Smooth Test of Goodness-of-Fit for Negative Binomial Distribution with Application to Unscheduled HIV Care Visits in a Tertiary Hospital

Abstract

Since the roll-out of antiretroviral therapy (ART) in Kenya, significant resource implications arising from regular treatment has attracted huge research interest, more specifically, unscheduled HIV care visits. Anticipating unscheduled HIV care visits for high-frequency regular groups is useful in helping clinics to focus efforts on reducing the burden of clinical appointments for families and facilities. In this paper, we fit data of unscheduled HIV care visits to a Negative Binomial Distribution and assess the fit using smooth tests of goodness-of-fit. The smooth tests applied here are an extension of Neyman's test where the score test is derived by embedding the null probability to form a larger class of alternative distribution. We conducted simulations by varying sample size and levels of dispersion for a negative binomial sample and compare performance of chi-square test, Kolmogorov- Smirnov test, Crammer-Von Misses test, Andersen-Darling and smooth test. We then utilized data on unscheduled HIV care visits, collected retrospectively from a tertiary referral hospital. The simulation results show that a smooth test does well under varying negative binomial conditions. Understanding patterns of unscheduled visits allows service providers to develop strategies to minimize this occurrence, particularly at a tertiary hospital.