Smoothing splines for longitudinal data

1995 ◽  
Vol 14 (11) ◽  
pp. 1235-1248 ◽  
Author(s):  
Stewart J. Anderson ◽  
Richard H. Jones
Author(s):  
Arunas P. Verbyla ◽  
Brian R. Cullis ◽  
Michael G. Kenward ◽  
Sue J. Welham

Brain ◽  
2020 ◽  
Author(s):  
Alexis Moscoso ◽  
Michel J Grothe ◽  
Nicholas J Ashton ◽  
Thomas K Karikari ◽  
Juan Lantero Rodriguez ◽  
...  

Abstract Tau phosphorylated at threonine 181 (p-tau181) measured in blood plasma has recently been proposed as an accessible, scalable, and highly specific biomarker for Alzheimer’s disease. Longitudinal studies, however, investigating the temporal dynamics of this novel biomarker are lacking. It is therefore unclear when in the disease process plasma p-tau181 increases above physiological levels and how it relates to the spatiotemporal progression of Alzheimer’s disease characteristic pathologies. We aimed to establish the natural time course of plasma p-tau181 across the sporadic Alzheimer’s disease spectrum in comparison to those of established imaging and fluid-derived biomarkers of Alzheimer’s disease. We examined longitudinal data from a large prospective cohort of elderly individuals enrolled in the Alzheimer’s Disease Neuroimaging Initiative (ADNI) (n = 1067) covering a wide clinical spectrum from normal cognition to dementia, and with measures of plasma p-tau181 and an 18F-florbetapir amyloid-β PET scan at baseline. A subset of participants (n = 864) also had measures of amyloid-β1–42 and p-tau181 levels in CSF, and another subset (n = 298) had undergone an 18F-flortaucipir tau PET scan 6 years later. We performed brain-wide analyses to investigate the associations of plasma p-tau181 baseline levels and longitudinal change with progression of regional amyloid-β pathology and tau burden 6 years later, and estimated the time course of changes in plasma p-tau181 and other Alzheimer’s disease biomarkers using a previously developed method for the construction of long-term biomarker temporal trajectories using shorter-term longitudinal data. Smoothing splines demonstrated that earliest plasma p-tau181 changes occurred even before amyloid-β markers reached abnormal levels, with greater rates of change correlating with increased amyloid-β pathology. Voxel-wise PET analyses yielded relatively weak, yet significant, associations of plasma p-tau181 with amyloid-β pathology in early accumulating brain regions in cognitively healthy individuals, while the strongest associations with amyloid-β were observed in late accumulating regions in patients with mild cognitive impairment. Cross-sectional and particularly longitudinal measures of plasma p-tau181 were associated with widespread cortical tau aggregation 6 years later, covering temporoparietal regions typical for neurofibrillary tangle distribution in Alzheimer’s disease. Finally, we estimated that plasma p-tau181 reaches abnormal levels ∼6.5 and 5.7 years after CSF and PET measures of amyloid-β, respectively, following similar dynamics as CSF p-tau181. Our findings suggest that plasma p-tau181 increases are associated with the presence of widespread cortical amyloid-β pathology and with prospective Alzheimer’s disease typical tau aggregation, providing clear implications for the use of this novel blood biomarker as a diagnostic and screening tool for Alzheimer’s disease.


2019 ◽  
Author(s):  
Jaroslaw Harezlak ◽  
Samiha Sarwat ◽  
Kara Wools-Kaloustian ◽  
Michael Schomaker ◽  
Eric Balestre ◽  
...  

AbstractObjectivesWe extend the method of Significant Zero Crossings of Derivatives (SiZer) to address within-subject correlations of repeatedly collected longitudinal biomarker data and the computational aspects of the methodology when analyzing massive biomarker databases. SiZer is a powerful visualization tool for exploring structures in curves by mapping areas where the first derivative is increasing, decreasing or does not change (plateau) thus exploring changes and normalization of biomarkers in the presence of therapy.MethodsWe propose a penalized spline SiZer (PS-SiZer) which can be expressed as a linear mixed model of the longitudinal biomarker process to account for irregularly collected data and within-subject correlations. Through simulations we show how sensitive PS-SiZer is in detecting existing features in longitudinal data versus existing versions of SiZer. In a real-world data analysis PS-SiZer maps are used to map areas where the first derivative of weight change after antiretroviral therapy (ART) start is significantly increasing, decreasing or does not change, thus exploring the durability of weight increase after the start of therapy. We use weight data repeatedly collected from persons living with HIV initiating ART in five regions in the International Epidemiologic Databases to Evaluate AIDS (IeDEA) worldwide collaboration and compare the durability of weight gain between ART regimens containing and not containing the drug stavudine (d4T), which has been associated with shorter durability of weight gain.ResultsThrough simulations we show that the PS-SiZer is more accurate in detecting relevant features in longitudinal data than existing SiZer variants such as the local linear smoother (LL) SiZer and the SiZer with smoothing splines (SS-SiZer). In the illustration we include data from 185,010 persons living with HIV who started ART with a d4T (53.1%) versus non-d4T (46.9%) containing regimen. The largest difference in durability of weight gain identified by the SiZer maps was observed in Southern Africa where weight gain in patients treated with d4T-containing regimens lasted 52.4 weeks compared to 94.4 weeks for those with non-d4T-containing regimens. In the other regions, persons receiving d4T-containing regimens experienced weight gains lasting 51-61 weeks versus 59-77 weeks in those receiving non-d4T-based regimens.DiscussionPS-SiZer, a SiZer variant, can handle irregularly collected longitudinal data and within-subject correlations and is sensitive in detecting even subtle features in biomarker curves.


Author(s):  
Lynn M. Milan ◽  
Dennis R. Bourne ◽  
Michelle M. Zazanis ◽  
Paul T. Bartone
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