La mesa de desarrollo y las dimensiones en el impulso de acuerdos concertados

6.6.1 Outline estimate of sample required

The incidence of cardiovascular events was the primary outcome used for the power calculation. Assuming a cardiovascular event rate of 1260 events per 100,000 person-

years (all ages) in the control arm (9, 10) and 10% lower event rate in the intervention arm (rate ratio of intervention to control of 0.9) I estimated that a total sample of about 70,000 patients followed up for 2 years would give 80% power at 5% significance (two-tailed), allowing for 15% withdrawal (11). This calculation was based on all age event rate as I was unable to find an event rate specifically for the over 50s. The intervention was applied to the over 50 year population and I measured the outcome in this age group only. I assumed that the cardiovascular event rate followed a Poisson distribution, in keeping with other studies of vascular outcomes such as OXVASC (10).

6.6.2 Individual or cluster randomisation?

I considered the option of cluster randomisation, which had been raised by two local reviewers of the e-Nudge protocol and also during the seminar that I gave at ScHARR, discussed in Chapter 5. This approach removes any risk of contamination of the intervention into the control arm and is generally preferable for trials of complex interventions, but usually requires a significantly (and often prohibitively) larger sample size. I estimated the necessary inflation of the sample (the ‘design effect’) due to clustering (12).

The design effect is related to the cluster size and the intra-class correlation coefficient (ICC). The ICC can be estimated using the formula:

ICC = variance between clusters/(variance between + variance within clusters)

If clustering effects are marked (giving a high ICC) then observations within the cluster have a tendency to be similar, and a higher proportion of the variability is between clusters. More clusters are then required to provide the same power. If the ICC is low then the design effect is reduced. In the extreme case the ICC would be zero, indicating that observations of the intervention effect on all individuals in the study are

independent measures of the effect and unrelated to the cluster to which the individual belongs.

The formula for the inflation in sample size to account for clustering is:

N+= N(1+(m-1)ICC)

Where: N+ = sample size following inflation

N = initial sample size

m = cluster size

ICC = Intra-class correlation coefficient

When designing the trial I did not have a reliable estimate of the ICC related specifically to this area of care. However it was clear that m would inevitably be large. The mean number of patient records to be randomised per practice was estimated using Primary Care Trust data to be 2355 based on the mean over 50 year population in all practices in South Warwickshire during 2005. Even if I interpreted ‘m’ to be the number of patients identified in the groups by the e-Nudge rather than the whole over- 50 year population, and if by excluding the large Group 2 whose size was defined arbitrarily, I was still left with m=111 as a minimum. In fact these assumptions were not strictly valid (as the primary outcome denominator was the over-50 year population, not the population identified in the e-Nudge groups), but in an early discussion document I derived the necessary sample sizes based on this value for m and a range of ICC values taken from the published literature. I also sought informal advice on this from Sandra Eldridge of Queen Mary’s University of London, who has special expertise on cluster-randomisation. She suggested that a value of around 0.03 might be appropriate for a trial of this type. Table 6.1 gives the values obtained.

ICC Source Design effect Necessary sample size

Zero (disregards clustering)

1 70,000

0.0036 Kerry and Bland

(12, 13) 1.4 98,000 0.03 Advice from Sandra Eldridge 4.3 301,000 0.045 Kinmonth et al (14) 5.95 416,500

0.0644 Fahey and Peters

(for UK) 15)

8.1 567,000

0.199 Cosby et al (for

mean systolic blood pressure) (16)

21.9 1,533,000

Table 6.1: A range of possible values for the intra-class correlation co-efficient and their implications for the e-Nudge sample required based on m=111.

This very conservative approach (i.e. using the above assumption for the value of m) demonstrated that only if the ICC were extremely small would cluster-randomisation be an option given the practice capacity available. I considered whether there might be some way of estimating the ICC using locally available data. I approached Greg Wells, Consultant in Public Health at South Warwickshire Primary Care Trust for data on the recording of vascular diagnoses across practices in the region. He provided prevalence estimates of coronary heart disease and stroke/TIA at the practice level as well as the indirectly standardised prevalence ratios (Figure 6.4). Whilst these data were different from the outcomes of a trial, they were a potentially useful indicator of the extent to which practice specific processes might influence the recording of cardiovascular events, my primary outcome measure.

The indirectly standardised prevalence ratio (ISPR) is the ratio of observed/expected prevalence of the condition. Expected prevalence is based on PRIMIS data (17) and is adjusted for practice demographics. If all practices were recording the expected number of cases electronically then the crude prevalence would vary by practice but the ISPRs would all be about 100 if variation in practice

demography had been sufficiently accounted for in determining expected prevalence. Whilst this is an imprecise process, practices varied in their ISPRs from 60.5 to 124 for CHD (a 2.1 fold difference) and from 17 to 179 for Stroke/TIA (a 10.5 fold difference, although one of these practices was quite an extreme outlier).

I concluded from this that despite recent improvements in the recording of these conditions described in Chapter 2, the observed variation was likely to be at least partly a reflection of practice-level processes, and not just the risk of the condition itself, particularly for stroke/TIA. Important factors might include the tendency of the practice team to investigate possible vascular symptoms, the handling of hospital discharge reports, the process through which neurovascular or chest pain clinic referral outcomes were recorded, and the threshold for attributing symptoms to vascular events within the practice team. Whilst there is variation in the practices of all clinicians across UK primary care, these tendencies might be influenced by team communication and shared learning at the practice level.

An individual patient’s risk of being on a vascular disease register was probably determined therefore not only by the actual presence of the condition but also by the practice that he or she happened to be registered with. This provided indirect evidence that clustering of recorded vascular data would be significant. It was probably unrealistic to assume a low ICC for e-Nudge study outcomes, and the option of individual randomisation was taken.

South Warwickshire PCT practice registers: coronary heart disease crude prevalence and indirectly standardised prevalence ratios

0% 1% 2% 3% 4% 5% 6% 7% 1 2 3 4 5 6 7 8 9 ₁0 ₁1 ₁2 ₁3 ₁4 ₁5 ₁6 ₁7 ₁8 ₁9 ₂0 ₂1 ₂2 ₂3 ₂4 ₂5 ₂6 ₂7 ₂8 ₂9 ₃0 ₃1 ₃2 ₃3 ₃4 ₃5 ₃6

Sources: Registers at Mar 2005; FHS population July 2004 adjusted for non-residents; national prevalence rates from PRIMIS 2005

C ru d e p re v a le n c e 0 25 50 75 100 125 150 175 IS P R s

Figure 6.4: Crude prevalence (columns) and indirectly standardised prevalence ratios (joined points) for Coronary Heart Disease and Stroke/TIA among the 36 practices of South Warwickshire in March 2005. The practice numbers are unrelated to those used for e-Nudge trial practices elsewhere in this thesis.