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

Introduction

Globally, prostate cancer is the second most commonly diagnosed cancer in 112 countries and the fifth leading cause of death among men in 48 countries, with 1.41 million new cases and 375,304 deaths reported in 2020 (1). A cancer prevalence projection study in Japan showed that the highest prevalence among men is prostate cancer in 2050 (2). The treatment for prostate cancer depends on the cancer’s stage and grade (3). One of the treatments for advanced stage of disease is surgical removal of prostate cancer (radical prostatectomy). Radical prostatectomy frequently causes urinary, sexual, and bowel dysfunction, which can be troubling for men and may contribute to the onset of depressive symptoms (4).

In Australia, prostate cancer is the most commonly diagnosed cancer and the second most common cause of cancer-related deaths in men (5). It is estimated that 18,110 new cases of prostate cancer are diagnosed every year (6). Studies conducted by Sharpley et al. (7) found that one in six men with prostate cancer experience clinical depression. Friberg et al. (8) reported that depression was higher among men with prostate cancer who had undergone surgery compared to cancer-free men. Another study done by Friberg et al. (9) reported that depression was higher among men with prostate cancer who had undergone surgery as compared to cancer-free men (10). Research by Bensley et al. (11) based on the Prostate Cancer Outcomes Registry (PCOR) registry, showed that the rate of patient-reported depressive feelings was 10%. Sweden population based cohort study conducted by Crump et al. (12) showed that men diagnosed prostate cancer had major depression than men free of prostate cancer. A systematic review from 25 article conducted by Dinesh et al. (13) shown that depressive symptoms affect functional outcomes of prostate cancer. Another systematic review conducted by Brunckhorst et al. (14) showed that depression, anxiety and suicidal symptoms were common among prostate cancer patients.

The field of spatial epidemiology is rapidly evolving, focusing on the analysis of health data with geographic reference by considering factors such as demographics, environment, behaviours, socio-economic status, genetics, and infectious risks (15). Small area analysis, a novel discipline, quantifies geographic variations in diseases and their correlation with environmental factors (16,17). Disease mapping involves the spatial analysis, estimation, and presentation of disease incidence and prevalence (18). Traditional measures like the standardized incidence ratio (SIR) and standardized mortality ratio (SMR) may not be suitable for small populations or rare cases, as they fail to account for spatial correlations in the data (19). To address this, the Besag-York-Mollié (BYM) model incorporates structured and unstructured random effects for relative risk smoothing (20). For rare outcomes, models can be further refined by incorporating adjacent neighbour information based on Tobler’s first law of geography, which suggests that nearer things are more similar than distant things (21).

Similar to other regression models, small area risk mapping models such as BYM have their own constraints, such as the Modifiable Area Unit Problem (MAUP). The MAUP is a source of statistical bias when data are aggregated spatially to different geographic units (22). Since the 1950s, MAUP has been a fundamental issue in spatial analysis and continues to be a major challenge for scholars in fields like public health, environmental science, urban planning, and geography (23). The statistical bias that arises due to the aggregation of spatial data is known as an ecological fallacy (24-26). To address MAUP, researchers have developed a variety of methods, including spatial autocorrelation techniques, geographically weighted regression, and multi-level hierarchical modelling (14,15). In addition, using available smaller spatial units can help to address potential bias caused by aggregated data (27).

Standard hierarchical/multilevel models assume independence between observations across geographical areas, disregarding spatial and temporal dependencies among adjacent regions (28). However, assuming independence among observations in neighbouring areas and timeframes may not accurately reflect reality when working with geographically referenced data (29). The BYM model addresses spatial dependence among neighbouring areas by incorporating structured spatial random effects, typically through the integration of conditional autoregressive (CAR) priors (20). However, no studies have examined area-level determinants of depressive feelings by accounting for spatial and temporal dependencies using a Bayesian framework within Victoria. Therefore, we investigated the area-level determinants of depressive feelings among prostate cancer surgery patients using a Bayesian spatio-temporal model (30).

