Statistical analysis
All analyses were conducted in Stata version 17.6 [The distributions of respondent sociodemographic characteristics (listed under outcomes) for the women who responded in the paper, push-to-web and social media surveys were described and compared using Chi-square tests. The representativeness of the respondents in each survey was assessed by comparing the distributions of sociodemographic characteristics to those for all women who gave birth in England during 2020 (with the exception of education, which is unavailable at population-level).Due to sociodemographic differences between the respondents and non-respondents in the paper and push-to-web surveys, and the potential impact of these differences on prevalence estimates based on survey data, non-response survey weights were derived for the paper and push-to-web surveys using data on non-respondents provided by ONS [Finally, the total financial costs were calculated and compared (in 2020/21 UK£) across the paper, push-to-web and social media surveys. The main costs incurred in the paper and push-to-web surveys were administrative costs for ONS to draw the sample from birth registration records, supply and printing of paper questionnaires and study documents, mail-out and return postage, data capture and supply, design and management of the online survey, and individual incentives for respondents. The main costs incurred in the social media survey were for the design and management of the online survey, advertising the survey on social media platforms, and the prize draw incentives. No financial discounts were received when purchasing the various resource components required to administer the surveys and so costs likely reflect market prices and could be generalisable to similar types of surveys. The cost per respondent was calculated for the paper, push-to-web and social media surveys by dividing the total cost for each survey by the number of usable responses in each survey (for women living in England only in the social media survey).