# 2.3 Statistical methods

Page last updated: August 2010

## 2.3.1 Population rates

Crude, age–standardised and age–specific rates are presented, as indicated, in this report. Rates are adjusted for age to facilitate comparisons between geographic regions and across time, because the age structures of populations may vary across time or between areas. Standardised rates were calculated using the direct standardisation method with the Australian estimated resident population (persons) as at 30 June 2001 as the standard population (as per ABS and Australian Institute of Health and Welfare (AIHW) convention). For ease of interpretation, rates of Better Access uptake and other services are expressed per 1,000 population, unless noted otherwise.

## 2.3.2 Deflators

Expenditure (benefits charged, fees charged and co–payments) on Medicare services was converted to 2009 dollars to adjust for inflation, using the ratio of Consumer Price Index values in each year to 2009.31

## 2.3.3 Statistical analyses

All analyses were undertaken using PASW Statistics version 17.0 (SPSS Inc., Chicago IL, 2009) and Stata version 11.0 (StataCorp LP, College Station TX, 2009).

### Predictors of uptake of Better Access and other services

Negative binomial rate regression models were used to examine predictors of uptake of Better Access and other services, using a range of aggregated datasets depending on the question being addressed. Negative binomial regression was selected because it is an efficient approach to analysis that allows for the overdispersion (i.e. where the variance is greater than the mean) that commonly characterises count data such as health service utilisation data. It also accommodates non–normal distributions that are also common in health service utilisation data, and thus avoids the need to transform non–normally distributed data in order to satisfy the assumptions of general linear model analyses.32 In cases where overdispersion is not present, Poisson regression techniques are preferred. Hence for each of the models evaluated, the Pearson chi–square statistic (χ2) was calculated. In all relevant cases the value of χ2 divided by the number of observations (n) was greater than 1, which indicates overdispersion, hence the negative binomial model was considered more appropriate. The dependent variable is specified as the count of the health service measure of interest (e.g., number of persons using Better Access services or number of Better Access services used). The negative binomial rate regression model adjusts for the size of the population in each stratum of the dataset (e.g., a Division of General Practice) by incorporating the logarithm of the population size as an offset term. Thus, taking the exponent of each β regression coefficient provides the rate ratio (RR) for a one unit change in the corresponding independent variable.
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### Time trends in uptake rates of Better Access and other services

Negative binomial regression models were also used to assess the magnitude and statistical significance of trends in uptake rates for Better Access and other services over time. In chapter 3 and chapter 4 these analyses examined trends in uptake of Better Access services (in total, and by various groupings) since the introduction of the initiative, and whether there has been a change in trend as the initiative has become more established. The period of interest for these analyses was from the March 2006 quarter (the first full quarter of Better Access operation) to the end of the March 2010 quarter (the most recent data available to us). The period of establishment of Better Access was defined as the first calendar year of operation (i.e., 2007) and the period post-establishment as being from 2008 onwards.

Three models were used (based on the procedure outlined by Chapman and colleagues33) reflecting the research questions outlined above: Model (a) estimates the trend (measured as the average quarterly change in rate) in uptake in the first calendar year of Better Access; Model (b) estimates the trend (measured as the average quarterly change in rate) in uptake after the first calendar year of Better Access; and Model (c) estimates the effect on trends in uptake preand post– the establishment period. In Model (c) the relative trends in pre/post rates are estimated by the interaction term in a model including terms for pre/post group, time and pre/post group by time.

In chapter 8 and chapter 9 negative binomial regression was used to examine trends in uptake of other services (i.e., use of antidepressant and anxiolytic medications as recorded on the PBS, non–Better Access MBS services, and ATAPS psychological services) before and after the introduction of Better Access, and whether there has been a change in trends in uptake of these services associated with the introduction of Better Access. The period of interest for these analyses was from the March 2004 quarter (two years prior to the first full quarter of Better Access operation) to the March 2009 quarter (for non–Better Access MBS services, and ATAPS psychological services) and the December 2009 quarter for PBS data. Because Better Access services were introduced part–way into the December 2006 quarter, models of trends pre/post Better Access exclude the December 2006 quarter.

