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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.
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.
Exact P-Values For Discrete Models Obtained By Estimation And Maximisation, Chris Lloyd
Exact P-Values For Discrete Models Obtained By Estimation And Maximisation, Chris Lloyd
Chris J. Lloyd
In constructing exact tests, one must deal with the possible dependence of the P-value on the nuisance parameter/s psi as well as discreteness of the sample space. A classical but heavy handed approach is to maximise over psi. We prove what has previously been understood informally, namely that maximisation produces the uinique and smallest possible P-value subject to the ordering induced by the underlying test statistic and test validity. On the other hand, allowing for the worst case will be more attractive when the P-value is less dependent on psi. We investigate the extent to which estimating psi under the …
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 …