Participants and procedure
Data were collected from 247 infants from the British Autism Study of Infant Siblings , across two phases of the study based on time of recruitment. Infants were considered at high (n = 170) and low (n = 77) familial risk for ASD based on having or not an older biological sibling with ASD. Fifty-four high-risk and 50 low-risk infants participated to phase 1 , while an independent cohort of 116 HR and 27 LR participated to phase 2. LR controls were full-term infants recruited from a volunteer database at the Birkbeck Centre for Brain and Cognitive Development. At the time of enrolment, none of the infants had been diagnosed with any developmental condition. Infants were followed longitudinally on four visits: 8 months (mean = 8.1, standard deviation (SD) = 1.2), 14 months (mean = 14.5, SD = 1.3), 24 months (mean = 25.0, SD = 1.8), and 36 months (mean = 38.8, SD = 3.0). To allow testing for quadratic growth, the final sample included infants with data available from at least 3 visits, leading to a final sample of 240 infants (74 LR and 166 HR). Study researchers were aware of infants’ risk status but were blind to clinical outcome.
The Vineland Adaptive Behavior Scale (VABS-II ) is a semi-structured parent-report questionnaire (at 8 and 14 months) or parent interview (at 24 and 36 months) assessing infant’s adaptive behaviour in everyday settings. The items address personal and social functioning in four different domains (standard scores; mean = 100, SD = 15): communication (Comm), daily living skills (DL), socialisation (Soc), and motor abilities (Mot). Standard scores from the 4 domains between 8 and 36 months were included in our main analysis to identify homogeneous classes of infants.
Verbal and non-verbal cognitive development was measured at each visit by the Mullen Scales of Early Learning (MSEL ), a standardised developmental measure used to assess cognitive functioning between birth and 68 months. Scores are obtained in the following five domains: gross motor (GM), visual reception (VR), fine motor (FM), receptive (RL), and expressive language skills (EL). The Mullen Scale provides normative scores for each scale (T-scores mean = 50, SD = 10) and a single composite score representing general intelligence (early learning composite (ELC) standard score mean = 100, SD = 15). ELC scores between 8 and 36 months were included in our analyses to characterise the developmental level of the identified classes.
Early ASD symptoms
The Autism Diagnostic Observation Schedule (ADOS ), a standardised diagnostic instrument; the Autism Diagnostic Interview-Revised (ADI-R ), a structured parent interview; and the Social Communication Questionnaire (SCQ ), a screening tool for ASD, were administered at 36 months to assess autism symptoms. Of note, the ADI-R was not administered to LR infants from phase 1 (n = 47) and missing values were imputed through expectation maximisation on SPSS .
To evaluate the end level of symptom severity of the identified classes, we included in our analysis the ADOS Calibrated Severity Score (CSS) obtained from the raw total scores (CSS-Tot), and Social Affect (CSS-SA) and Restricted and Repetitive Behavior (CSS-RRB) domains; the ADI-R domain scores for the Social (ADI-Soc), Communication (ADI-Comm), and Repetitive Behaviors and Interests domains (ADI-RBI); and the SCQ total score (SCQ-Tot).
The LR group was based on having an older full sibling with typical development. LR infants received no formal clinical diagnoses, but none of them had a community clinical ASD diagnosis at 36 months. In particular, no ADI-R was administered to LR in phase 1, who did not receive an outcome evaluation. In phase 2, LR infants were administered the ADOS and ADI-R and received an outcome evaluation at 36 months, but none of them raised any concern for ASD or atypical development. HR siblings received a clinical outcome evaluation at 36 months and were subsequently grouped into siblings with ASD (HR-ASD), with atypical (non-ASD) development (HR-Atypical), and with typical development (HR-Typical).
