We thank Professor Ford and Ms McManus for raising some important questions and welcome extending the debate in this important area. We understand the questions raised by the author to be fourfold and respond to each in turn below.

First, whether estimates presented in our paper^{Reference Deighton, Lereya, Casey, Patalay, Humphrey and Wolpert1} are more reliable than the recent England's Mental Health of Children and Young People (MHCYP) study.² We would like to confirm that we did not claim our data are more reliable than the MHCYP data. Our paper draws on data collected as part of a large-scale, school-based study to explore the extent of mental health problems reported by children and young people and the factors that increase the odds of experiencing these problems. As we noted in the introduction to our paper, the national MHCYP study only reported after our paper was accepted for publication; however, we were able to add reference to the MHCYP survey at the point of revisions as we wanted to alert readers to this important work. We agree that both mental health and mental ill health ‘can be conceptualised in a number of ways’. We would also want to note that there is much debate about how best to determine levels of need and much evidence of lack of precision even when using clinically experienced assessors.^{Reference Clark, Cuthbert, Lewis-Fernández, Narrow and Reed3,Reference Regier, Narrow, Clarke, Kraemer, Kuramoto and Kuhl4} No cut-offs are perfect for estimating prevalences of children with mental health difficulties. In our paper we focus on raised levels of child-reported mental health difficulties in this school-based sample as likely indicators of level of difficulties that might be distressing for the child and potentially disruptive for the class and thus may be important in relation to potential early intervention.^{Reference Calear and Christensen5,Reference Wolpert, Humphrey, Deighton, Patalay, Fugard and Fonagy6}

Second, whether the more deprived sample contributes to higher levels of reported mental health difficulties. We highlight in the paper the slightly more deprived survey population relative to national figures and also explicitly note that deprivation is associated with mental health problems, so we feel comfortable that we have been very transparent about this potential limitation.

Third, whether the single-informant Strengths and Difficulties Questionnaire (SDQ) is a less reliable predictor of child mental disorder than the multi-informant SDQ. Relying only on self-report always has its limitations and this has been acknowledged in the paper. However, there is also much evidence of disagreement between different perspectives so it is not clear how best to determine whose view takes precedence. We think considering the child's perspective is a worthwhile endeavour.^{Reference Deighton, Croudace, Fonagy, Brown, Patalay and Wolpert7,Reference Patalay, Deighton, Fonagy, Vostanis and Wolpert8}

Four, rationale around three-band versus four-band categorisation and use of subscale scores rather than total difficulties. The three-band cut-offs used in the paper are well used in the existing literature and as such are comparable with previous published research.^{Reference Wolpert, Görzig, Deighton, Fugard, Newman and Ford9} Although we are aware of the newer four-band scoring, we are not aware of any published evidence of how these newer four-band thresholds were established or their advantages or disadvantages relative to the older bandings. In the light of the queries raised we have reanalysed our findings with these new categories and also with total difficulties and impact scores (see details in list below). We note that the ‘very high’ threshold for the four-band categorisation has remained equivalent with the ‘abnormal’ threshold for the three-band version for emotional difficulties, so proportions remain the same. The thresholds for both conduct problems and inattention/hyperactivity problems have been increased by one point yielding reductions of around 10% in those scoring in the highest range. The thresholds for peer problems have been reduced by one point in the four-band categorisation leading to a larger proportion of children scoring in the highest range. Using the four-band rather than three-band categorisation for the three problem scales we initially focused on (emotional problems, conduct problems and hyperactivity/inattention) still yield very high levels of children scoring above the highest threshold in any one of these problem (32.5%).

Comparison of three-band versus four-band thresholds are as follows.

1. (a) Emotional problems: three-band (abnormal): 518 (18.4%); four-band (high): 7847 (27.9%); four-band (very high): 5181 (18.4%).

2. (b) Conduct problems: three-band (abnormal): 5197 (18.5%); four-band (high): 5197 (18.5%); four-band (very high): 2664 (9.5%).

3. (c) Inattention/hyperactivity: three-band (abnormal): 7135 (25.3%); four-band (high): 7135 (25.3%); four-band (very high): 4451 (15.8%).

4. (d) Peer problems: three-band (abnormal): 2058 (7.3%); four-band (high): 7066 (25.1%); four-band (very high): 4093 (14.5%).

5. (e) Total difficulties: three-band (abnormal): 5407 (19.3%); four-band (high): 7789 (27.7%); four-band (very high): 5407 (19.3%).

6. (f) Impact: three-band (abnormal): 6885 (24.8%); four-band (high): 6885 (24.8%); four-band (very high): 4495 (16.2%).

7. (g) Any mental health problem (emotional, behavioural or inattention/hyperactivity): three-band (abnormal): 11 976 (42.5%); four-band (high): 13 563 (48.2%); four-band (very high): 9151 (32.5%)

In terms of the question about why we looked at subscales rather than total difficulties – this was because we were interested in understanding the type of problems young people experienced. This is an approach that has been used before and now forms the basis of analysis being considered in relation to child mental health outcomes for children seen across the National Health Service.^{Reference Wolpert, Zamperoni, Napoleone, Patalay, Jacob and Fokkema10,Reference Wolpert, Jacob, Napoleone, Whale, Calderon and Edbrooke-Childs11}

We hope this helps clarify the points raised. We would want to thank Professor Ford and Ms McManus again for engaging with us on this important topic in our shared aim to understand levels of mental health need in children and young people in order to determine how best to meet this need.