Three models were used, reflecting the three research questions outlined above: Model (a) estimates the trend (measured as the average quarterly change) in uptake of relevant services before the introduction of Better Access; Model (b) estimates the trend in uptake of relevant services (measured as the average quarterly change in rate) in uptake after the introduction of Better Access; and Model (c) estimates the effect on trends in uptake of relevant services associated with the introduction of Better Access. In Model (c) the relative trends in pre/post rates are estimated by the interaction term in a model including terms for pre/post group, time and pre/post group by time.

### Synthetic modelling of population need (Chapter 5)

Chapter 5 uses a synthetic estimation and modeling approach to investigate whether Better Access services and expenditure are being distributed among Australian adults according to need. The procedure is based on previous studies34, 35 and involves 5 steps:

#### Step 1: Defining geographic units.

Divisions of General Practice were chosen as the geographic unit for analysis. Divisions are funded by the Australian Government Department of Health and Ageing to co–ordinate local primary care services, and to improve the quality of general practice care and health outcomes for local communities.36 As already described, the Medicare Financing and Analysis Branch of the Department of Health and Ageing provided population structure estimates for each of the 113 Divisions of General Practice in Australia. For the current analyses, the relevant population structures within each Division involved gender (male, female), age group (16–19, 20–24, 25–29, 30–34, 35–39, 40–44, 45–49, 50–54, 55–59, 60–64, 65–69, 70–74, 75–79, 80–84 years)h and section of state (capital cities, other metropolitan regions, remainder). This yielded 84 strata (2 gender x 14 age group x 3 section of state categories) within each Division.

#### Step 2: Deriving a measure of mental health need.

Level of adult population–based mental health need was modelled using data from the 2007 NSMHWB (see section 2.2.4 for an overview of the survey and explanation of the measures used in the current evaluation). For the current study, mental health need was defined as having at least one of the following: (1) an ICD–10 12–month affective, anxiety or substance use disorder; (2) 12–month symptoms (but no ICD–10 lifetime disorder); (3) any psychiatric hospitalisation in the past 12 months; (4) high or very high level of psychological distress on the K10 measure; (5) 7 or more days out of role; or (6) any suicidality in the past 12 months.

The approach to modelling mental health need was inclusive. That is, it took into consideration the groups to whom Better Access services are principally targeted (namely the common mental disorders including affective, anxiety and substance use disorders), as well as other factors that may prompt individuals to seek treatment. This decision was guided by a previous study which, using data from the 2007 NSMHWB, estimated that 81.7% of users of Better Access services provided by allied health professionals had a 12–month ICD–10 affective, anxiety or substance use disorder, and a further 11.5% of users had at least one other indicator of potential need (which included lifetime disorder, 12–month symptoms or lifetime hospitalisation for a mental disorder).37 Definitions of mental health need based on diagnostic criteria alone were also considered, but were thought to be too restrictive in scope and to not fully represent the range of reasons for which people may use Better Access services.

Using age , gender, and section of state information collected by the 2007 NSMHWB, the rates of mental health need for each of the 84 population strata were calculated. By taking this population category data from the 2007 NSMHWB, and weighting each Division of General Practice according to its population structure, it was then possible to model the percentage of each Division with mental health need.
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#### Step 3: Other explanatory variables.

A range of other Division–level variables were also obtained for consideration as independent variables in the analyses. These included:

• A measure of GP workforce supply. The supply measure was the count of full–time workload equivalence (FWE) of GPs in each Division in 2008–09. The GP FWE is a measure of workload that takes into account the differing working patterns of GPs. FWE is calculated by dividing each doctor's Medicare billing by the average billing of full–time doctors for the year. The FWE are allocated to the Division in which the GPs' services are claimed, thus accounting for instances where a GP has worked in more than one Division of General Practice. The GP FWE estimates were obtained from the Primary Health Care Research and Information Service website25, and are based on data from the Department of Health and Ageing.

