Table 2 Activities associated with each step of the case study process (modified from Molnar et al. [5])

 Consult literature

We collected literature on HiAP for each case by undertaking a systematic search for peer-reviewed, government and grey literature that was relevant for the testing of hypotheses

 Conduct key informant interviews with Health in All Policies (HiAP) experts

We identified HiAP experts with substantial experience in working on HiAP by undertaking a search for prominent authors of reports on the case as well as by snowball sampling. Expertise and experience were confirmed through screening potential interviewees and, within each case, we interviewed 10–15 individuals representing civil servants from various sectors, politicians and researchers; we inquired about evidence related to the hypotheses using a semi-structured interview guide (the hypotheses as such were not mentioned) and transcribed the interviews for the systematic coding of the data

 Code literature and interview transcripts for evidence on hypotheses

We coded and summarised all interview transcripts and literature for evidence of the hypotheses, specifically looking for data on context–mechanism–outcome (CMO) configurations; within each CMO, we indicated whether they directly confirmed or refuted the hypothesis, or whether they served as counterfactual evidence; in particular, we considered how and why certain actions and activities were effective in convincing stakeholders to participate in HiAP initiatives, paying considerable attention to contextual factors that conditioned the mechanisms at play

 Summarise findings

Thick interview/literature CMOs (i.e. those with clear links between a mechanism and an outcome) were summarised by a hypothesis; thin interview/literature CMOs (i.e. unclear links between a mechanism and an outcome) were used as supporting evidence

 Assess for quality and strength of evidence

We described evidence according to triangulation (i.e. whether the mechanism was supported by both interview and literature sources)

 Write case reports

Our end-product for case-specific analyses was a case report

 Synthesise findings for each hypothesis across single case study reports to draw cross-case conclusions

Use results on support for hypothesis from single case studies to (1) categorise cases as literal replications or theoretical replications for each hypothesis and (2) synthesise findings for each hypothesis across cases to draw cross-case conclusions; undertake member checking by sharing findings with advisory group