Previous studies have identified the determinants of depressive feelings among prostate cancer patients at an individual level (8-10). However, they failed to account for area-level determinants such as the index of relative socio-economic disadvantage (IRSD) and remoteness. Additionally, there is lack of evidence on area-level determinants of depressive feelings in Victoria. Therefore, we have two objectives in this study: (I) to identify area-level determinants of depressive feelings among prostate cancer surgery patients in Victoria. This study gives a more detailed picture of the depression feelings among prostate cancer surgery patients, enabling more effective and targeted intervention to improve well-being of patients. Moreover, this study will provide useful evidence for researchers, planners, and healthcare administrators in planning intervention measures and allocating resources. (II) To evaluate the effect of different spatial scales on the results.

Methods

Study settings

Victoria has an estimated population size of 6.68 million out of a total population of 25.69 million (31) in Australia. Based on the Australia Bureau of Statistics (ABS) (32) Victoria has a total of 80 local government areas (LGAs) of which 48 regional and 32 metropolitan and represent the third level of government, situated between states and territories. Based on 2019 Australian Bureau of Statistics, the median population size of LGA was 12,905 with inter quartile range 42,872 (33). LGAs act as standard units for the collection and analysis of statistical data, aiding in the understanding of regional demographics, economic activities, health statistics, education levels, and other key metrics. This information is crucial for policymaking, research, and planning at both state and national levels (34).

Data source

The Prostate Cancer Outcomes Registry-Victoria (PCOR-Vic) dataset currently captures 90% of all newly diagnosed cases of prostate cancer in Victoria. The PCOR-Vic collects data on treatment, diagnostic, demographic, and quality of life indicators 12 months after treatment (35). At 12-month post treatment follow-up was conducted to assess their functional outcomes like sexual function, bowel function, urinary function, and depression symptoms using Expanded Prostate Cancer Index Composite-26 (EPIC-26) questionnaire. All prostate cancer patients enrolled into PCOR-Vic and who had surgery between September 2015 to June 2021 were included in this study. PCOR-Vic administers the validated EPIC-26 (36). From a total of 7,405 prostate cancer surgery patients between 2015 to 2021, 1,450 (19.6%) prostate cancer surgery patients had not responded to EPIC-26 questionnaire. The consent for PCOR-Vic follows an opt-out model. The three main methods of completing the questionnaire were telephone, email, and mail for self-completion.

Inclusion and exclusion criteria

Prostate cancer patients who underwent surgery and completed the EPIC-26 questionnaire were included in our study. A total of 5,955 patients were included in the final analysis (Figure 1).

Figure 1 Inclusion and exclusion criteria of the studies. EPIC-26, Expanded Prostate Cancer Index Composite-26; PCOR-Vic, Prostate Cancer Outcomes Registry-Victoria.

Measures of variables

Dependent variable

The dependent variable, i.e., patient-reported depressive feelings, was extracted from the EPIC-26 questionnaire. Prostate cancer patients who underwent surgery 12 months after treatment, were asked the question “Do you experience depressive feelings?” The original codes for the response were as follows: 1= no problem, 2= very small problem, 3= small problem, 4= moderate problem, and 5= big problem (37). For this analysis, based on clinical importance and ease of interpretability, we recategorized them into “not a big problem” (by merging no problem, very small problem, and small problem) and “a big problem” (by merging moderate problem and big problem). Then, the total number of patients who experienced depressive feelings was aggregated at each postcode and LGA level.

Individual level variables

Individual-level variables considered for this study were hospital type (metro, regional, interstate/overseas), age (≤55, 56–65, 66–75, 76–85, ≥86 years), diagnostic institution (public and private), Gleason risk (ISUP1, ISUP2, ISUP3, ISUP4, ISUP5) (38), prostate specific antigen (PSA) at diagnosis (≤10, 10.1–20.0, >20.0 ng/mL), National Comprehensive Cancer Network (NCCN) risk group (low risk, intermediate risk, high risk), and clinical T stage (T1, T2, T3, T4, unknown).

Area level variables

Area-level variables such as the IRSD, remoteness, smoking status, population density, proportion of indigenous men, and pollution data were obtained from ABS (39). Additional area-level variables like the NCCN risk group, age greater than 65 years, and men who attended private hospitals, available in the PCOR registry, were used for this study. The relevant proportions in each category were calculated and classified into quartiles. The proportion of the NCCN high-risk group was calculated for each LGA and postcode and then classified into quartiles. Similarly, the proportion of men aged greater than 65 years and the proportion of men who received services from private hospitals were calculated for each LGA and postcode and then classified into quartiles.

