We thank Batra and colleagues for their comments about our article and respond to their queries below.

The design of the Longitudinal Study of Australian Children has been thoroughly described previously,Reference Soloff, Lawrence and Johnstone¹ we provide a brief overview in our article but did not have the space to go into detail. In regards to the areas of particular concern raised: all children enrolled in the Australian Medicare system who were aged 4 years or <12 months during recruitment were eligible to participate; the only exclusion was that only one child from each family could participate, thus in the instance of multiple births only one child from the family was eligible. The data were collected using a combination of surveys and interviews. In instances where parents had insufficient English reading ability to complete the survey then an interview was conducted and for those of non-English speaking background interpreters were available.

We agree that the exclusion of those with less educated parents, more mental health problems and disturbed family dynamics from analyses may have skewed the results. However, our primary finding was that children are not having their mental health needs met under the current healthcare system. Thus, having data to analyse from these more vulnerable groups would likely not have had an impact on our conclusions.

We used Mplus to conduct our latent class growth analysis, using full information maximum likelihood (FIML) to account for missing data. To ensure our findings were rigorous and reflected the actual data as closely as possible we chose to only include participants with data from at least three time points in analyses. The Medicare data we used for health service usage is collected through administrative data linkage and as such there is not an impact from attrition. Although there was sample attrition in terms of surveys completed over the six waves of data collection, few families withdrew from the study. Thus, our use of FIML and data linkage resulted in our analytic sample of n = 4348.

Batra & Sharma raise an excellent point about whether children who receive services benefitted from these. We have since completed further analyses that show that the receipt of intervention does not appear to improve outcomes for these children.Reference Ride, Huang, Mulraney, Hiscock, Coghill and Sawyer²

Thank you for pointing out that the supplementary figure was missing, we have sent this to the Journal and requested they add it to the supplementary material. Figure 1 in the article contains a typo, the number ‘15’ on the x-axis should be the number ‘12’.