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Estimated P-Values In Discrete Models: Asymptotic And Non-Asymptotic Effects, Chris Lloyd
Estimated P-Values In Discrete Models: Asymptotic And Non-Asymptotic Effects, Chris Lloyd
Chris J. Lloyd
The exact null distribution of a P-value typically depends on nuisance parameters unspecified under the null. For discrete models and standard approximate P-values, this dependence can be quite strong. The estimated (or bootstrap) P-value is the exact probability of the P-value being no larger than its observed value, with the null estimate of the nuisance parameter substituted. For continuous models, it is known that such `bootstrap' P-values deviate from uniformity by terms of order m^{-3/2}, where m is a measure of sample size. The main difficulty with discrete models is the breakdown of asymptotics near the boundary. The aim of …
More Powerful Exact Tests Of Equivalence, Chris Lloyd
More Powerful Exact Tests Of Equivalence, Chris Lloyd
Chris J. Lloyd
In randomized clinical trials, it is often required to demonstrate that a new medical treatment is neither substantially worse nor better than a standard reference treatment. Formal testing of such `equivalence hypotheses' is typcialyl done by combining two one-sided tests (TOST). A quite diferent strand of research has demonstrated that maximising P-values over nuisance parameters produces optimal tests (Rohmel and Mansmann (1999) and Lloyd (2008a)). In this paper we point out that, even if the one-sided tests are exact and optimal, the TOST will generally be conservative and requires a further adjustment to remove this conservatism. The appropriate procedure is …
A New Exact And More Powerful Unconditional Test Of No Treatment Effect From Binary Matched Pairs, Chris Lloyd
A New Exact And More Powerful Unconditional Test Of No Treatment Effect From Binary Matched Pairs, Chris Lloyd
Chris J. Lloyd
We consider the problem of testing for a difference in the probability of success from matched binary pairs. Starting with three standard inexact tests, the nuisance parameter is first estimated and then the residual dependence is eliminated by maximisation, producing what I call an E+M P-value. The E+M P-value based on McNemar's statistic is shown numerically to dominate previous suggestions, including partially maximised P-values as described in Berger and Sidik (2003). The latter method however may have computational advantages for large samples.
Exact Tests Of Non-Inferiority From Independent Binomial Data Based On Second Order Test Statistics, Chris Lloyd
Exact Tests Of Non-Inferiority From Independent Binomial Data Based On Second Order Test Statistics, Chris Lloyd
Chris J. Lloyd
Recent advances in likelihood asymptotics (Reid, 2003) lead to pivotal quantities that are closer to standard normal than standard pivotals and also respect some kind of conditionality. It is less clear the extent to which these methods work for discrete models. On the other hand, in the context of binomial trials conditional pivotals can lead to more efficient unconditional inferences, see Boschloo (1970) and Lloyd and Moldovan (2007). This suggests that second order pivotals that respect local conditionality might provide more powerful exact tests. For testing the rate ratio from independent binomial samples, we investigate 5 first order pivotals and …