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

The distributions of log-likelihood ratios (DeltaLL) obtained from fitting ion-channel dwell-time distributions with nested pairs of gating models (Xi, full model; Xi(R), submodel) were studied both theoretically and using simulated data. When Xi is true, DeltaLL is asymptotically normally distributed with predictable mean and variance that increase linearly with data length (n). When Xi(R) is true and corresponds to a distinct point in full parameter space, DeltaLL is Gamma-distributed (2DeltaLL is chi-square). However, when data generated by an l-component multiexponential distribution are fitted by l+1 components, Xi(R) corresponds to an infinite set of points in parameter space. The distribution of DeltaLL is a mixture of two components, one identically zero, the other approximated by a Gamma-distribution. This empirical distribution of DeltaLL, assuming Xi(R), 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 Xi, when true, from short datasets. A new decision strategy, which considers both the parameter estimates and DeltaLL, yields more symmetrical errors and a larger discrimination power for small n. These observations are explained by the distributions of DeltaLL when Xi or Xi(R) is true.