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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. …
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 …
Exact Confidence Bounds For The Risk Ratio In 2x2 Tables With Structural Zero, Chris J. Lloyd, Max Moldovan
Exact Confidence Bounds For The Risk Ratio In 2x2 Tables With Structural Zero, Chris J. Lloyd, Max Moldovan
Chris J. Lloyd
This paper examines exact one-sided confidence limits for the risk ratio in a 2x2 table with structural zero. Starting with four approximate lower and upper limits, we adjust each using the algorithm of Buehler (1957) to arrive at lower (upper) limits that have exact coverage properties and are as large (small) as possible subject to coverage, as well as an ordering, constraint. Different Buehler limits are compared by their mean size, since all are exact in their coverage. Buehler limits based on the signed root likelihood ratio statistic are found to have the best performance and recommended for practical use.
Unconditional Efficient One-Sided Confidence Limits For The Odds Ratio Based On Conditional Likelihood, Chris Lloyd, Max Moldovan
Unconditional Efficient One-Sided Confidence Limits For The Odds Ratio Based On Conditional Likelihood, Chris Lloyd, Max Moldovan
Chris J. Lloyd
We compare various one-sided confidence limits for the odds ratio in a 2x2 table. The first group of limits relies on first order asymptotic approximations and includes limits based on the (signed) likelihood ratio, score and Wald statistics. The second group of limits is based on the conditional tilted hypergeometric distribution, with and without mid-P correction. All these limits have poor unconditional coverage properties and so we apply the general transformation of Buehler (1957) to obtain limits which are unconditionally exact. The performance of these competing exact limits is assessed across a range of sample sizes and parameter values by …
Efficient And Exact Tests Of The Risk Ratio In A Correlated 2x2 Table With Structural Zero, Chris Lloyd
Efficient And Exact Tests Of The Risk Ratio In A Correlated 2x2 Table With Structural Zero, Chris Lloyd
Chris J. Lloyd
For a correlated 2x2 table where the (01) cell is empty by design, the parameter of interest is typically the ratio of the probability of secondary response conditional on primary response to the probability of primary response, also known as a risk ratio. It is common to test whether or not the risk ratio equals one. One method of obtaining an exact P-value is to maximise the tail probability of the test statistic over the nuisance parameter. It is argued that better results are obtained by first replacing the nuisance parameter by its profile estimate in the calculation of its …