This study followed the reporting principles of the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement [16].

The DNBC consists of approximately 100,000 pregnancies enrolled via general practitioners from across Denmark in 1996–2003 [17]. Mothers and their offspring have participated in multiple follow-ups, with the most recent 18 years after offspring birth. At the 11-year follow-up (2010–2014), approximately half of the caregivers (mostly mothers) responded to an online questionnaire regarding their child’s health and a wide range of questions regarding housing and indoor home environment at the time their child turned 11 years. At the 18-year follow-up, DNBC children were invited to reply to an online questionnaire in which questions on asthma diagnosis, medication and symptoms were asked. Individuals who had relevant data available from the 11-year and 18-year follow-ups were included in this study (Fig. 1).

Flowchart of the invited and participating populations in the 11-year & 18-year data collections of the Danish National Birth Cohort a Individuals who have not withdrawn their consent as of December 2021. b The latest available update from registers was in 2015 when most DNBC children had not yet turned 18 years old c The invitation was mailed by postal service to the parent(s) for whom the child had residential address d One parent could answer more than one questionnaire if more than one of their children was enrolled in the DNBC  e Four individuals were excluded due to very small missing values f Number of parental questionnaires returned and completed, 98.3% filled out by the biological mother, 1.2% by the biological father, 0.1% by others (none biological father or mother, grandparents)  and 0.4 unknown  g Includes 3383 individuals excluded due to returning incomplete questionnaires

Parentally reported data on offspring’s housing conditions in the 11-year follow-up of the DNBC were included as indicators in the LCA model. About forty questions related to housing and indoor home environment were included in the 11-year follow-up questionnaire [18]. This study focuses on the following items:

Second hand smoking (SHS) anywhere inside the house (yes/no), winter candle-burning (seldom/often), exhaust hood use (never-rarely/often-always), type of cooking stove (electrical/gas), fireplace use (no-rarely/yes: weekly or daily), mold in child’s bedroom (yes/no), mold in other rooms (yes/no), moisture in child’s bedroom (yes/no), moisture in other rooms (yes/no), flooding (yes/no), cats and dogs ownership (yes/no), ownership of other pets (yes/no).

Housing age (old < 1994/new ≥ 1994),Footnote 1 housing type (apartment/house (detached and semi-detached)/farm), ownership (own/rent), household density gathered from two variables, dwelling size and number of individuals in the household. The size of the dwelling was reported as square meters, in intervals of 10, so the middle value was taken for all intervals between the lowest and highest value intervals. Household density (individuals/square meter) was divided into tertiles and then dichotomized (low-medium/high).

Following the definition by the MeDALL consortium [19], self-reported current asthma at 18-year was defined based on answering yes to any two of the following three questions: “Have you had wheezing or whistling breathing in the past 12 months”; “Has a doctor ever told you that you had asthma?”; “Are you currently taking medicine for your asthma (inhalators, spray or pills) (Supplementary Table 1).

The following covariates were selected a priori: Offspring’s sex was dichotomized as male or female based on data from the Danish Civil Registration System (DCRS).

Information about child’s age when moving to the current dwelling were retrieved from the DNBC 11-year questionnaire “F025 How old was [child name] when you moved to your current home?”. The variable was dichotomized as (moved/stayed). Individuals who moved after their first birthday were excluded to ensure residential indoor characteristics did not vary substantially during childhood.

Data on the highest attained maternal education, the year before offspring’s birth in the DNBC, were obtained from the Population Education’s Register. Educational level was classified according to the International Standard Classification of Education (ISCED) version 2011, as low (ISCED 0–2), medium (ISCED 3–4), and high (ISCED 5–8) [18]. The highest attained maternal education the year before offspring’s birth was chosen, as the majority of women’s highest education achievement did not change between offspring’s birth and the child’s 11th birthday.

Data on equivalized total disposable household income for the year before offspring's  birth in the DNBC were obtained from the Income Statistics Register [20]. Quartiles were created for each year of study enrolment. The year before birth was chosen since individuals who moved during childhood (after age one) were excluded. This means that purchasing power in the form of equivalized household income around time of birth will generally be most relevant. Additionally, income is more stable prior to child birth than shortly thereafter, due to temporary decreases in income during parental leave [18].

Several maternal and paternal non-communicable diseases (asthma, diabetes, mental disorders, allergies and cardiovascular disease (CVD)), which have been reported to be determinants of housing choices and behaviors influencing indoor environment [18], were retrieved from the 11-year follow-up questionnaire and, for mothers only, combined with diagnoses from the Danish National Patient Register (DNPR) (Supplementary Table 2) [21].

