2015 Scottish Maternity Care Survey Technical Report

4 Sample Design

Sampling frame

4.1 Women eligible to be sampled for the survey were those who had given birth between 01 February and 31 March 2015, and aged 16 or over at that date. Eligible women were identified by NHS Central Register (NHS CR), using the Birth Registrations from the National Records of Scotland and the Community Health Index (CHI) database.

4.2 Permission for access to identifiable patient data to send the questionnaire to mothers was granted by the Community Health Index Advisory Group (CHIAG). All data was accessed, managed and stored in accordance with the data confidentiality protocols^[2].

4.3 Birth registrations take place within 21 days of the birth and contain information about the child (date, place and time of birth, full name, sex), the parents/partners' names (including maiden surname of mother), the mother’s normal place of residence, the mother’s occupation (or last occupation).^[3]

4.4 NHS CR provided birth registration details such as birth registration numbers, and hospital codes from the birth registration forms to Health ASD to allow a random sample to be drawn.

Sample design

4.5 The survey used a stratified sample design rather than a simple random sample approach. Those included in a simple random sample are chosen randomly by chance giving an equal probability of being selected. Simple random samples can be highly effective if all subjects return a survey; giving precise estimates and low variability. However, simple random samples are expensive and cannot guarantee that all groups are represented proportionally in the sample.

4.6 Stratified sampling involves separating the eligible population into groups (i.e. strata) and then assigning an appropriate sample size to each group to ensure that a representative sample size is taken. This survey was stratified by the hospital where women gave birth (with separate strata for home births) and was based on a disproportionate stratified sample design, because the sampling fraction was not the same for each birth site. Some birth sites were over-sampled relative to others (i.e. had a higher proportion of their mothers included in the sample) in order to achieve the minimum number of responses required for analysis.

Sample size calculation

4.7 Sampling was based on the numbers of births in Scottish hospitals, to aim for sufficient responses to achieve a reasonably reliable result for each hospital. The reliability of the result depends on the number of questionnaires returned, and also the variability of the responses.

4.8 The sample size that was calculated for each hospital was based on the minimum number of responses that would be required to achieve an estimate of a percentage that has a 95% confidence interval with width +/- 5 percentage points, sampled from a finite population.

4.9 The formula for the minimum sample required (M) is M = B/(1+(B-1)/N).

Where:

• N is the number of births in a hospital on the sampling frame
• B = z²p(1-p)/c²
• p = the proportion answering in a certain way (assume 0.5 as this gives maximum variability)
• z is 1.96 for a 95% confidence interval (from standard normal distribution)
• c gives maximum acceptable size of confidence interval, in this case 0.05 (5 percentage points).

Based on the above, B=384

4.10 Table 4 below shows examples of this minimum number of responses required (M) based on the assumptions above for some example birth numbers.

Table 4 Minimum sample size required for different sites, based on number of births

4.11 In practice, if the underlying proportion is actually higher, or lower, than 0.5, then these numbers of responses would give narrower confidence intervals (or fewer responses would be required for the same accuracy).

4.12 The minimum sample size required (Table 4) is adjusted upwards to allow for assumed non-response to the survey. The response rates from the 2013 Maternity Care Experience Survey were used to estimate the expected responses for this survey, on a site by site basis (the national response rate in 2013 was 48%).

Sample selection

4.13 A random sample of infants was prepared by Health ASD, using the information provided by NHS CR. For the majority of birth sites in Scotland, a random sample of the required number of patients from each birth site was made using the “surveyselect” procedure within the SAS software package. For some sites with very small numbers of eligible patients, all patients were included in the survey in order to meet the minimum sample size requirements identified from the calculation above.

4.14 This list of infants was then returned to NHS CR who added on the mothers’ information, including name and address for the survey mail out, and removed any women who had either lost a baby or who had died.

4.15 Women were also excluded from the survey if they were not resident in Scotland. We made the assumption that in most cases, if women were resident in Scotland, they would have had their whole maternity care in Scotland. Women who had given birth to more than one baby were only eligible for sampling once, therefore other babies’ registrations were removed from the file we took the sample from.

4.16 Additionally, women who gave birth somewhere other than a hospital or their home were excluded, as many questions would not apply.

4.17 A total of 5,025 women were sampled for inclusion in the Scottish Maternity Care Survey 2015. Table 5 provides the number of women selected to take part in the survey for each NHS Board and Scotland.

Table 5 Women selected to take part in the survey