Data management and statistical analysis

Data management

Data on depressive feelings 12 months after treatment were extracted from the PCOR, which collects information using EPIC-26 tools. The LGA was used as the basic geographic level to aggregate cases, and the results were compared to those based on postcodes. The number of men with prostate cancer who experienced depressive feelings was aggregated to determine the number of observed and expected cases for each postcode. Postcode to LGA mapping was undertaken in ArcGIS software using the ‘intersection’ tool. Data management and analysis were undertaken using ArcGIS, Stata, Excel, GeoDA, and WinBUGS softwares.

Statistical analysis

Bayesian spatio-temporal CAR models were fitted. The observed number of depressive feelings (i = 1, 2, 3, …, 80) at the LGA level was aggregated with the year of surgery (t = 1, 2, 3, …, 7). We utilised the BYM model to account for spatial dependence (30). Based on the observed number of depressive feelings, we calculated the expected numbers at both the postcode and LGA levels. Then, we calculated the crude relative risk by dividing the observed number of cases by the expected number of cases at the postcode and LGA levels. However, the crude relative risk may not be reliable when the cases or population size is sparse. To overcome this, Bayesian spatio-temporal models were fitted to obtain smoothed relative risks by borrowing information from neighbouring areas and timeframes.

Let’s Yit represent count observed number of patients reporting depressive feelings at LGA i and time t represented as

Yit~Poisson(Eitθit)[1]

where θit is relative risk and Eit is the expected number of cases in area i and time t in which i=1,2,3,⋯⋯,80 for LGA and time t=1,2,3,⋯⋯,7

log(θit)=α+∑xitkβk+ui+vi+φt[2]

Where the observed number of cases for i^th area represent (i=1,2,3,⋯⋯,80) for LGA, and time interval, t=1,2,3,⋯⋯,7, α is the intercept term, xitk k^th covariate for the i^th area in the t^th period. βk is the regression coefficient, ui is spatially structured random effect and vi is the unstructured random effect, and φ is the mean linear time trend.

CAR model

In the BYM model, the random effect ui is assigned a CAR model distribution, which smooths the data based on neighbourhood structure that specifies the two areas are neighbours if they share common boundary (40). Mathematically, spatial structured random effect ui represented as

(ui|uj,i≠j)~N(ul¯,τi2)[3]

Where ul¯=1∑jwij∑ujwij, τi2=τu2∑jwij

Where wij={1,iftheyhadcommonboundryand0,iftheyhadnocommonboundryi and j are locations of LGA.

The unstructured random component vi is represented as

vi~iidN(0,σv2)[4]

Relative contribution of spatial structured and unstructured variations in model at postcode and LGA level

The relative contribution of spatial variation was calculated by dividing variance of structured random effect var(u) by sum of variance of structure random effect var(u) and variance of unstructured random effect var(v) at postcode and LGA level, empirically represented as (41)

∅=var(u)var(u)+var(v)[5]

If value of ∅ is closed to 1 means that structured random variation dominates while value of ∅ is closed to 0 means that unstructured random variation dominates.

We calculated the percentage change in the relative risk estimates of covariates between the postcode and LGA levels after fitting the Bayesian spatio-temporal CAR models, using postcode as the reference. Percentage changes were calculated as the relative risk (on the log scale) of postcode minus the relative risk of the LGAs, divided by the relative risk of the postcode, expressed as a percentage to quantify the MAUP effect.

For this study, a non-informative normal prior was assumed for coefficients, with a mean of zero and a variance of 100. A CAR prior distribution was assumed for the structured random effect (40). Hyperprior distribution was assumed for the inverse variance parameter with exchangeable normal prior with N (0, τu2) where τu2 is the precision (1/variance) with a prior uniform prior distribution dunif(0,10) set for the standard deviation. For model comparison, we used deviance information criteria (DIC) (42). DIC is a model fit statistic that penalizes the model complexity. A model with a lower DIC is a better fit. Mathematically, DIC is represented as follows:

DIC=D(θ)¯+2pD[6]

Where D(θ)¯ represents the mean deviance of the posterior distribution, and pD represents effective number of parameters.

