We agree with the author that in this initial paper we present broad findings exploring novel relationships at scale in a large longitudinal electronic cohort linking primary care and educational data. We agree that a finer-grain analysis of individual pupils’ achievements and scores within key stages may give interesting results. We focused on dichotomised achievements at key stages as this is the indicator relevant to and generally acted on by schools.

We agree that we have used the terms intellectual disability and difficulty interchangeably and this may be considered problematic. We have defined intellectual disability within the paper and this is based on previously published work.Reference Brophy, Kennedy, Fernandez-Gutierrez, John, Potter and Linehan¹ However, pupils with intellectual disability will be less likely to achieve their key stage results (exposure) and may be more likely to have depression or self-harm (the outcome). As such having intellectual disabilities is considered a confounder related to both the outcome and the exposure. If we had considered it as a variable with co-linearity (for example achievement can be predicted from having an intellectual disability so there is no need to include both in the model) and left it out of the model we run the risk of confounding bias in our analysis. We chose to take a conservative approach and treat it as a confounder and include it in the model.

In our paper, we included, as supplementary material, the Read codes used to identify conduct disorder. These were developed in conjunction with two clinicians. Lists developed in this way are used frequently in e-cohort studies of this type. However, ideally when using Read code lists we would hope to use externally validated lists. We have done this for depression and self-harmReference Cornish, John, Boyd, Tilling and Macleod^2, Reference John, McGregor, Fone, Dunstan, Cornish and Lyons³ but at the time of extracting data for this study we did not have access to a validated list for conduct disorder.

Children with special educational needs were identified using a variable in the educational data-set. They have been included in the analysis. Although we adjusted for intellectual disability we did not for special educational needs. We made this decision based on the broad nature of special educational needs status, which includes those with hearing impairment and dyslexia. The majority of children with special educational needs status follow the national curriculum.

We disagree with the letter authors in that one of the advantages of linked primary care data in Wales is the whole population coverage rather than a sampled one, such as that currently available in England. We are, therefore, able to anonymously link across general practices and individuals in Wales so we can identify house moves and continue to follow any pupil registered with a general practitioner or attending any hospital in Wales. This also applies to deprived populations. Therefore, we do not believe we have underestimated the association for the reason suggested.

In Wales the ethnic minority group is only approximately 2.1% of the population in 2001. We do not feel ethnicity will greatly affect the results in this analysis. Adverse childhood experiences, bullying, absence, exclusion from school and other events are important factors. However, we would argue that rather than confounders these are on the pathway to explaining the link between educational achievement and poor mental health and self-harm. As such it would be a mistake to adjust for them.

We strongly refute that there is ‘no analysis in support of this interpretation’ regarding no evidence among those who self-harm of decline in attainment in primary school. We demonstrated that the children who self-harm were doing as well as those who do not self-harm at age 11 (the end of primary school). They cannot be identified from primary school using key stage attainment results. We used the cut-off that schools use for ‘achieved’ key milestones or did ‘not achieve’ key milestones. These are the cut-offs that schools report and act upon. As such they are the most useful in feeding findings back to schools to enable them to translate these findings into practice. Self-harm and attainment were associated in secondary school in our study.