Study design and participants
Our study was a cross-sectional analysis of a nationally representative dataset, the 2007 National Survey of Mental Health and Wellbeing (NSMHWB), which consisted of a series of face-to-face interviews conducted by the Australian Bureau of Statistics (ABS) from August to December 2007. Respondents were randomly selected from a stratified, multistage area probability sample of respondents’ homes. More methodological information could be found elsewhere . There were 14,805 eligible dwellings out of an initial sample of 17,352 dwellings due to all household members being out of scope or vacant dwellings. Of these, the final data set consisted of 8,841 respondents (60% response rate) aged 16 to 85 years of age and living in private dwellings . No missing data strategy was used due to the low rate of missing data (2.6%): 21 due to no HRQoL score, 34 due to log-transformed HRQoL score, 180 due to BMI and 6 due to exercise level.
Multimorbidity was identified from a pre-specified list including the following self-reported conditions that significantly contribute to the global burden of illness and injury [12–14]: asthma, cancer, stroke, heart or circulatory conditions (CVD), gout, rheumatism or arthritis, diabetes or high sugar levels, major depressive disorder (MDD) and anxiety disorder (including agoraphobia, with or without panic disorder, generalized anxiety disorder (GAD) and social phobia). Each chronic condition was coded as present or absent . The diagnosis of mental disorders was established using the World Mental Health Survey Initiative version of the World Health Organization's Composite International Diagnostic Interview, version 3.0 (WMH-CIDI 3.0) , which is a comprehensive and fully structured diagnostic interview. The timeframe was a diagnosis in the 12 months prior to the interview. Diagnosis of physical chronic conditions was determined from a pre-specified list by whether the respondent had ever been told by a doctor or nurse that they had these conditions, and stroke was assessed using self-reported stroke symptoms .
In the count method, multimorbidity was defined as “two or more” chronic conditions occurring at the same time. To test the validation in cut-off of count based method, the definition of multimorbidity “having 3+ chronic conditions at the same time in one individual” (known as complex multimorbidity)  was used as well. In the cluster-based method, hierarchical clustering was used to identify the common clusters of multimorbidity as chronic health conditions can co-occur via some sharing underlying genetic, environmental, or behavioural risk factors [16–18]. Assuming N variables, the hierarchical approach initially treated each variable as a cluster before merging the two closest variables into a new cluster. This step was repeated until all variables were merged into one cluster of size N. Jaccard’s coefficient was used to calculate the distance of the binary variables (absence or presence of conditions) [16, 19]. The results may vary depending on the different distance calculation methods. Both Ward’s and the average linkage methods have been widely used, with the former considered more appropriate for clusters with equal numbers of observations  and the latter recommended to avoid large or tight compact clusters that result from the single linkage and the complete linkage methods . Therefore, we used the average linkage method in this study and used the cluster stopping rule to aid in selecting partitions .
The Assessment of Quality of Life (AQoL-4D) instrument was used to measure quality of life due to its brevity , sensitivity and robustness . Four dimensions (independent living, mental health, relationships and senses) consisting of three items each were included for scoring. Then, five new variables, four dimension scores and one overall instrument score, which ranged from −0.04 to 1, were created. A score of 1.00 indicated the best quality of life equal to perfect health, and 0.00 indicated quality of life equal to death, and negative values (0 to −0.04) indicated quality of life worse than death .
Univariate analyses with a 0.25 p-value cut-off were performed to screen the covariates before the second round of screening, involving multivariate analyses. A cut-off of a 10% change in the exposure variable’s coefficient estimate in the multivariate model was adopted to identify the “important” variables influencing the association between outcome and exposure. Covariates that remained after these procedures were utilized throughout all subsequent analyses conducted in this study.
The covariates screened in this study included sex, age, registered marital status (married, unmarried), labour force status (employed, unemployed, not in the labour force), area of relative socioeconomic disadvantage (decile 1 = most disadvantaged, decile 10 = least disadvantaged), body mass index (BMI = self-reported weight/self-reported height2), smoking status (current, ex-smoker, never) and level of exercise (low: <1600 min; moderate: 1600–3200 min, or >3200 min but <2 h of vigorous exercise; high: >3200 min, including ≥2 h of vigorous exercise), which was also used to assess exercise intensity (exercise intensity scores were multiplied by minutes per fortnight) .
Due to the complex survey design used in the NSMHWB2007, a weighting strategy was applied to infer results for the total in-scope population by allocating a ‘weight’ to each sample unit. The weight was an indication of how many population units were represented by the sample unit . As a result, Jack-knife delete-a-group survey adjustment replication methods were used to calculate the standard errors (SEs) . This process accounted for the stratified multistage sampling framework used in the NSMHWB2007 and adjusted for non-response, which may cause some groups to be over- or under-represented . The theory behind the Jack-knife delete-A-group replication method is that, the sampling variability between repeated samples can be estimated by repeatedly taking random but unbiased sub-samples from the achieved sample and then computing the variance of the sub-samples (after taking the smaller sample size into account). Jack-knife estimation replicates are created by deleting one group at a time, and then weighting the other groups from the same stratum to adjust for the removal. Therefore, each replicate provides an unbiased estimate of the population mean, and the variance of those estimates provides an estimate of the full-sample of the variance. In short, application of these methods ensures the sample is representative of the Australian population, which ensures that subsequent findings are generalizable to Australian adults (n = 16,015,000) in 2007 .
Frequencies and percentages calculated with jack-knife SEs were used for the descriptive analysis. Hierarchical clustering analysis was used to identify common clusters of multiple chronic conditions. Linear regression models were used to examine the associations between the HRQoL scores and the multimorbidity clusters. In each regression model, the dependent variable was the HRQoL score, and the independent variable was one cluster (present or absent), for example, “whether presenting 2+ chronic conditions” in model-1. The p value for the trend of continuous variables in the linear regression models was given. A log-transformed HRQoL score was used due to its negatively skewed distribution, which resulted in 55 missing values. A two-tailed p-value of <0.05 was considered statistically significant. To test the validation in clusters of hierarchical clustering, sensitivity analyses were performed that including factor analysis , principal component analysis  and K-means clustering , which have been used in previous studies. All analyses were performed using Stata/SE Version 12.1 (StataCorp, College Station, TX, USA).