Details of the PROGRESS trial have been described previously.7
We analysed the dual treatment arm, for which active treatment was a regimen of perindopril 4 mg and indapamide 2.0-2.5 mg daily, using data from the visit at three months after randomisation until the three year visit. We restricted analyses to the active treatment arm because our objective was to assess long term variability after starting blood pressure lowering treatment. At each visit, recorded blood pressure was the mean of two measurements taken five minutes apart with the patient in the seated position, with each measurement being recorded to the nearest 2 mm Hg with a standard mercury sphygmomanometer. For the purpose of this analysis, the three month visit after randomisation was fixed as the time at which a patient will have achieved a reduction in blood pressure as a result of antihypertensive treatment and the time at which long term monitoring is initiated. We estimated long term change in blood pressure from this baseline measurement from the difference between it and the subsequent follow-up “observed” blood pressure measurements at each time point (three months, six months, nine months, etc).
The observed blood pressure at each follow-up point comprises an underlying “true” average blood pressure plus the “short term variability” caused by technical measurement error and short term biological fluctuations (often called “within person” variability or simply “measurement error”). We use the term short term variability to describe fluctuations in blood pressure over a short time period (such as a few days or a week5
). Short term variance is the statistical measure of short term variability. Squaring the standard deviation (SD) gives the “variance,” which is an additive measure convenient for calculating changes in variability. Short term variability is part of each follow-up measurement—that is,
- [observed follow-up blood pressure] = [true blood pressure] + [short term variability].
The short term variance can be estimated by halving the observed variance of the difference between two measurements made within a short time interval. As a first approximation, we obtained the short term variance from the difference between the measurements at six and three months. Because the three month time delay might incorporate some true long term change, however, we ultimately estimated the expected short term variance using the variogram approach8
(see appendix 1 on bmj.com).
Observed long term changes in blood pressure will incorporate the “true” average change in the blood pressure, twice the short term variability (once for the initial measurement and once for the subsequent measurement), and the “long term variability”—that is,
- [observed change in blood pressure from baseline] = [true average change in blood pressure] + 2 × (short term variability) + (long term variability)].
The long term variability is the “between person” variability caused by individuals’ long term changes in blood pressure deviating above or below the average change of the group. The long term variance can be estimated from the total observed variance of the difference in blood pressure measurements from the baseline to each subsequent time point. The above equation shows that subtracting twice the short term variance from the total observed variance of the change will give an estimate of the long term variance (see appendix 1 on bmj.com).
Using the calculated change in variance at each time point, we estimated the proportion of patients whose assumed true baseline systolic blood pressure of 130 or 120 mm Hg would truly increase by 10 or 20 mm Hg (called true positives) to a threshold of 140 mm Hg or above while receiving treatment. We also estimated the proportion of patients who would be observed to be above the thresholds but who actually had true blood pressure levels below the threshold (that is, false positives). We repeated this for an assumed true baseline diastolic blood pressure of 85 or 80 mm Hg and used changes in blood pressure of 5 or 10 mm Hg to reach a threshold of 90 mm Hg or above. For both systolic and diastolic blood pressure we estimated these assuming no change in mean blood pressure over the three year period. In sensitivity analyses we also estimated the true and false positive probabilities assuming an average 1.0 mm Hg per year increase in systolic blood pressure and a 0.5 mm Hg per year increase in diastolic blood pressure.9
The calculations assume that the baseline value and the true change with time are normally distributed and are independent of each other. See appendix 1 on bmj.com for full details of the methods.
Previous research has shown distributions of systolic blood pressure to be skewed to the right and variability to be correlated with blood pressure levels.5 10 11 12 13
Therefore, we checked the distributions of systolic and diastolic blood pressure for normality and examined Bland-Altman plots of the difference in the measurements from baseline to three months against the average of these two measurements. Use of a natural log transformation normalised distributions of systolic blood pressure and reduced the correlation between variability and blood pressure level, and we subsequently repeated analyses after natural log transformation of systolic blood pressure measurements.
Because the methods described above assume independence between baseline blood pressure and the true change from baseline blood pressure, we also repeated the analyses using an approach based on mixed models, which do not assume independence between baseline level and the true change from baseline level.