Bayesian spatio-temporal modelling of depressive feelings among patients who underwent surgery for prostate cancer in Victoria, Australia

Background: In Australia, prostate cancer is the most commonly diagnosed cancer and the 2^nd most common causes of cancer-related deaths in men. It imposes significant health-related consequences such as mental health problems including depression. One in six men with prostate cancer reported depression after prostate cancer surgery. Based on our literature review, there is limited evidence on area level factors associated with depressive feelings and the effect of different spatial scales on the model estimates. Our objective is two-fold: (I) to identify area level determinants of depressive feelings among prostate cancer surgery patients; and (II) to evaluate the effect of different spatial scales on inference, called Modifiable Area Unit Problem (MAUP). Methods: We analysed the data on Prostate Cancer Outcomes Registry-Victoria, comprising 5,955 patients who underwent surgery. The smoothed area-specific relative risk of depressive feelings was mapped at the local government area (LGA) level. This areal level constitutes the third level of government, following the federal and state/territory levels. It provides a crucial overlay in overseeing local services and infrastructure, including community health services, local roads, parks, and recreational facilities. A Bayesian spatio-temporal conditional autoregressive Poisson model was fitted. Multiple models were fitted and evaluated using deviance information criteria; the model with the lowest Deviance was selected as the best fit. For the final chosen model, relative risk (RR) along with the 95% credible intervals (CrI) were reported. Model convergence was assessed using the Brooks-Gelman-Rubin statistics plot. In addition, the effect of different spatial scales (MAUP) on inference was evaluated. Results: The prevalence of reported depressive feelings was 11%. It was significantly associated with the index of relative socio-economic disadvantage (IRSD). Being in the fourth quartile (most advantaged) of the IRSD reduced the risk of depressive feelings by 14% (RR =0.86; 95% CrI: 0.67–0.97) compared to quartile one (most disadvantaged). At the postcode level, the structured random effect contributed to 70% of the variation, while at the LGA level, it explained 64% of the variation. This indicates that the place where people live has a significant impact on the levels of depressive feelings. Conclusions: The area-specific relative risk of depressive feelings was associated with IRSD. Spatiotemporal variations in the risk of depressive feelings across LGA level were observed. This finding is consistent with previous studies and reinforces the need to design effective interventions targeting high-risk areas to reduce depressive feelings. Based on these findings, this statistical methodology may also be useful to apply to other population-based clinical registry settings.