#### Percentage of women known to be smokers at time of delivery

This measure is calculated as:

Number of women known to be smokers at the time of delivery / (Number of maternities - Number of women whose smoking status was not known at the time of delivery) * 100

Prior to April 2017, this calculation included women with an unknown smoking status in the denominator i.e. the total number of maternities. This meant that women with an unknown smoking status were being treated in the same way as non-smokers. Thus poor data quality (i.e. having a lot of unknowns) could have masked poor performance. The tables in this report showing a time series have been recalculated to use the current new definition. More information is available in the methodological change note.

The methodology used in the Public Health Outcomes Framework (PHOF) indicator has also changed to exclude those maternities with an unknown status from the denominator. More information is available in the Government response to the consultation on the Public Health Outcomes Framework (PHOF).

#### Confidence intervals

A confidence interval gives an indication of the likely error around an estimate that has been calculated from measurements based on a sample of the population. It indicates the range within which the true value for the population as a whole can be expected to lie, taking natural random variation into account.

Throughout this report, 95% confidence intervals are used. These are known as such because if it were possible to repeat the same programme under the same conditions a number of times, we would expect 95% of the confidence intervals calculated in this way to contain the true population value for that estimate.

This approach is consistent with that used throughout the public health community.

The significance of the difference between two rates or proportions has been carried out throughout this report using the method described by Wilson and Newcombe below:

**1.** Calculate the proportions of women with and without the feature of interest (e.g. percentage of maternities who smoke at the time of delivery).

r = recorded number of maternities that smoke at the time of delivery for the designated time period

n = sample size

p = ( r / n ) proportion with feature of interest

q = ( 1 - p ) proportion without feature of interest

z = appropriate value z1-a/2 from the standard Normal distribution (1.96 for the 95% confidence interval).

**2.** Calculate three values (A, B and C) as follows:

\(A = 2r + z^2\)

\(B = z \sqrt{z^2+4rq}\)

\(C = 2(n+z^2)\)

**3**. Then the confidence interval for the population proportion is given by

\({A-B \over C}\) to \({A+B \over C}\)

This method has advantages to other approaches as it can be used for any data.

When there are no observed events, then r and hence p are both zero, and the recommended confidence interval simplifies to 0 to \({z^2 \over n+z^2}\) . When r = n so that p = 1, the interval becomes \({n \over n+z^2}\) to 1.

#### Significance testing

The steps for the approach outlined by Altman et al. are:

**1.** Calculate the absolute difference between the two proportions, \(\widehat{D} = \widehat{p}_{2} - \widehat{p}_{1}\)

**2**. Then calculate the confidence limits around \(\widehat{D}\) as:

\(\widehat{D} - \sqrt {(\widehat{p}_{2} - l_{2})^2 + (u_{1} - \widehat{p}_{1})^2}\) to \(\widehat{D} + \sqrt {(\widehat{p}_{1} - l_{1})^2 + (u_{2} - \widehat{p}_{2})^2}\)

where \(\widehat{p}_{i}\) is the estimated prevalence for year *i, *and \(l_{i}\) and \(u_{i}\) are the lower and upper confidence intervals for \(\widehat{p}_{i}\) respectively.

**3.** A significant difference exists between proportions \(\widehat{p}_{1}\) and \(\widehat{p}_{2}\) only if zero is not included in the range covered by the confidence limits around the difference \(\widehat{D}\).