The purpose of this study is to investigate whether there has been a change in low birth weight and perinatal and infant mortality following the July 2007 introduction of a ban on smoking in public places and workplaces in England.

Primary research question Has there been a change in the numbers of babies being born with low birth weight or dying in the perinatal or infant period following the 1 July 2007 introduction of a ban on smoking in public places in England?

Study design Retrospective cohort study (using prospective routinely collected health care data)

Study population All singleton births in England between 1 January 1995 and 31 December 2011.

Intervention The intervention under study is the ban on smoking in enclosed public places and the workplace implemented in England overnight on 1 July 2007.

Inclusion and exclusion criteria We will include all registered singleton births in England occurring between 1 January 1995 and 31 December 2011. This is the maximum time period surrounding the ban's introduction for which the required birth data are available through the data source. Data were originally extracted for 1 January 1993 to 31 December 2011. However, postcode was not recorded in 1993-1994, leading to missing values for Index of Multiple Deprivation (IMD) quintile, region, and urbanisation level in this period. As these variables were considered key potential confounders in the primary analyses, a decision was made to restrict the modelling to the time period 1 January 1995-31 December 2011.

International Classification of Disease (ICD) coding changed from version 9 to 10 as of January 2001, leading to an important drop in recorded SIDS cases. Therefore, analyses of SIDS are restricted to the time period 2001-2011.

Babies with chromosomal anomalies will be excluded.

Outcome

The primary outcomes are:

• Low birth weight (birth weight < 2500 grams)
• Stillbirth (intrauterine death from 24+0 weeks gestation)
• Neonatal mortality (death within the first 28 days of life)
• Sudden infant death syndrome (SIDS; death within first year of life with mentioning on the death certificate of ICD-10-U code R95, or R99 with no other specification)

To assess whether smoke-free legislation had a selective impact on certain subgroups of outcomes we furthermore identified a number of secondary outcomes:

• Very low birth weight (birth weight < 1500 grams)
• Early neonatal mortality (death within first week of life)
• Late neonatal mortality (death between 7 and 28 days of life)
• Post-neonatal mortality (death between 28 days and 1 year of life)
• Infant mortality (death within the first year of life)

Data sources Data are obtained via the Office for National Statistics (ONS). All registered stillbirths and livebirths occurring in England between 1 January 1995 and 31 December 2011 are included. These are linked to death certificates for all deaths occurring before the first birthday.

Data extraction and handling Individual perinatal and mortality data are linked by ONS in a single database including the following individual-level covariates: month of birth, year of birth, month of death, year of death, age at death, sex, birth weight, maternal age, maternal marital status, parity, IMD, region, urbanisation level.

The following covariates are categorised for information governance reasons:

• Age at death: early neonatal, late neonatal, post-neonatal
• Birth weight: <1000 grams, 1000-1499 grams, 1500-2499 grams, 2500-3999 grams, ≥4000 grams
• Maternal age: <20 years, 20-24 years, 25-29 years, 30-34 years, 35-39 years, >40 years
• Parity: 0, 1, 2, ≥3
• IMD: quintiles
• Region: 10 regions
• Urbanisation level: urban, rural

Sample size Sample size calculation for time-oriented analyses is complicated given the complexity of the models. We will use national data for the current study, which will - to the best of our knowledge - be the largest evaluation of the impact of smoke-free legislation on perinatal health, both regarding population size and time span. As we use the maximum time span and population available, sample size calculation can in a way be considered redundant.

We are aware of only one published study on smoke-free legislation and early-life mortality (reference 1). Due to design issues it is not possible to involve data from this study for comparison to the current study.

A number of studies have previously assessed the impact of smoke-free legislation on low birth weight. Our proposed approach is best comparable to that performed earlier in Scotland (reference 2). Using Scottish data on 757,795 deliveries occurring between 1996 and 2009, they showed an immediate -9.9% (95%CI -14.2; -5.2) drop in low-birth-weight-babies. Given the longer study period (1993-2011) and the much larger population size (n>10 million) our study can be expected to have sufficient power to detect a similar reduction in low-birth-weight-babies in England, if present.

Statistical analysis

Relevant population characteristics will be described. Logistic regression analysis will be performed to investigate the association between introduction of smoke-free legislation and sudden ('step') and/or gradual ('slope') changes (as appropriate) in the odds of developing each outcome. Analyses will be adjusted for birth weight, sex, maternal age, maternal marital status, parity (secondary analyses only, see below), IMD quintile, region, and urbanisation level. Seasonal patterning and non-linearity of the underlying time trend will be accounted for as appropriate. Final model selection will be based on Akaike's and Bayesian information criteria (AIC and BIC). The denominator for the analyses will differ according to the various outcomes:

• stillbirths: all births in the dataset
• low birth weight, very low birth weight, neonatal mortality, early neonatal mortality, infant mortality: all livebirths in the dataset
• late neonatal mortality: all livebirths in the dataset surviving the early neonatal period
• post-neonatal mortality: all livebirths in the dataset surviving the neonatal period

The primary analyses will be performed on cases with complete data on all covariates. Parity is the only variable that has >10% missing data (approximately 40-50%), as it is only recorded in married women. As parity is not expected to be a key confounder, we will perform the primary analyses without involving parity in the models in order to maximise population size.

Sensitivity analyses To assess possible confounding by parity, sensitivity analyses will be performed that include parity in the model. In a second set of sensitivity analyses, imputation will be performed to investigate the robustness of the findings to missing data. In order to minimise issues regarding multiple testing, sensitivity analyses will be performed for the primary outcomes only.

All analyses will be performed using Stata 12.0.

Inclusion Criteria:

• singleton birth occurring in England between 1 January 1995 and 31 December 2011

Exclusion Criteria:

• chromosomal anomalies
• stillbirth (applies to all outcomes other than stillbirth)

All singleton births in England. See 'statistical analysis' for specification of base population for each outcome.