• Indicators of potential to access services. These included: (1) eight State/Territory indicators (yes, no) specifying the state or territory in which each Division of General Practice is located; and (2) the percentage of the population in each Division living in a remote locality (as judged by RRMA categories 6 and 7). This measure was selected because, as shown in Chapter 3 of this report, the most marked differences in Better Access uptake rates are between people in remote locations as compared to all other locations.

• Measures of other Divisional characteristics. These included: (1) the percentage of Division population (aged 15 years and over) participating in the labour force; (2) the percentage of Division population unemployed; (3) the percentage of Division population living in localities of greater relative socioeconomic disadvantage (as defined by IRSED deciles 1 to 2). The latter measure was selected because it takes into account that the distribution of IRSD deciles in each Divisions varies. As shown in chapter 3 of this report, the most marked differences in Better Access uptake rates tend to be between people in areas of greater socioeconomic disadvantage compared to all other locations. Information about the distribution of IRSD deciles by Division of General Practice was provided by the Medicare Financing and Analysis Branch of the Department of Health and Ageing.25 All other measures of Division characteristics were obtained from the Public Health Information Development Unit website.38

#### Step 4: Defining the outcome measures.

Two outcome variables were derived: (1) total MBS–subsidised Better Access services received in 2009 (crude rate per 1,000 population); and (2) total MBS–subsidised allied health Better Access services received in 2009 (crude rate per 1,000 population). The Medicare Financing and Analysis Branch of the Department of Health and Ageing provided the Better Access service use and population data required to calculate these outcome variables for each of the 113 Divisions. Analyses were conducted using 2009 data, as these are assumed to better represent established Better Access utilisation patterns than earlier years.

#### Step 5: Data analysis.

A series of multivariate regression equations was developed (using Ordinary Least Squares regression) in which total Better Access services used and total allied health Better Access services used were predicted by mental health need and the other explanatory factors. The distributions of the two outcome measures were examined to assess whether they satisfied the assumption of normality for linear regression. The ratio of the skewness and kurtosis statistics to their standard errors indicated no significant departure from normality for either measure.

The best fitting models for the data were obtained using an hierarchical model–building process comprising 5 steps. Step 1 included the GP supply factor variable: GP FWE. Step 2 included the measures of potential to access services: remoteness, and state/territory. Step 3 included the measure of mental health need. Step 4 included other Division characteristics: labour force participation, unemployment, and relative socioeconomic disadvantage. The successive contribution of the variables in each step to the explanatory power of the model was examined using the R2 statistic. Variables that were associated with the outcome variables in univariate analyses at or below the 0.15 probability level were considered for inclusion in the models. In addition, each predictor was retained only if it contributed at least an additional 1% to the variance explained by the model. All candidate variables for analysis were screened for multicollinearity using standard regression diagnostics, including tolerance, variance inflation factors, and variance decomposition proportions. With respect to outliers, extreme cases (standardised residuals > 3) were excluded from the final models.

Divisions of General Practice were weighted to reflect their population size. In an unweighted analysis, each Division of General Practice would have had equal bearing, regardless of its population size. However, as some Divisions are many times larger than others, it was considered that analyses should take this into account.

Data from the 2007 NSMHWB Basic Confidentialised Unit Record File, April 2009 version39 were weighted to account for the differential probability of survey selection and to ensure conformity to known population distributions. Standard errors and 95% confidence intervals (CIs) were calculated using jackknife repeated replication to take account of the complex survey design.

## Footnotes

h The age range was restricted to individuals aged 16 to 84 years because this is the group for which the full range of data required for analysis was available. The 2007 NSMHWB provided individual level information on adults aged 16 to 85 years. MBS Better Access service use data and population structure were available by single year of age up to 84 years, but were aggregated for all ages 85 years and above.