Statistical methods

We anticipated that some patients would be assigned a named accountable GP even though they were aged below 75 years, whereas some patients older than age 75 would not be offered a named accountable GP. Therefore, we employed a fuzzy regression discontinuity design to estimate the effect of being assigned a named accountable GP for compliers (ie, for those patients who would in practice receive a named accountable GP if eligible under the policy, but not receive one if ineligible).²⁵ As sensitivity analysis, we employed a sharp regression discontinuity design to estimate an average treatment effect across all people aged 75, like intention-to-treat analysis of randomised data.

The regression models used to estimate these treatment effects were similar to those from a previous paper and were applied to patients within a certain number of years of age 75 (ie, aged within a certain ‘bandwidth’).²⁶ The models allowed for a difference in the level and slope of study end points at age 75 and likewise for a change in the level and slope of the percentage of patients at each age receiving a named accountable GP (see technical appendix, online supplementary material). As noted above, we conducted a limited amount of extrapolation when estimating treatment effects, since the lack of full date of birth meant that we excluded patients born in 1939. Thus, for example, adopting a bandwidth of 4 years meant that we estimated outcomes under the control treatment by fitting a model on data for people aged between 70 and 74 and then extrapolating this model to estimate outcomes under control at age 75. We tested several bandwidths and selected the order of the polynomial function used in the regression models using a combination of formal goodness of fit tests, visual analysis of the data and previous literature.²⁷ We assessed the plausibility of our model estimates graphically by examining our outcomes binned by the assignment variable. A bias-correction method was necessary because the lack of full date of birth meant that age could only be approximated.²⁶ Bootstrapped 95% CIs are reported for the estimated treatment effects for each of the study end points.²⁸

bmjopen-2016-011422supp_appendix.pdf