Abstract:
ObjectivesWeextendthemethodof SignificantZeroCrossingsof Derivatives(SiZer)to address within-subject correlations of repeatedly-collected longitudinal biomarker data and the computational aspects of themethodology when analyzing massive biomarke rdatabases.SiZeris a powerful visualization tool fo rexploring structures in curves by mapping areas wherethe first derivativeis increasing,decreasing or does not change(plateau)thus explore-ing changes and normalizationof biomarkersin thepresenceof therapy.MethodsWeproposea penalizedsplineSiZer(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-SiZeris in detecting existing features in longitudinal data versus existing versions of SiZer.In a real-world data anal-ysis PS-SiZer maps are used to map areas where the firstderivative of weight change after antiretroviral therapy(ART)startis significant lyincreasing,decreasing or does not change,thus exploring the durability of weight increase after the start of therapy.WeuseweightdatarepeatedlycollectedfrompersonslivingwithHIVinitiatingARTin five regions in theInterna-tionalEpidemiologicDatabasesto Evaluate AIDS(IeDEA) worldwide collaboration and com-pare the durability of weight gain between ART regimens containing and no containing the drugs tavudine(d4T),which has been associated with shorter durability of weight gain. ResultsThroughsimulationsweshowthatthePS-SiZeris more accurate in detecting relevant fea-turesin longitudinaldatathanexistingSiZervariantssuchasthelocallinearsmoother(LL)SiZerandtheSiZerwithsmoothingsplines(SS-SiZer).In theillustrationweincludedatafrom185,010personslivingwithHIVwhostartedARTwitha d4T(53.1%)versus non-d4T(46.9%)containing regimen.The largest difference in durability of weightgainidentifiedbytheSiZermapswasobservedin SouthernAfricawhereweightgainin patientstreatedwithd4T-containingregimenslasted59.9weekscomparedto 133.8weeksforthosewithnon-d4T-containing regimens.In the other regions,personsreceivingd4T-containingregimensexperiencedweightgainslasting38–62weeksversus55–93weeksin those receiving non-d4T-based regimens. Discussion PS-SiZer, a SiZervariant, can handle irregularly collected longitudinal data and within-subject correlations and is sensitive in detecting even subtle features in biomarker curves