For this study, we used Markov chain Monte Carlo (MCMC) methods, which comprise a class of algorithms for sampling from a probability distribution. Two chains with different starting points were used to ensure model convergence. The first 200,000 iterations in each chain were discarded as burn-in. Subsequently, an additional 800,000 iterations were performed for each chain, from which the sample distributions for each parameter were calculated. Thinning (including every other iteration) was utilised to decrease autocorrelation between samples. Model convergence was evaluated using Gelman-Rubin statistic plots. We reported the relative risks (RRs) and 95% credible intervals (CrIs) for the posterior estimates and visualized the smoothed relative risks at the LGA level on a map.

Ethical statement

The study was conducted in accordance with the Declaration of Helsinki (revised in 2013). Approval for the study was obtained from the Monash University Human Research Ethics Committee (project No. 35284), and individual consent for this retrospective analysis was waived.

Results

Characteristics of study population

The median age of the patients was 64 years. The majority (72.35%) of patients were from metropolitan hospitals. Nearly three-fourths (73.38%) were diagnosed and treated at private hospitals. Approximately 70% of men were categorized as intermediate risk, and 22.14% as high risk, according to NCCN risk groups (Table 1).

Trends of depressive feelings 12 months after surgery

The overall prevalence of depressive feelings among prostate cancer surgery patients was 11%. The highest prevalence of depressive feelings was recorded in 2017 (11.94%), and the lowest was recorded in 2019 (9.19%) (Figure 2).

Figure 2 Line graph of depressive feelings among prostate cancer surgery patients from 2015 to 2021.

Smoothed relative risk of depressive feelings at LGA

Smoothed RRs were mapped across all LGAs in Victoria. Adjacency matrices were created to smooth the RRs by borrowing information from neighbouring LGAs. Based on the results, smoothed RRs were obtained for each LGA across Victoria. The smoothed RRs of depressive feelings varied across LGAs in Victoria. From these maps, we demonstrated the level of risk by assigning colours to each LGA. The high-density colour indicates high RRs of depressive feelings, while the less dense colour indicates low RRs of depressive feelings (Figure 3).

Figure 3 Smoothed relative risk of depressive feelings among prostate cancer surgery patients at LGA. LGA, local government area.

Model convergence and comparison

For model convergence, the BGR diagnostic statistics were used. Convergence is assumed when the potential scale reduction factor values approach 1. Based on the results, we found that the model is well converged (Figure S1). Finally, the models were compared using the DIC, where lower values indicate a better fit (Table S1).

Risk factors

A separate regression model was fit at both geographic scales (postcode and LGAs), and the percentage change of RRs in the covariates was calculated. The IRSD was significantly associated with depressive feelings. Being in the fourth quartile (most advantaged) socioeconomic status reduced depressive feelings by 14% compared to quartile one (most disadvantaged) (RR =0.86; 95% CrI: 0.67–0.97). The most significant percentage change of RR from postcode was 9% in the inner region remoteness category, while the smallest percentage change was observed in the first quartile of the covariate proportion of indigenous males (1.4%) compared to LGAs (Table 2).

Relative contribution of spatial structured and unstructured random effect variation

At the postcode level, the structured random effect accounted for 70% of the total variation in depressive feelings, while at the LGA level, this was 64%. These statistics indicate that the place where people live whether it is a specific postcode or a larger LGA has a significant impact on the levels of depressive feelings. Understanding these spatial effects is important for public health planning and intervention strategies because it suggests that addressing area-specific factors could help to reduce depressive feelings (Table 3).

Discussion

This study examined the spatio-temporal distribution and area-level determinants of depressive feelings among prostate cancer surgery patients in Victoria. There is no previous research on this topic analysed based on a Bayesian framework. According to the results of this study, spatial and temporal variations in depressive feelings among prostate cancer surgery patients in Victoria from 2015 to 2021 at the LGA level were observed. One possible reason for this might be variability in the accessibility of healthcare services across different areas of Victoria, which might contribute to differences in depressive feelings. Patients in areas with limited access to specialized care, mental health services, or rehabilitation support might experience more difficulties. Additionally, COVID-19 may have its own effect on this variation. This finding is supported by a systematic review conducted by Dasgupta et al. (43).

