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Zhong-Lin Lu, Yukai Zhao, Luis Andres Lesmes, Michael Dorr, Peter Bex; Unbiased Threshold Estimates in Bayesian Adaptive qCSF and qFC with Mismatched Psychometric Function Slopes. Invest. Ophthalmol. Vis. Sci. 2019;60(9):3908.
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© ARVO (1962-2015); The Authors (2016-present)
To improve data quality in basic and clinical applications, Bayesian methods have been developed to adaptively assess thresholds on single [1,2] or multiple psychometric functions (e.g., the contrast sensitivity function [3,4]). To simplify these procedures – reduce model parameters and increase estimation efficiency - the slope of the psychometric function can be fixed [3,4]. However, a model mismatch occurs when the assumed slope differs from observer’s true slope. What is the impact of this mismatch on the accuracy, precision, and efficiency of adaptive estimation? In this study, we used Monte Carlo simulations to show that, for methods with fixed slopes, the qFC  in m-alternative forced choice tasks (m=2, 4, 8, and 10) and qCSF [3,4]: (1) there exists a d’ performance level at which the estimated threshold is unbiased, and (2) precision and efficiency increase with the observer’s true slope.
For qFC, seven simulated observers, one with matched (3.05, 3.45, 3.90, and 4.05 for m=2, 4, 8, and 10, respectively) and six with mismatched slopes (0.5, 1, 2, 5, 6, 8) were simulated in each m-alternative task. The thresholds (d’=0.5 to 3.5) of each simulated observer were estimated with the qFC (100 trials) method 1000 times. For qCSF, six observers, one with matched (4.05), four with a single mis-matched (1, 2, 6, and 8, respectively) across all spatial frequencies (SFs), and one with two mis-matched slopes (8 when SF < 4 cpd; 1 when SF ≥4 cpd), were simulated. The CSFs (d’=0.5 to 3.5) of each simulated observer were estimated with the qCSF (200 trials) method 500 times.
The results are shown in Table 1. We found that the value of d’ where bias = 0 depended on the number of alternatives in forced choice tasks. Precision and the 68.2% half-width confidence intervals (HWCI) of the estimated thresholds increased with slope. Efficiency increased with slope and with the number of alternatives in forced choice tasks.
Even under mismatched conditions, Bayesian adaptive methods with a fixed slope can generate unbiased threshold estimates in certain d’ performance levels. The results provide the theoretical basis to use psychometric functions with fixed slopes in parametric Bayesian adaptive procedures.REFS:  Kontsevich & Tyler, 1996;  Lesmes et al., 2015;  Lesmes et al., 2010;  Hou et al., 2015.
This abstract was presented at the 2019 ARVO Annual Meeting, held in Vancouver, Canada, April 28 - May 2, 2019.
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