TY - JOUR

T1 - Statistical evaluation of ion-channel gating models based on distributions of log-likelihood ratios

AU - Csanády, László

PY - 2006/5

Y1 - 2006/5

N2 - The distributions of log-likelihood ratios (ΔLL) obtained from fitting ion-channel dwell-time distributions with nested pairs of gating models (Ξ, full model; ΞR, submodel) were studied both theoretically and using simulated data. When Ξ is true, ΔLL is asymptotically normally distributed with predictable mean and variance that increase linearly with data length (n). When ΞR is true and corresponds to a distinct point in full parameter space, ΔLL is Γ-distributed (2ΔLL is χ-square). However, when data generated by an l-component multiexponential distribution are fitted by l+1 components, ΞR corresponds to an infinite set of points in parameter space. The distribution of ΔLL is a mixture of two components, one identically zero, the other approximated by a Γ-distribution. This empirical distribution of ΔLL, assuming ΞR, allows construction of a valid log-likelihood ratio test. The log-likelihood ratio test, the Akaike information criterion, and the Schwarz criterion all produce asymmetrical Type I and II errors and inefficiently recognize Ξ, when true, from short datasets. A new decision strategy, which considers both the parameter estimates and ΔLL, yields more symmetrical errors and a larger discrimination power for small n. These observations are explained by the distributions of ΔLL when Ξ or ΞR is true.

AB - The distributions of log-likelihood ratios (ΔLL) obtained from fitting ion-channel dwell-time distributions with nested pairs of gating models (Ξ, full model; ΞR, submodel) were studied both theoretically and using simulated data. When Ξ is true, ΔLL is asymptotically normally distributed with predictable mean and variance that increase linearly with data length (n). When ΞR is true and corresponds to a distinct point in full parameter space, ΔLL is Γ-distributed (2ΔLL is χ-square). However, when data generated by an l-component multiexponential distribution are fitted by l+1 components, ΞR corresponds to an infinite set of points in parameter space. The distribution of ΔLL is a mixture of two components, one identically zero, the other approximated by a Γ-distribution. This empirical distribution of ΔLL, assuming ΞR, allows construction of a valid log-likelihood ratio test. The log-likelihood ratio test, the Akaike information criterion, and the Schwarz criterion all produce asymmetrical Type I and II errors and inefficiently recognize Ξ, when true, from short datasets. A new decision strategy, which considers both the parameter estimates and ΔLL, yields more symmetrical errors and a larger discrimination power for small n. These observations are explained by the distributions of ΔLL when Ξ or ΞR is true.

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U2 - 10.1529/biophysj.105.075135

DO - 10.1529/biophysj.105.075135

M3 - Article

C2 - 16461404

AN - SCOPUS:33646165887

VL - 90

SP - 3523

EP - 3545

JO - Biophysical Journal

JF - Biophysical Journal

SN - 0006-3495

IS - 10

ER -