In the multivariable Bayesian spatio-temporal CAR model at the LGA level, the IRSD was a significant area-level determinant of depressive feelings among prostate cancer surgery patients in Victoria. The most advantaged LGAs had lower risks of depressive feelings compared to the most disadvantaged LGAs. This reveals that there are differences in depressive feelings based on economic status. This finding is supported by previous studies (44-46). Prostate cancer patients in lower economic categories may have limited access to healthcare resources, low social support, and financial burdens, all of which can increase their feelings of depression (47). Investigating the correlation between socio-economic status and depressive feelings among prostate cancer patients is vital for designing effective interventions to reduce variation and promote health equity across different LGAs in Victoria (45).

The MAUP issue has been investigated in this study. We aggregated postcode data to LGAs and then investigated the effect of different spatial scales of analysis (postcode versus LGAs) on inference of the covariates’ coefficients and quantified the relative structured random effect variation across postcodes and LGAs. Based on the analysis results, the most significant percentage change of relative risk from postcode was 9.0% in the remoteness category’s inner region, while the smallest percentage change was observed in the first quartile of the proportion of indigenous males (1.4%). The possible reason may be that the result of the spatial study depends on the spatial scale being studied (24). In some studies, it is acknowledged that data aggregation can introduce ecological fallacies, concealing relevant information due to the use of large geographic units (48,49). Thus, using smaller geographic units of analysis increases the geographic precision of the estimates compared to large geographic units (50); however, using smaller geographic units may increase data complexity, and managing and processing the data may be challenging. In addition, performing data analysis at a finer scale necessitates increased computational resources and a longer time commitment.

A comparison of spatial fraction between postcode and LGA was made by including different variables in the model to determine how much of the geographical variation was explained by the two geographic scales. Both structured and unstructured random effect components were part of the model. The proportion of total spatial structured random effect variation of depressive feelings at the postcode and LGA levels was 70% and 64%, respectively. These statistics show that the place where people live, whether at the postcode or LGA level, has a significant impact on depressive feelings. Higher variability was explained by the smaller geographic scale. This finding is in line with previously published work by Fairley et al. (41) which concluded that spatial variance is inversely proportional to the number of neighbouring areas, and studies conducted by Dasgupta et al. (51) which found that using finer-geographic units of analysis enhances the accuracy of the estimates.

Implications

This study examined the spatio-temporal distribution and area-level factors influencing depressive feelings among prostate cancer surgery patients in Victoria, and provides several implications. We found that socioeconomic status, as indicated by the IRSD, is a significant determinant of depressive feelings among prostate cancer patients. This underscores the importance of integrating socioeconomic factors into healthcare planning. In addition, this study examined the effect spatial scale, highlighting the importance of selecting appropriate spatial scales for analysis and policy planning. Overall, this study highlights the need for a multifaceted approach to address the mental health challenges faced by prostate cancer surgery patients. By focusing on improving access to care, addressing socioeconomic disparities, and utilizing precise spatial data, healthcare practitioners and policymakers can enhance the well-being of patients and promote health equity across Victoria.

Strength and limitation of the study

Strengths

The main strength of this study is the application of a Bayesian spatio-temporal CAR model, which considers structured and unstructured random effects. This study also evaluated the effect of different spatial scales on inference, primarily addressing the MAUP issue. In addition, the developed model, under the Bayesian framework, was applied to population-based, large multi-hospital registry data, which assures statistical power and generalizability. Furthermore, we believe that this statistical methodology could be useful for application to other population-based registries.

Limitations

The limitation of this study is due to its reliance on retrospective data. Since we do not have baseline levels of depressive feelings, it is not possible to establish a cause-and-effect relationship. The outcome variable used is a single question regarding self-reported depressive feelings. It is a crude measure and was asked at a single time point, 12 months after treatment. It is not a clinical definition of depression and should be interpreted with caution. By aggregating individual-level data at the LGA and postcode level, there is a potential for information loss and a tendency towards ecological fallacy. In addition, the absence of data on psychiatric history and the onset of depressive symptoms may significantly bias the results and caution is needed when we interpret the findings. Finally, our study results need to be externally validated in other datasets in a different geographic setting.