From the Danish medical birth register [22] we retrieved the following variables: Maternal smoking during pregnancy defined as maternal active smoking during early pregnancy (yes/no); parity (nulliparous/parous); Maternal age at delivery (≤ 25/26–30/31–35, > 35); gestational age at birth (term/preterm < 37 weeks of gestation); year of birth (1996–2003) and season of birth defined as follows: Winter (December, January, February), Spring (March, April, May), Summer (June, July, August), Fall (September, October, November).

Asthma among the child’s siblings was retrieved from the DNBC 11-year questionnaire “F098 How many of [child name]’s full siblings (biological) have ever had asthma?” and was dichotomized as (yes/no) answer.

Offspring smoking status at 18 years was retrieved from the DNBC 18-year questionnaire and was dichotomized as (yes/no).

Because participants in the DNBC constitute a selected sample of the general population [23], we performed a loss to follow-up analysis exploring the extent to which our study population, at the 11-year and 18-years follow-up, differed on several important characteristics from those lost to follow-up. In addition, we used inverse probability weighting (IPW) [24] using a reference population, referred to as the eligible population, consisting of all children born in Denmark between 1 June 1997 and 2003, alive and residing in Denmark at their 18th birthday (n = 438,697) (Supplementary Fig. 1). The probability of participation in the study was estimated for each individual using a given set of variables (offspring sex, gestational age at birth, parity, maternal education at birth, maternal age at delivery, maternal smoking and equivalized household income the year before birth) predicting selection into the cohort and loss to follow-up. These variables were obtained from Statistics Denmark and therefore available for all participants as well as non-participants. We estimated a weight for each child (i.e., the inverse of the probability of selection) such that each participant represented not only themselves but also children with similar characteristics that did not participate in the study. Further, we estimated the weights based on the best possible set of existing prediction variables for individuals for whom some of the prediction variables were missing.

To address the first aim of the study, to identify latent classes (i.e., clusters) of children from the DNBC who share similar patterns of exposure to indoor pollutant sources, we performed the following analyses:

First, we determined the optimal number of latent classes by fitting and comparing models using only the indicator variables (secondhand smoking indoor, winter candle-burning, exhaust hood use, type of cooking stove, fireplace use, mold in child’s bedroom, mold in other rooms, moisture in child’ bedroom, moisture in other rooms, flooding, cats and dogs’ ownership, ownership of other pets, housing age, housing type, ownership, household density) without covariates included in the model (Fig. 2). The following criteria for comparing latent class solutions were used: (a) multiple fit statistics starting with 2 classes up to 10 classes based on goodness-of-fit statistics such as G2, the Bayesian information criterion (BIC), the Akaike information criteria (AIC) and the Consistant Akaike information criteria (CAIC), and entropy to evaluate the appropriate number of classes as well as (b) theoretical interpretability [14, 15, 25, 26].

Elbow plot of information criteria values for all latent class analysis models

To address the second aim of the study, to examine the association between membership in the latent classes and current asthma at 18-year, we used the corrected three-step approach by Bolck, Croon, and Hagenaars (2004) (BCH), as adapted by Vermunt (2010) [27,28,29]. Using the BCH method, (1) the parameters of the chosen LCA model were first estimated with covariates (offspring sex, year of birth, season of birth, gestational age at birth, maternal education, maternal smoking, maternal age at delivery, parity, household income, maternal and paternal chronic diseases, asthmatic siblings), then (2) the posterior probabilities of class membership based on this model were used to compute a special weighting variable using the BCH-Adjusted Modal Assignment. In short, the BCH-Adjusted Modal Assignment calculates and applies weights that correct for misclassification or measurement error [27]. Finally, (3) the expected probability of the distal outcome, current asthma at 18-year, within each latent class was estimated by taking a weighted average of the observed values for all class participants using pairwise comparisons of latent classes with Wald Chi-Squared Test providing odds-ratios (OR) [27].

To assess asthma incidence at the 18-year follow-up, analyses excluding individuals with a diagnosis of asthma at the 11-year follow-up were performed (see Supplementary Table 1 for asthma definition at 11-year follow-up). In addition, another set of analyses assessing current asthma at age 18, including smoking status at age 18 in addition to the other covariates, was conducted.

All analyses were conducted in Stata version 17. The following two plugins were used: Lanza, S. T., Dziak, J. J., Huang, L., Wagner, A. T., & Collins, L. M. (2018). LCA Stata plugin users' guide (Version 1.2.1). University Park: The Methodology Center, Penn State [26]; and, Huang, L., Dziak, J. J., Bray, B. C., & Wagner, A. T. (2017). LCA_Distal_BCH Stata function users’ guide (Version 1.1). University Park, PA: The Methodology Center, Penn State [27]. Available from methodology.psu.edu.