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Spatial temporal modeling of hospitalizations for fall-related hip fractures in older people

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Abstract

Summary

The study determined the spatial temporal characteristics of fall-related hip fractures in the elderly using routinely collected injury hospitalization and sociodemographic data. There was significant spatial temporal variation in hospitalized hip fracture rates in New South Wales, Australia.

Introduction

The study determined the spatial temporal characteristics of fall-related hip fractures in the elderly using routinely collected injury hospitalization data.

Methods

All New South Wales (NSW), Australia residents aged 65+ years who were hospitalized for a fall-related hip fracture between 1 July 1998 and 30 June 2004 were included. Bayesian Poisson regression was used to model rates in local government areas (LGAs), allowing for the incorporation of spatial, temporal, and covariate effects.

Results

Hip fracture rates were significantly decreasing in one LGA, and there were no significant increases in any LGAs. The proportion of the population in residential aged care facilities was significantly associated with the rate of hospitalized hip fractures with a relative risk (RR) of 1.003 (95% credible interval 1.002, 1.004). Socioeconomic status was also related to hospitalized hip fractures with those in the third and fourth quintiles being at decreased risk of hip fracture compared to those in the least disadvantaged (fifth) quintile [RR = 0.837 (0.717, 0.972) and RR = 0.855 (0.743, 0.989) respectively].

Conclusions

There was significant spatial temporal variation in hospitalized hip fracture rates in NSW, Australia. The use of Bayesian methods was crucial to allow for spatial correlation, covariate effects, and LGA boundary changes.

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Acknowledgement

Robin Turner was employed as part of the New South Wales Biostatistical Officer Training Program funded by the New South Wales Department of Health while undertaking this work based at the New South Wales Injury Risk Management Research Centre. Caroline Finch was supported by a National Health and Medical Research Council Principal Research Fellowship.

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Correspondence to C. F. Finch.

Statistical appendix

Statistical appendix

Case selection criteria

We investigated our case selection criteria through the use of a linked dataset, in which a unique identifier allows all episodes of care for an individual to be identified. We selected all episodes of care with a principal diagnosis code of hip fracture (S72.0–S72.2) and first external code of a fall (W00–W19) for the period July 2003 to June 2004 for period aged 65+ years. Our aim was to see whether our case selection criteria—i.e., excluding episodes of care for which the source referral was a transfer from another hospital or a type change admission—would correctly identify an individual’s first episode of care for a hip fracture.

Table 3 Case selection criteria versus linked dataset

We found that, of the 5,300 first episodes of care for hip fracture, our case selection criterion was able to identify 4,763/5,300 = 89.9%. Of the 1,276 subsequent episodes of care, the criterion successfully excluded 889 = 69.7% of these. In total, the use of the case selection criterion would underestimate the number of first episodes of care for hip fractures by about 0.9%.

Bayesian modeling

We fitted a Poisson regression model for the SARs across the 6 years for each of the 175 LGAs [20]. The model took the form Y ij ∼Poisson (E ij θ ij ), where log (θ ij ) = overall rate + spatial effect + uncorrelated heterogeneity + boundary change effect + covariates of interest + temporal effect, or put mathematically:

$$\begin{aligned} & \log {\left( {\theta _{{ij}} } \right)} = \alpha + u_{i} + v_{i} + \beta _{1} X_{{1ij}} + \delta _{1} X_{{1ij}} + \beta _{2} X_{{2ij}} + \delta _{2} X_{{2ij}} \\ & \quad \quad \quad \quad + \beta _{3} X_{{3ij}} + \delta _{3} X_{{3ij}} + \beta _{4} X_{{4ij}} + \beta _{5} X_{{5i}} + \beta _{6} X_{{6i}} \\ & \quad \quad \quad \quad + \beta _{7} X_{{7i}} + \beta _{8} X_{{8i}} + \beta _{9} t_{j} + \delta _{i} t_{j} , \\ \end{aligned}$$

In this model, θ ij represents the relative risk of hospitalized hip fracture for the ith LGA at the jth year, and the term α denotes the overall relative risk. The terms u i and v i denote the spatial correlation term and uncorrelated heterogeneity, which is extra variation that is spatially uncorrelated, respectively. Spatial correlation typically means that rates are more similar in areas that are geographically closer. Using standard Bayesian approaches [20], it is assumed that u i has a conditional autoregressive prior distribution, so that

$$u_{i} |u_{j} ,j \ne i\tilde{}N{\left( {\frac{1}{{{\sum\limits_j {w_{{ij}} } }}}{\sum\limits_j {w_{{ij}} u_{j} } },\frac{{\tau ^{2}_{u} }}{{{\sum\limits_j {w_{{ij}} } }}}} \right)},$$

for weights w ij  = 1 if i and j are adjacent and 0 otherwise. The term τ u has a gamma prior distribution and accounts for the spatial correlation in the model by smoothing the estimates in a LGA using the information from adjacent neighbors.

The term \(\beta _1 X_{1ij} + \delta _1 X_{1ij} + \beta _2 X_{2ij} + \delta _2 X_{2ij} + \beta _3 X_{3ij} + \delta _3 X_{3ij} \) was used to represent the three boundary change terms (X 1, X 2, X 3). This means that the boundary change is modeled as a step function at the time the boundary change occurs, using a step function rather than a gradual change with was considered appropriate given that the data is being modeled per year, and we do not expect boundary changes to have an impact greater than the year they occurred in. Each boundary change term included an interaction with a conditionally autoregressive spatial term (δ 1, δ 2, δ 3), to allow the boundary change to be different in each LGA. This was necessary because only a small number of LGAs (26) had boundary changes over the study period, and this model allows each change to be different. In a similar manner, the regression coefficients for changes across time were included in the model as β 9 j  + δ i j to allow for a different time trend in each LGA.

Finally, the term \(\beta _4 X_{4ij} + \beta _5 X_{5i} + \beta _6 X_{6i} + \beta _7 X_{7i} + \beta _8 X_{8i} \) represents the covariates included in the model. The first term represents the number of residents in aged care facilities by time and LGA. The next four terms model the effects of four levels of socioeconomic status when compared to the most disadvantaged quintile. In this particular formulation of the model, the relationship between the population in aged care facilities, SES, and the rate of hip fractures is assumed to not depend on LGA. All the β’s in the model have normal prior distributions.

Using standard Bayesian approaches [20], the posterior distributions for the parameters in the model were sampled using Markov Chain Monte Carlo methods. A burn-in of 25,000 iterations was used to ensure stationarity for each chain. A further 20,000 iterations were then retained for the posterior samples.

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Turner, R.M., Hayen, A., Dunsmuir, W.T.M. et al. Spatial temporal modeling of hospitalizations for fall-related hip fractures in older people. Osteoporos Int 20, 1479–1485 (2009). https://doi.org/10.1007/s00198-008-0819-4

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