Conclusions

One in every ten prostate cancer patients who underwent surgery reported depressive feelings. The area-specific relative risk of depressive feelings was significantly associated with IRSD. Spatio-temporal variations in the risk of depressive feelings across LGAs 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, our statistical methodology may also be useful for other population-based clinical registries. Further model development that includes additional covariates both individual and area-level factors would be highly recommended in future work.

Acknowledgments

We sincerely thank Monash University for their generous support through tuition fee sponsorship and scholarship funding. We also express our gratitude to the Prostate Cancer Outcomes Registry for providing the dataset essential for this study.

Funding: None.

Footnote

Data Sharing Statement: Available at https://jhmhp.amegroups.com/article/view/10.21037/jhmhp-24-83/dss

Peer Review File: Available at https://jhmhp.amegroups.com/article/view/10.21037/jhmhp-24-83/prf

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://jhmhp.amegroups.com/article/view/10.21037/jhmhp-24-83/coif). The authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. The study was conducted in accordance with the Declaration of Helsinki (revised in 2013). Approval for the study was obtained from the Monash University Human Research Ethics Committee (No. 35284), and individual consent for this retrospective analysis was waived.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

References

1. Wang L, Lu B, He M, et al. Prostate Cancer Incidence and Mortality: Global Status and Temporal Trends in 89 Countries From 2000 to 2019. Front Public Health 2022;10:811044. [Crossref] [PubMed]
2. Nguyen PT, Hori M, Matsuda T, et al. Cancer Prevalence Projections in Japan and Decomposition Analysis of Changes in Cancer Burden, 2020-2050: A Statistical Modeling Study. Cancer Epidemiol Biomarkers Prev 2023;32:1756-70. [Crossref] [PubMed]
3. Litwin MS, Tan HJ. The Diagnosis and Treatment of Prostate Cancer: A Review. JAMA 2017;317:2532-42. [Crossref] [PubMed]
4. Chambers SK, Chung E, Wittert G, et al. Erectile dysfunction, masculinity, and psychosocial outcomes: a review of the experiences of men after prostate cancer treatment. Transl Androl Urol 2017;6:60-8. [Crossref] [PubMed]
5. Pathirana T, Sequeira R, Del Mar C, et al. Trends in Prostate Specific Antigen (PSA) testing and prostate cancer incidence and mortality in Australia: A critical analysis. Cancer Epidemiol 2022;77:102093. [Crossref] [PubMed]
6. Ong WL, Evans SM, Evans M, et al. Trends in Conservative Management for Low-risk Prostate Cancer in a Population-based Cohort of Australian Men Diagnosed Between 2009 and 2016. Eur Urol Oncol 2021;4:319-22. [Crossref] [PubMed]
7. Sharpley CF, Christie DRH, Bitsika V. Depression and prostate cancer: implications for urologists and oncologists. Nat Rev Urol 2020;17:571-85. [Crossref] [PubMed]
8. Fervaha G, Izard JP, Tripp DA, et al. Depression and prostate cancer: A focused review for the clinician. Urol Oncol 2019;37:282-8. [Crossref] [PubMed]
9. Friberg AS, Dalton SO, Larsen SB, et al. Risk of Depression After Radical Prostatectomy-A Nationwide Registry-based Study. Eur Urol Oncol 2021;4:601-8. [Crossref] [PubMed]
10. Pan LH, Lin MH, Pang ST, et al. Improvement of Urinary Incontinence, Life Impact, and Depression and Anxiety With Modified Pelvic Floor Muscle Training After Radical Prostatectomy. Am J Mens Health 2019;13:1557988319851618. [Crossref] [PubMed]
11. Bensley JG, Dhillon HM, Evans SM, et al. Self-reported lack of energy or feeling depressed 12 months after treatment in men diagnosed with prostate cancer within a population-based registry. Psychooncology 2022;31:496-503. [Crossref] [PubMed]
