This study adheres to the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) reporting guidelines [13]. We also referred to the Guidelines for Reporting on Latent Trajectory Studies (GRoLTS) checklist where relevant to this cross-sectional analysis [14].

The Longitudinal Study of Australian Children (LSAC) is a nationally representative, dual cohort cross-sequential study of children and families in Australia. Initiated in 2004 and followed up biennially, it collects information on child development and wellbeing over the life course in relation to topics such as housing, family, peers, education, health, and healthcare utilization [15]. For its Kindergarten cohort (K cohort), 4983 children born between March 1999 and February 2000 (aged 4 to 5 at Wave 1 data collection) were randomly selected from the Medicare database. Survey instruments were tested for reliability and validity [16], and details of the study design were described elsewhere [17]. We analyzed Wave 1 data of the K cohort. Participants with missing data on housing variables were excluded, leaving a final sample of 4355 children aged 4 to 5 years.

All questions related to housing in LSAC were examined, and nine binary variables were used to identify latent classes. Unaffordability was indicated by parents paying more than 30% of income on housing costs when the household income is below 40% of the national income distribution(0, no; 1, yes). Fuel poverty was measured by parents indicating they have been unable to heat or cool their home (0, no; 1, yes). Noise was measured by interviewer-reported background noise (0, moderate or no background noise; 1, loud background noise). External condition was derived from interviewer-assessed external conditions of the dwelling (0, well-kept condition; 1, poor or badly deteriorated condition). Housing tenure was broadly grouped into two categories (0, homeownership; 1, renting). Dwelling type was categorized according to whether the family lives in the house or not (0, living in houses; 1, not living in houses (e.g., living in apartments and mobile homes)). Cleanness was measured by interviewer-observed clutters in visible rooms (0, uncluttered; 1, cluttered). Crowding was measured by the ratio of bedrooms to the number of people in the household. Drawing on previous Australian research on crowding, we determined households as crowded if the ratio is equal to or greater than two [18]. Instability was indicated by parents reporting moving three times or more since the birth of the child.

The following self-reported sociodemographic variables were obtained from the Wave 1 survey: gender (1, male; 2, female); main language spoken at home (1, English; 2, others); maternal education (1, year 11 or below; 2, year 12 or certificate; 3, bachelor degree or above); single parenthood (0, no; 1, yes); low income (defined by income below the 40% of national distribution, 0, no; 1, yes); residing area remoteness (1, urban cities; 2, regional or remote area).

The 23-item pediatric quality of life inventory (PedsQL) was used to measure general health and development in children and young people [19]. It includes four constructs: physical functioning (8 items), emotional functioning (5 items), school functioning (5 items), and social functioning (5 items). The score of each construct ranges between 0 and 100, with higher scores indicating better quality of life. A change of 4.5 points on the PedsQL score is considered a clinically important difference [20].

We also assessed the prevalence of disability and injury. Disability (yes/no) was self-reported by mothers through a question “Does your child have any long-term limiting health conditions?,” and injury (yes/no) was also reported by mothers through a question “Was your child injured in the last 12 months?”.

For a subsample who indicated use of healthcare services in the last 12 months (n = 3375), we described the type of services used, including uses of GP services, use of maternal and health services (i.e., a primary health service for families with children from birth to school age, including 24-h phone line, nurse visits, and education programs), use of emergency wards, and hospital outpatient care.

Latent class analysis (LCA) is a statistical technique that seeks to identify an underlying categorical latent variable that divides a population into mutually exclusive and exhaustive subgroups [21]. The aim of LCA is to maximize homogeneity within subgroups and maximize heterogeneity between groups. We use this technique to identify subgroups of children experiencing similar housing disadvantages. The numbers of latent classes (i.e., housing typologies) were tested incrementally from 2 to 7. The decision on the best-fit model was made considering the Akaike information criteria (AIC), Bayesian information criteria (BIC), and interpretation of the typologies. Lower values of AIC and BIC indicate a better balance between goodness-of-fit and complexity [22]. Alternative indices, such as the adjusted BIC (aBIC), were not used given the adequacy of our sample size [23]. Individuals were then assigned to the typology in which they had the highest posterior probability. Then, we described and compared the social and economic characteristics of each typology by crosstabulation and chi-square tests.

To assess health inequities by each housing typology, we used generalized linear regression with robust standard errors. For continuous health outcomes (i.e., quality of life measures), linear regression with identity link was used; for binary health outcomes (i.e., injury, disability, and health services use), log-binomial regression was used [24]. We then plotted the posterior prevalence/score of health, developmental, and health service use outcomes by each housing typology, adjusting for children’s gender, maternal age, and sample weights. Analyses were done in STATA SE 17.0 (StataCorp, 2021).

The study funders had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.