. The event of interest is seizure relapse and our interest is to pool the time to first seizure relapse after surgical treatment. To measure the seizure freedom the clinical method call Engel class I was used. The univariate and metasurvival of fixed and random effect model were used to measure the proportion of seizure freedom. Our focus was only in single arm treatment (surgical treatment) . There were a total of 18 studies that satisfy the inclusion criteria with observations at 6 time points measured in months after post-operative (6, 12, 24, 36, 60 and 120 months). In the univariate analysis, the probabilities of seizure freedom of the fixed effects models were systematically larger than the random effect results. There was evidence of significance of heterogeneity between studies, and the true variation between studies test was large. The result that we got in univariate random effect model were for time-points 6, 12, 24, 36, 60 and 120 months were 0.74 95% confidence interval (CI)(0.66- 0.82), 0.69 95% CI (0.61- 0.77), 0.64 95% CI (0.56- 0.71), 0.60 95% CI (0.52- 0.68), 0.56 95% CI (0.48- 0.63) and 0.47 95% CI (0.38- 0.56) respectively. The meta-survival analysis also systematically showed that, the seizure free probability were larger in a fixed effects model than in a random effects model. The summary survival estimates of the random effect model that were pooled in the following time points 6, 12, 24, 36, 60 and 120 were 0.7655 95% CI (0.6808- 0.8613), 0.7140 95% CI (0.6246- 0.8163), 0.6462 95% (0.5614, 0.7438), 0.6105 95% (0.5225, 0.7133), 0.5700 95% (0.4892, 0.6641) and 0.4755 (0.4078, 0.5545) respectively. The median time to relapse was found using the meta-survival analysis in random effects model to be 104.46 months (8.87 years). We can conclude that the meta-survival analysis may be the method to pool the time-to-event data in one-arm treatment..