This　article　concerns　evaluating　the　effectiveness　of　a　continuous　diagnostic　biomarker　against　a　continuous　gold　standard　that　is　measured　with　error.　Extending　the　work　of　Obuchowski　(2005,　2016),　Wu　et　al　(2016)　suggested　an　accuracy　index　and　proposed　an　estimator　for　the　index　with　error-prone　standard　when　the　reliability　coefficient　is　known.　Combining　with　additional　measurements　(without　measurement　errors)　on　the　continuous　gold　standard　collected　from　some　subjects,　this　article　proposes　two　adaptive　estimators　of　the　accuracy　index　when　the　reliability　coefficient　is　unknown,　and　further　establish　the　consistency　and　asymptotic　normality　of　these　estimators.　Simulation　studies　are　conducted　to　compare　various　estimators.　Data　from　an　intervention　trial　on　glycemic　control　among　children　with　type　1　diabetes　are　used　to　illustrate　the　proposed　methods.