Exploring the Socio-Demographic Profile of Non-Completion in Public Oral Healthcare Services: A Cross-Sectional Study in Melbourne, Victoria

(1) Background: Completion of the full oral health course of care (CoC) is essential to prevent further deterioration of oral and overall health. Understanding these patterns, particularly in public oral healthcare services, is crucial for improving access to and the delivery of care. This study aims to identify the socio-demographic and clinical characteristics of adult patients who did not complete required dental treatments within a 12-month period at Monash Health Dental Services (MHDS), Melbourne, Victoria. (2) Methods: Data were collected on patients’ course of care (CoC), socio-demographic characteristics, and clinical information from the MHDS Titanium electronic database. This study represents a secondary data analysis from adult patients who attended MHDS between November 2022 and October 2023, excluding emergency dental care visits. Logistic regression analyzed the socio-demographic and clinical variables affecting CoC. (3) Results: Our findings identified several significant predictors of incomplete CoC; being a non-priority group, mental health clients, refugees, and identifying as Aboriginal or Torres Strait Islanders (OR = 1.41; 95% CI: 1.08–1.84). Conversely, speaking a language other than English increased the odds of completing treatment (OR = 0.85; 95% CI: 0.74–0.98). By age, patients in the 36-to-55- or the 56-to-75-year-old age groups were more likely to be in the incomplete group (OR = 1.65; 95% CI: 1.37–1.98; and OR = 1.43; 95% CI: 1.22–1.66, respectively). (4) Conclusions: This study identified predictors of discontinued care, emphasizing accessibility and equitable outcomes for users of public oral healthcare. The findings indicate that the predictors of course of care (CoC) completion differ from barriers to accessing care. This highlights key objectives in public health dentistry, focusing on improving accessibility and promoting equitable oral health outcomes for vulnerable populations.