12. Crump C, Stattin P, Brooks JD, et al. Long-term Risks of Depression and Suicide Among Men with Prostate Cancer: A National Cohort Study. Eur Urol 2023;84:263-72. [Crossref] [PubMed]
13. Dinesh AA, Helena Pagani Soares Pinto S, Brunckhorst O, et al. Anxiety, depression and urological cancer outcomes: A systematic review. Urol Oncol 2021;39:816-28. [Crossref] [PubMed]
14. Brunckhorst O, Hashemi S, Martin A, et al. Depression, anxiety, and suicidality in patients with prostate cancer: a systematic review and meta-analysis of observational studies. Prostate Cancer Prostatic Dis 2021;24:281-9. [Crossref] [PubMed]
15. Kirby RS, Delmelle E, Eberth JM. Advances in spatial epidemiology and geographic information systems. Ann Epidemiol 2017;27:1-9. [Crossref] [PubMed]
16. Beale L, Abellan JJ, Hodgson S, et al. Methodologic issues and approaches to spatial epidemiology. Environ Health Perspect 2008;116:1105-10. [Crossref] [PubMed]
17. López-Abente G, Hernández-Barrera V, Pollán M, et al. Municipal pleural cancer mortality in Spain. Occup Environ Med 2005;62:195-9. [Crossref] [PubMed]
18. Rezaeian M, Dunn G, St Leger S, et al. Geographical epidemiology, spatial analysis and geographical information systems: a multidisciplinary glossary. J Epidemiol Community Health 2007;61:98-102. [Crossref] [PubMed]
19. Kim EA. Standardized Incidence Ratio and Standardized Mortality Ratio of Malignant Mesothelioma in a Worker Cohort Using Employment Insurance Database in Korea. Int J Environ Res Public Health 2021;18:10682. [Crossref] [PubMed]
20. Morris M, Wheeler-Martin K, Simpson D, et al. Bayesian hierarchical spatial models: Implementing the Besag York Mollié model in stan. Spat Spatiotemporal Epidemiol 2019;31:100301. [Crossref] [PubMed]
21. Sui DZ. Tobler's first law of geography: A big idea for a small world? Annals of the Association of American Geographers 2004;94:269-77. [Crossref]
22. Buzzelli M. Modifiable areal unit problem. International encyclopedia of human geography. International Encyclopedia of Human Geography 2019:169-173. doi: 10.1016/B978-0-08-102295-5.10406-8.10.1016/B978-0-08-102295-5.10406-8
23. Fotheringham AS, Wong DW. The modifiable areal unit problem in multivariate statistical analysis. Environment and planning A 1991;23:1025-44. [Crossref]
24. Openshaw S. The modifiable areal unit problem: Concepts and techniques in modern geography. Norwich: Geobooks, 1984.
25. Chen X, Ye X, Widener MJ, et al. A systematic review of the modifiable areal unit problem (MAUP) in community food environmental research. Urban Info 2022;1:22. [Crossref]
26. Wong DW. Modifiable Areal Unit Problem. In: Kitchin R, Thrift N, editors. International Encyclopedia of Human Geography. Oxford: Elsevier; 2009:169-74.
27. Lehtonen R, Veijanen A. Design-based methods of estimation for domains and small areas. In: Rao CR, Pfeffermann D, editors. Handbook of statistics. New York: Elsevier; 2009:219-49.
28. Bivand R, Sha Z, Osland L, et al. A comparison of estimation methods for multilevel models of spatially structured data. Spatial Statistics 2017;21:440-59. [Crossref]
29. Jackson C, Best AN, Richardson S, et al. Hierarchical related regression for combining aggregate and individual data in studies of socio-economic disease risk factors. Journal of the Royal Statistical Society Series A: Statistics in Society 2008;171:159-78. [Crossref]
30. Besag J, York J, Mollié A. Bayesian image restoration, with two applications in spatial statistics. Ann Inst Stat Math 1991;43:1-20. [Crossref]
31. ABS. Census of population and housing: Socio-Economic Indexes for Areas (SEIFA). Australian Bureau of Statistics Australia; 2011.
32. Ross S. Australian Bureau of Statistics. The Encyclopedia of Research Methods in Criminology and Criminal Justice. 2021;2:767-73.