Expert clinical researchers reviewed all available information at 24 months and 36 months and assigned clinical consensus best estimate diagnosis of ASD (HR-ASD) according to ICD-10  or DSM-5 criteria depending on the recruitment phase . Diagnoses were reviewed for differences in categorisation and considered to be similar. Among high-risk infants who did not meet criteria for ASD, a subgroup of siblings was classified as “atypical” (HR-Atypical) based on ADOS and/or ADI-R above ASD threshold, and/or MSEL more than 1.5 standard deviations below average on visual reception and/or receptive language and/or expressive language and/or early learning composite (n = 15) scores. Finally, siblings who did not meet the criteria for ASD or atypical development were classified as HR-Typical.
Data analysis: an overview
We used a three-step approach to identify latent classes of adaptive behaviour and profile them through associations with external variables. First, the four domains of the Vineland were modelled in parallel through growth mixture modelling to identify latent class trajectories of adaptive behaviour on 4 time-points between 8 and 36 months. Second, infants were assigned to latent classes based on posterior probabilities of class membership. Third, the identified classes were characterised in terms of clinical outcome and symptom severity at 36 months and longitudinal cognitive development.
Identification of latent class trajectories
We chose growth mixture modelling to identify distinct mixtures of trajectories within population. As opposed to other methods such as latent class growth curve modelling , which assumes a homogeneous pattern of behaviour within class, growth mixture modelling  allowed us to capture the complexity of adaptive behaviour in developmental variation across individuals.
We investigated the pattern of missing data for the four domains of adaptive behaviour by testing its association with gender and clinical outcome at 36 months. Differences in gender were not significant, while the proportion of missing data at 24 months was significantly dependent on clinical outcome at 36 months (χ2  = 8.23, p = 0.04), with HR-Atypical having most missing data. However, differences in outcome were not significant at other time-points, providing reasonable evidence for a pattern of data missing at random. Thus, individuals with missing data were included in the analysis, allowing us to use all available information. In fact, individual trajectories of adaptive behaviour were modelled on data available at an individual level.
Real age was included as a fixed effect while random effects on intercept and slope were modelled on an individual level. Multiple models were tested based on the polynomial degree of the growth curve, the variance/covariance matrix, and the number of classes. Models were run with 1 to 6 classes, and each class number was run separately 50 times to control for local maxima. The best model was determined in terms of data fitting and parsimony based on having lower values of Bayesian information criterion (BIC), Akaike information criterion (AIC), negative log-likelihood, and higher average class posterior probability . Analyses were performed using the multlcmm function from the lcmm package in R .
The classes derived from parallel process growth mixture modelling were subsequently compared on adaptive behaviour over time through hierarchical mixture modelling . A quadratic mixed model was tested with VABS-II domain scores as outcome variables and real age and class membership as fixed factors, while gender was included as a covariate and random effects on intercept and slope were modelled on an individual level. We investigated the main effects of class, age, age2 and their interaction effects using Wald tests with Satterthwaite approximation for degrees of freedom. Post hoc Tukey’s tests for multiple comparisons were performed for class comparisons and simple main effects analysis. Analyses were implemented using the lme4 software package on R .
Characterisation of latent classes
Classes in adaptive behaviour, as derived from parallel process growth mixture modelling, were further characterised by examining the association of class membership with independent outcome variables. First, we examined the association with ASD symptom severity at 36 months, as measured by the CSS-Tot, CSS-SA, CSS-RRB, ADI-Comm, ADI-Soc, ADI-RBI, and SCQ-Tot scores, through an analysis of variance. For significant differences, classes were compared through post hoc Tukey’s tests for multiple comparisons.
Then, we examined the association of class membership with trajectories of cognitive development, as measured by the MSEL ELC score between 8 and 36 months, through hierarchical mixture modelling . Models were built using the lme4 software package on R , with MSEL ELC scores as outcome variables, real age and class membership as fixed factors, and gender as a covariate, while random effects on intercept and slope were modelled on an individual level. We compared linear and quadratic models on age to select the best fit based on chi-squared tests on the log-likelihood values.