MODELING SURGICAL OUTCOMES OF VESICO-VAGINAL FISTULA PATIENTS USING BETA-BINOMIAL DISTRIBUTION WITHIN THE GAMLSS FRAMEWORK

CHAPTER ONE

INTRODUCTION

1.0 Background of the Study

A vaginal fistula is a condition characterized by an abnormal hole connecting the vagina to the urinary bladder or the rectum. This often results in the continuous leakage of urine or feaces. The connection between the vagina and the urinary bladder is referred to as vesicovaginal fistula while that between the vagina and the rectum is referred to as rectovaginal fistula. It is a chronic debilitating condition with serious medical and social complications and consequences (Maheu-Giroux et al., 2015).The diagnosis of fistula is done by a clinical evaluation and diagnostic tests (Morhason-Bello et al., 2020). The prominent and most distressing symptoms are continuous urinary incontinence and leakage of the urine from the vagina and recurrent urinary tract infection (Ijaiya et al., 2011). A thorough medical interview and examination are essential to elucidate the history of obstetric trauma or pelvic surgery. The diagnostic tests include a cystoscopy, cystography, and vaginoscopy. These tests help to grant a direct visualization of the fistulous tract and the communication between the bladder and the vagina(El-Azab et al., 2019)

Obstetric fistula is preventable, for instance, if all women who experience protracted obstructed labour have early access to surgical interventions to alleviate the obstruction and deliver the baby. Obstetric fistula has been virtually eliminated in affluent countries with highly functional and effective maternal healthcare facilities. In developing countries, however, this is still a problem that must be addressed(FMOH, 2023).

Effective surgical repair procedures exist, but complete recovery and reintegration are challenging, with variations in individual experiences (Ijaiya et al., 2011). Factors like pre-existing conditions, surgery type, post-operative care,age, weight, height, and parity significantly influence healing time and outcomes(Ngoma & Author, 2010). These factors do not exist in isolation but interact with each other in a non-linear fashion to determine the recovery period of individual patients(Derso et al., 2020).

Understanding the complex interplay of factors affecting fistula patient recovery is crucial for better treatment strategies and optimized care. Statistical analysis using different models have been used to elucidate the role of the different factors in the outcome of fistula surgeries and enable healthcare providers to deliver effective treatment and make useful predictions(Derso et al., 2020). However, single-distribution statistical models often fall short, leading to inaccurate predictions and suboptimal interventions(Goffard et al., 2022).A compound distribution is a probability distribution resulting from a two-step procedure. In this process, the outcome of one random variable influences the distribution of another. The final distribution combines the distributionsof the two steps(Baayen & Linke, 2020).

Compound distributions are widely used in a variety of domains, including statistics, probability theory, and actuarial science. They occur when one random variable influences the distribution of another, as in insurance risk modeling, reliability analysis, and queueing theory.

Modeling factors or variables with a compound distribution entail incorporating the compound character of the data generation process into the statistical models. This usually involves describing a model for both the primary variable of interest (the response variable) and the auxiliary variable that influences its distribution (the compound variable)(Hastie & Tibshirani, 1986). It is also very important to state that modeling using compound distributions might include more than two variables. Indeed, the concept of compound distributions readily applies to situations in which numerous variables influence the distribution of a response variable. This can be accomplished by using multivariate compound distributions or include more predictor variables in the modeling framework. Modeling using compound distribution can be done using several different types of models(Liu, 2008). These includes Generalized Additive Models (GAM), Generalized Linear Models(GLMs), Mixed-effects Models, Bayesian Models, Generalized Additive Mixed Models (GAMMs), Machine Learning Models, and Survival Analysis Models.

The compound distribution models such as Generalized Additive Models (GAMs) differ from typical linear models in numerous important ways, including their ability to model complicated relationships, handle nonlinearity, and accommodate interactions(Rigby et al., 2005). For instance, whereas, traditional models such as linear regression assumes a linear relationship between the predictor variable and the response variable which implies that changes in the predictor variable leads to proportional changes in the response variable, the compound distribution models such as GAMs allow for the incorporation of smooth functions of the predictor variables, enabling the modeling of non-linear relationships. This flexibility allows GAMs to capture complex patterns and trends in the data that may not be adequately represented by linear models.Generalized Additive Models (GAMs) come in a variety of variants, each adapted to unique modeling requirements and data characteristics(Fasiolo, 2018). In this study, the Generalized Additive Models for location, scale and shape(GAMLSS) was utilized.

The GAMLSS statistical modeling approach helps us understand how different factors affect the distribution of data The model is very flexible and can handle a variety of data distributions, not just the standard normal (bell-shaped) distribution. This makes it ideal for a variety of data types, including skewed or lengthy tails(Voncken et al., 2019). By combining several "smooth" functions of the predictor variables, they are able to capture nonlinear interactions. The average or center of the distribution is referred to as the location in GAMLSS. Put differently, it indicates the central tendency of our data. The data's variability or distribution around the center is depicted by the scale. The data points are more widely distributed when the scale is large, while they are tightly packed around the center when it is tiny. The distribution's shape conveys information about its characteristics, including its symmetry, skewness, and number of peaks(Rigby et al., 2005). Additionally, in GAMLSS, the beta-binomial distribution is one of the available distributions for modeling binary or proportion data.The beta-binomial distributionadds unpredictability to the success probability, which is approximated as a beta distribution making it more sophisticated than ordinary binomial distribution which has the limitation of assuming that the success chance is constant over all trials, which may not be true in real-world data(Guimarães, 2005).

1.1 Statement of Problem

Despite advancements in medical care, the recovery journey for fistula patients remains complex and multifaceted, influenced by a myriad of interconnected factors. Understanding these factors and their dynamic interplay is crucial for optimizing treatment strategies and improving patient outcomes. Without a comprehensive understanding of patient-specific risk factors, it becomes difficult to tailor interventions and allocate resources effectively, leading to suboptimal care and potentially poorer long-term outcomes.

1.2 Aim and Objectives

Aim

To investigate the influence of specific factors on the surgical outcome of VVF patients using Beta Binomial Distribution Model.

Objectives

To identify the factors that significantly influence the outcome of surgeries in VVF patients.
To evaluate the overall fit and adequacy of Beta Binomial model on surgical outcomes based on selected patient characteristics.

1.3 Significance of the Study

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