33. Statistics ABo. Digital boundary files 2024. Available online: https://www.abs.gov.au/statistics/standards/australian-statistical-geography-standard-asgs-edition-3/jul2021-jun2026/access-and-downloads/digital-boundary-files
34. Grant B, Drew J. Local government in Australia: History, Theory and Public Policy. Singapore: Springer; 2017;10:978-81.
35. Evans SM, Millar JL, Wood JM, et al. The Prostate Cancer Registry: monitoring patterns and quality of care for men diagnosed with prostate cancer. BJU Int 2013;111:E158-66. [Crossref] [PubMed]
36. Szymanski KM, Wei JT, Dunn RL, et al. Development and validation of an abbreviated version of the expanded prostate cancer index composite instrument for measuring health-related quality of life among prostate cancer survivors. Urology 2010;76:1245-50. [Crossref] [PubMed]
37. Chang P, Szymanski KM, Dunn RL, et al. Expanded prostate cancer index composite for clinical practice: development and validation of a practical health related quality of life instrument for use in the routine clinical care of patients with prostate cancer. J Urol 2011;186:865-72. [Crossref] [PubMed]
38. Epstein JI, Egevad L, Amin MB, et al. The 2014 International Society of Urological Pathology (ISUP) consensus conference on Gleason grading of prostatic carcinoma. The American Journal of Surgical Pathology 2016;40:244-52. [Crossref] [PubMed]
39. Statistics ABO. Census of population and housing. Canberra: Australian Government, 2006.
40. Lee D. A comparison of conditional autoregressive models used in Bayesian disease mapping. Spat Spatiotemporal Epidemiol 2011;2:79-89. [Crossref] [PubMed]
41. Fairley L, Forman D, West R, et al. Spatial variation in prostate cancer survival in the Northern and Yorkshire region of England using Bayesian relative survival smoothing. Br J Cancer 2008;99:1786-93. [Crossref] [PubMed]
42. Spiegelhalter DJ, Best NG, Carlin BP, et al. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society Series B: Statistical Methodology 2002;64:583-616. [Crossref]
43. Dasgupta P, Baade PD, Aitken JF, et al. Geographical Variations in Prostate Cancer Outcomes: A Systematic Review of International Evidence. Front Oncol 2019;9:238. [Crossref] [PubMed]
44. Koo K, Papa N, Evans M, et al. Mapping disadvantage: identifying inequities in functional outcomes for prostate cancer survivors based on geography. BMC Cancer 2022;22:283. [Crossref] [PubMed]
45. Koo K, Papa N, Evans M, et al. Mapping geographical disparities in population-level patient-reported quality of life following prostate cancer management. J Clin Oncol 2021;39:e18531. [Crossref]
46. Ilie G, Rutledge R, Sweeney E. An Examination of the Role of Socioeconomic Status in the Relationship between Depression and Prostate Cancer Survivorship in a Population-Based Sample of Men from Atlantic Canada. Oncology 2021;99:260-70. [Crossref] [PubMed]
47. Zhao X, Sun M, Yang Y. Effects of social support, hope and resilience on depressive symptoms within 18 months after diagnosis of prostate cancer. Health Qual Life Outcomes 2021;19:15. [Crossref] [PubMed]
48. Stein CJ, Colditz GA. Modifiable risk factors for cancer. Br J Cancer 2004;90:299-303. [Crossref] [PubMed]
49. Aregay M, Lawson AB, Faes C, et al., editors. Bayesian multiscale modeling for aggregated disease mapping data. Proceedings of the Third ACM SIGSPATIAL International Workshop on the Use of GIS in Public Health; 2014.
50. Muchie KF, Wanjoya AK, Mwalili SM. On Hierarchical Bayesian Spatial Small Area Model for Binary Data under Spatial Misalignment. Journal of Probability and Statistics 2022;2022:3865626. [Crossref]
51. Dasgupta P, Cramb SM, Aitken JF, et al. Comparing multilevel and Bayesian spatial random effects survival models to assess geographical inequalities in colorectal cancer survival: a case study. Int J Health Geogr 2014;13:36. [Crossref] [PubMed]