The study design included four phases: item generation, item reduction and writing, index derivation, and index validation.
For the item generation phase, a literature review was performed in October, 2013 to extract existing screening instruments for investigating deprivation, vulnerability or poverty at individual level, in PubMed (for main international references) and CAIRN (increasing exhaustiveness to articles in French). In addition, face-to-face semi-structured interviews with 13 senior experts in specific healthcare for deprived children collected their opinions on the domains to be measured, and on the complementary items to address. Interviews ended when data saturation was achieved.
For the item reduction and writing phase, a steering committee was set up. Eight of the 13 senior experts accepted to participate (one pediatrician, two nurses, two social workers, two healthcare and socio-educational managers, and one health mediator). They selected by oral consensus, relevant and acceptable items covering each dimension of social deprivation, proposed their wording and an informative appendix.
An independent reading group (one general practitioner, two pediatricians, three nurses and two social workers) validated the choice and wording of the items and appendix, via an online questionnaire with a semi-quantitative notation (from 1: total disagreement to 9: total agreement) of the wording and relevance of each question. Their agreement about appropriateness was calculated according to analysis rules .
For the index derivation and validation phases, 13 items judged as being appropriate or uncertain were tested, by healthcare professionals untrained in their use, on a sample of children. This sample was derived form a cross-sectional multicentric study conducted between April 2018 and October 2019, which recruited a convenient sample of children in two French university hospitals (Marseille, Nice). Children were eligible when aged 3 to 15 years old, admitted to paediatric emergency units without life-threatening conditions or ongoing medico-legal procedures. Children could only be selected once. Only one sibling was included. Informed consent was obtained from the participant’s legally authorized representative and the child him or herself when 8 years old or above. For non-French speaking children, a professional telephone interpretation service was used (ISO 13611:2014; 17100:2015). A sample size about 1,000 children was required to show a sensitivity and specificity of 80% with a 95% confidence interval (CI) and a precision of 5% for primary outcome, considering an expected prevalence of deprivation for at least 25% of the sample (one hospital being located in a deprived area) [12, 16].
The primary outcome of whole deprivation burden assessment was based on a blinded expert evaluation for each child. This expert was a trained healthcare professional working in a SMUFAH (social worker, nurse or pediatrician; with at least one year of experience caring for deprived children). He/she assessed the whole deprivation burden with several criteria: (1) the type and number of deprivation domains by following the concept of deprivation, in every domain of lifestyle at an individual level [5, 6], (2) the type and amount of specific healthcare required for deprived children (both lists mentioned in the introduction), and (3) the need for admission to SMUFAH (when at least two different types of specific healthcare for deprived children were needed) .
For the index derivation phase, item-internal consistency was assessed by correlating each FrenChILD-Index item with the deprivation domain they were logically related to. Items were retained if they had a significant moderate correlation (Pearson correlation coefficient |r| ≥ 0.3). Internal consistency was assessed using Cronbach's alpha coefficient. We performed two linear multiple regressions to test retained items for predicting the whole deprivation burden with: i) the number of deprivation domains affected and 2) the amount of specific healthcare needed for deprived children. For the FrenChILD-Index scoring, items were weighted on the standardized coefficients (average of the two regressions) and revised according to expert recommendations.
For the index validation phase, discriminant properties were assessed accordingly: i) at least one specific type of healthcare for deprived children = moderate deprivation; and ii) at least two specific types of healthcare for highly deprived children = severe deprivation, to be admitted to SMUFAH. Sensitivity and specificity were calculated with 95% confidence intervals.
FrenChILD-Index reproducibility was assessed via a phone call retest on a random sample (0.3%) of children after 5 to 6 months (this period was longer than schooling or health insurance applications if they had already been started). It included children in a situation perceived as stable by parents and not admitted to SMUFAH over the period and was stratified with no more than 1/3 of children without any deprivation criteria (initial FrenChILD-Index = 0).
Complete-case analysis was drawn. Statistical analysis used chi-squared, Fisher’s and Student’s tests, Pearson correlations, linear multiple regressions and ROC curve analyses with SPSS 20.0 (IBM, Armonk, NY, USA) and SAS 9.4 (SAS, Cary, NC, USA) softwares. Bootstrap confidence intervals were calculated using 1,000 samples generated by unrestricted random sampling with stratification according to expert assessment (mean sample size = 624). Significance threshold was 0.05.