New　biomarkers　continue　to　be　developed　for　the　purpose　of　diagnosis,　and　their　diagnostic　performances　are　typically　compared　with　an　existing　reference　biomarker　used　for　the　same　purpose.　Considerable　amounts　of　research　have　focused　on　receiver　operating　characteristic　curves　analysis　when　the　reference　biomarker　is　dichotomous.　In　the　situation　where　the　reference　biomarker　is　measured　on　a　continuous　scale　and　dichotomization　is　not　practically　appealing,　an　index　was　proposed　in　the　literature　to　measure　the　accuracy　of　a　continuous　biomarker,　which　is　essentially　a　linear　function　of　the　popular　Kendall＇s　tau.　We　consider　the　issue　of　estimating　such　an　accuracy　index　when　the　continuous　reference　biomarker　is　measured　with　errors.　We　first　investigate　the　impact　of　measurement　errors　on　the　accuracy　index,　and　then　propose　methods　to　correct　for　the　bias　due　to　measurement　errors.　Simulation　results　show　the　effectiveness　of　the　proposed　estimator　in　reducing　biases.　The　methods　are　exemplified　with　hemoglobin　A1c　measurements　obtained　from　both　the　central　lab　and　a　local　lab　to　evaluate　the　accuracy　of　the　mean　data　obtained　from　the　metered　blood　glucose　monitoring　against　the　centrally　measured　hemoglobin　A1c　from　a　behavioral　intervention　study　for　families　of　youth　with　type　1　diabetes.