Data management and statistical analysis were undertaken using Stata (Stata Version 14) and SPSS (SPSS Version 22).
5.6.7.1 Statistical power
This study uses a large cohort of children (n=114,097) which is the population of children who had a Child Health Surveillance assessment between 1st September 2010 and 30th September 2012. This is a large population cohort which is
geographically defined, with a pre-determined sample size, therefore a
conventional power/sample size calculation is not appropriate. With this large sample, small effect sizes may be statistically significant but not “important” from a public health perspective. We therefore placed more emphasis on the effect sizes and precision of estimates than on the p-values alone.
5.6.7.2 Descriptive statistics
Differences in outcomes (health visitor referral through the Childsmile referral pathway; referral through any pathway; ‘dosage’ of intervention; type of
contact) according to geographical (area-deprivation, health board, urban-rural classification) and family (feeding, smoking, HPI, level of risk) variables were explored descriptively and presented in stacked column charts and bar charts. Dental participation was examined descriptively by health visitor referral through the Childsmile referral pathway, DHSW intervention, area-based
deprivation and ‘level of risk’. This was presented descriptively in bar charts and plot point charts.
5.6.7.3 Univariable regression models
For each binary outcome (health visitor referral through the Childsmile referral pathway; referral through any pathway; ‘dosage’ of intervention), geographical and family variables were entered into a univariable logistic regression model.. Odds-ratios (OR) were calculated and Wald p-values and 95% confidence
intervals (95% CI) were given for each OR. The c-index was calculated as a measure of the predictive ability of each variable.
5.6.7.4 Multivariable regression models
Multivariable logistic regression modelling was carried out in order to examine the factors associated with following binary outcomes: health visitor referral, referral through any pathway, and ‘dosage’ of the DHSW intervention. For each outcome, a stepwise regression model was used, entering each geographical and
family variable in turn. P-values for entry were fixed at 0.05 due to the large sample size. ‘Local SIMD’ and ‘level of risk’ were not entered into the
multivariable models due to their strong association (inter-correlation) with other variables in the model (‘national SIMD’ and smoking, feeding and HPI at 6- 8 weeks). Adjusted odds-ratios (AOR) were calculated and Wald p-values and 95% confidence intervals were given for each AOR. The c-index was calculated as a measure of the predictive ability of each multivariable model.
Multi-level analysis was considered as a method for determining which ‘level’ of the data (e.g. family, health board, urban-rural geography) would best explain the variation in the selected outcomes. The reason a multi-level analysis was not carried out was due to descriptive statistics revealing that health board was indeed the most influential factor. As this study included data from the early phase of the national roll out of the DHSW intervention, there was not enough data available from all health board to conduct a multi-level analysis within each health board.
5.6.7.5 Interpretation of the c-index
A c-index is reported for each of the univariable and multivariable models. The c-index indicates the area under a Receiver Operating Characteristic (ROC) curve. This is a plot of sensitivity versus (1-specificity) for the model being tested. In a ROC curve, the accuracy of the model at separating the groups into those with or without the relevant outcome is being tested. We have taken this as a measure of the models’ “predictive ability” and, for clarity, used broad categories for the accuracy of prediction based on a ‘rule of thumb’ adapted from Zou et al. (2007) (1.0 is interpreted as excellent predictive ability through to less than 0.5, which is worse than chance). Calculating rates
In order to examine whether the rates of attempted DHSW interventions
improved over time, the rate of attempted interventions was calculated for each quarter (3 month period) from 1st September 2010. The rate was calculated as an incidence rate in order to account for varying time periods of follow-up for each child in the cohort as some children are in the cohort for longer than others.
The calculation was as follows:
Incidence rate Number of attempted DHSW interventions in each 3 month period Total person months in the cohort in each 3 month period
This incidence rate was multiplied by 1000 to give the rate of attempted DHSW interventions per 1000 person months.
5.6.7.6 Survival analysis
In order to explore the effect of the DHSW intervention on dental participation, while taking account of the fact that children in the dataset had unequal lengths of time in which to reach this outcome, survival analysis was undertaken.
In this survival analysis ‘time to event’ meant time taken for a child to
participate at a dental practice. This was calculated from the time of birth to time of dental participation. The effects of the DHSW intervention and
implementation of the Childsmile referral pathway were examined in relation to survival. Any differences in effect of the DHSW intervention between area-based deprivation categories and ‘level of risk’ were also examined.
Life tables were produced in order to ascertain the median number of months taken for children to participate. Following this, Cox regressions were performed in order to look at the effects of the DHSW intervention and the implementation of the Childsmile referral pathway. The results are presented as survival curves and regression tables.
The proportional hazards assumption that the hazard ratio remains constant for the groups being tested over time was deemed to hold by examining the plots produced for the Cox regression by SPSS. The lines of the survival curves did not overlap and we were satisfied that the assumption held.