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Full-Text Articles in Physical Sciences and Mathematics
More Powerful Exact Noninferiority And Equivalence Tests Based On Binary Matched Pairs, Chris Lloyd
More Powerful Exact Noninferiority And Equivalence Tests Based On Binary Matched Pairs, Chris Lloyd
Chris J. Lloyd
Assessing the therapeutic noninferiority or equivalence of one medical treatment compared to another is often based on the difference of response rates from a matched binary pairs design. This paper develops new exact unconditional tests for noninferiority and equivalence that are more powerful than available alternatives. There are three new elements presented in this paper. First we introduce the LR statistic as an alternative to the previously proposed score statistic of Nam (1997). Second, we eliminate the nuisance parameter by estimation followed by maximization as an alternative to the partial maximization of Berger and Boos (1994) or traditional full maximization. …
The Economic Value Of Improved Environmental Health In Victorian Rivers, Chris Lloyd
The Economic Value Of Improved Environmental Health In Victorian Rivers, Chris Lloyd
Chris J. Lloyd
The non market valuation technique known as choice modelling was used to general benefit estimates for a selection of hypothetical environmental improvements Victorian Rivers. Monetary values were estimated for four attributed of improvements. The relevance of the approach to management and policy issues is demonstrated.
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 …
On Approximate Conditioning And Higher Order Asymptotics For 2x2 Tables, Chris Lloyd
On Approximate Conditioning And Higher Order Asymptotics For 2x2 Tables, Chris Lloyd
Chris J. Lloyd
For testing canonical parameters in a continuous exponential family, P-values based on higher order asymptotic formulas such as p* approximate the exact conditional P-value with great accuracy. For discrete models, the conditional distribution can be extremely discrete or even degenerate which raises the questions (a) should one try to approximate the conditional P-value, (b) what does p* approximate? Pierce and Peters (1999) have argued that p* approximates an approximately conditional P-value and that this approximately conditional P-value is an inferentially sensible quantity worth approximating. Their arguments and numerical results are oriented towards problems where the conditioning variable has 3 or …
Multinomial Logistic Regression: An Application To Estimating Performance Of A Multiple Screening Test For Bowel Cancer When Negatives Are Unverified., Chris Lloyd, Don Frommer
Multinomial Logistic Regression: An Application To Estimating Performance Of A Multiple Screening Test For Bowel Cancer When Negatives Are Unverified., Chris Lloyd, Don Frommer
Chris J. Lloyd
This paper describes a method of estimating the performance of a multiple screening test where those who test negative do not have their true disease status determined. The methodology is motivated by a dataset on 49,927 subjects who were given K=6 binary tests for bowel cancer. A complicating factor is that individuals may have polyps present in the bowel, a condition that the screening test is not designed to detect but which may be worth diagnosing. The methodology is based on a multinomial logit model for Pr(S|R_6), the probability distribution of patient status S (healthy, polyps or diseased) conditional on …
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 …