The statistical analysis of treatment effects in 24‐hour ambulatory blood pressure recordings

Abstract

This paper presents a statistical analysis of treatment effects in 24-hour ambulatory blood pressure recordings. The statistical models account for circadian rhythms, subject effects, and the effects of treatment with drugs or relaxation therapy. In view of the heterogeneity of the subjects, we fit a separate linear model to the data of each subject, use robust statistical procedures to estimate the parameters of the linear models, and trim the data on a subject by subject basis. We use a meta-analytical method to combine the results of all subjects in the study.

Cumulative sums in quantifying circadian blood pressure patterns.

“…Halberg's cosinor method 1415 and subject-specific linear models 16 apply a smoothing process whereby a cosine curve with fixed frequency of 1 cycle/day is fitted to the data. This model implies an exactly symmetrical behavior of high and low blood pressure periods, both assumed to be of the same length, shape, and amplitude.…”

“…Calculation of the pressure difference 6 - 10 or the percent pressure difference 713 between average daytime and nighttime blood pressures assumes fixed sleep/wake timings. Halberg's "cosinor method" 1415 and other statistical analyses, such as separate linear models fitted to the data of each subject 16 or periodic spline models, 17 are complex necessitating remodeling of original data and thus are more suited to qualitative rather than quantitative analyses.…”

The sigmoidally transformed cosine curve: a mathematical model for circadian rhythms with symmetric non‐sinusoidal shapes

“…Patients all had probable or possible Alzheimer's disease (AD) with an average mini mental state examination (MMSE) score of 5.7 (median 4.0, SD = 5:6, range 0-22). The average level of education was 13.8 years (SD = 3:3, range [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

“…This is the linear projection of the data on the sine and cosine curves with periods of 24; 12; 8; : : : ; 1:2 h, i.e. the base frequency and its ÿrst 19 harmonics [5][6][7][8][9]. It is clear that this model is a better ÿt to the data than the plain cosine, but it has a total of 40 parameters (plus the mean estimate), and a non-parsimonious wiggly shape.…”

Bayesian statistics in medicine: a 25 year review

“…In 1988 there were papers, based on Normal approximations, advocating using a Bayesian approach to avoid a biased effect estimate after stopping a trial early [61], considering computational aspects of a Bayesian approach to two by two summaries from case-control studies, illustrating these with example of alcohol and oesophageal cancer, and DES and vaginal cancer [62] and on diagnosis of multiple diseases, avoiding assumption of independence [63]. Another [64] attempted a more highly dimensional problem of estimating treatment effects from 24-hour ambulatory bloodpressure monitoring, but could only adopt a 'partial empirical Bayes' approach because software could not deal with full empirical Bayes for an unbalanced experimental design. The floodgates now were opened, and from then on, Bayesian ideas featured regularly in papers in Statistics in Medicine either as the main approach, or as one approach being compared with others.…”