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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 …
Exact One-Sided Confidence Limits For The Difference Between Two Correlated Proportions, Chris Lloyd, Max V. Moldovan
Exact One-Sided Confidence Limits For The Difference Between Two Correlated Proportions, Chris Lloyd, Max V. Moldovan
Chris J. Lloyd
We construct exact and optimal one-sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well-established optimality theory of Buehler (1957). Starting with five different approximate loer and upper limits, we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size. Exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use.