An analysis of 24-h ambulatory blood pressure monitoring data using orthonormal polynomials in the linear mixed model

Abstract

Background The use of 24-hour ambulatory blood pressure monitoring (ABPM) in clinical practice and observational epidemiological studies has grown considerably in the past 25 years. ABPM is a very effective technique for assessing biological, environmental, and drug effects on blood pressure. Objectives In order to enhance the effectiveness of ABPM for clinical and observational research studies via analytical and graphical results, developing alternative data analysis approaches using modern statistical techniques are important. Methods The linear mixed model for the analysis of longitudinal data is particularly well-suited for the estimation of, inference about, and interpretation of both population (mean) and subject-specific trajectories for ABPM data. We propose using a linear mixed model with orthonormal polynomials across time in both the fixed and random effects to analyze ABPM data. Results We demonstrate the proposed analysis technique using data from the Dietary Approaches to Stop Hypertension (DASH) study, a multicenter, randomized, parallel arm feeding study that tested the effects of dietary patterns on blood pressure. Conclusions The linear mixed model is relatively easy to implement (given the complexity of the technique) using available software, allows for straight-forward testing of multiple hypotheses, and the results can be presented to research clinicians using both graphical and tabular displays. Using orthonormal polynomials provides the ability to model the nonlinear trajectories of each subject with the same complexity as the mean model (fixed effects).

Ambulatory Blood Pressure Trajectory and Perceived Stress in Relation to Birth Outcomes in Healthy Pregnant Adolescents

“…Model Estimation.-Hierarchical mixed model linear regression (HMMLR) was employed to estimate within-persons BP trajectories and between-persons differences in trajectories using a random effects maximum likelihood estimation approach via SPSS 23.0. This model is recommended for ABP data (58) and has been employed in several studies involving ambulatory measures during pregnancy, even with modest sample sizes (59)(60)(61)(62)(63). HMMLR is a robust technique because it utilizes every data point in variance estimations; with power to detect associations of interest being a function of both the number of individuals in the analysis (here, n=139) and the number of sampling moments (here, 3,852).…”

Exploring diurnal variation using piecewise linear splines: an example using blood pressure

“…It has been acknowledged there is not a generally accepted “standard” method of analysing 24-h ABPM [ 21 ]. Cosinor analysis has been highlighted as the most common approach [ 14 – 17 ] while fourier analysis [ 18 ], has also been implemented which are both based on the idea that any time series can be described by a series of cosine (and sine) waves of various frequencies [ 38 ].…”

“…Additionally Wang et al [ 41 ] suggests that the sinusoidal function is too restrictive and “rhythms with a shape closely approximating a cosine curve are uncommon” [ 42 ]. Alternative methods have examined restricted cubic splines and more recently orthonormal polynomials [ 13 , 21 ]. As we highlighted previously these approaches may model the data quite well and their curvature nature may look graphically appealing but it is difficult to understand and compare their resulting coefficients.…”

“…Although difficult to interpret the coefficients, polynomial regression can still be a useful tool in the analysis of medical data to plot the trajectory of non-linear or curvilinear relationships [ 37 ]. As a method of validation for our approach we additionally implemented a linear mixed model with orthogonal polynomials across time in both the fixed and random effects, similar to that of Edwards and Simpson [ 21 ]. We wanted to determine if linear splines were capable of capturing the circadian rhythm of BP.…”

“…Lambert et al extended on this by incorporating restricted cubic splines to model the mean BP profiles [ 13 ]. More recently, Edwards and Simpson [ 21 ] utilised orthonormal polynomials in a linear mixed model in a group of hypertensive subjects. Both polynomials and cubic splines, by their nature, have the ability to produce well-fitting curves to the data but have the disadvantage that the corresponding coefficients are challenging to interpret directly.…”