Biomedical subjects

Mark D Rothmann

Publications and source records attributed to Mark D Rothmann.

2 recordsLinked to original sources

PubMed2006

Inferences on a life distribution by sampling from the ages or the ages at death.

Consider a system where units having independent and identically distributed lifetimes enter according to a nonhomogeneous Poisson process. After the unit's life in the system, the unit departs the system. For a fixed system time, this paper relates the units' common underlying life distribution with the distribution of the ages of units in the system, the distribution for the system life of units that departed the system and the distribution for the system life of units that have recently departed the system. Results can be used to estimate the underlying life distribution or a truncated version of that distribution based on the ages and/or most recent ages at death in both one sample and two sample situations. Results include a complete characterization of the possible distribution of the ages of those units in the system, how to estimate the underlying life distribution from the most recent ages at death, and how to test for an underlying monotone failure rate function based on independent samples from the ages and most recent ages at death. Two sample inferences that involve a likelihood ratio ordering make use of the results in Dykstra et al. (1995, J Amer Statisc Assoc 90(431):1030-1040), which provides the maximum likelihood estimators and a likelihood ratio test when the two distributions satisfy a likelihood ratio ordering. For the ages of the active units and the ages at death among the departed units, limits for their distributions and strong limiting results for their empirical distributions will be provided.

Biometry↗

PubMed2003

On non-inferiority analysis based on delta-method confidence intervals.

For many indications where there is an effective standard therapy, active controlled trials are generally conducted when it is unethical to use a placebo. The efficacy objective of most such trials is the demonstration that the experimental therapy has superior efficacy to the active-control. The efficacy objective of a non-inferiority trial may be to rule out that the experimental treatment loses some prespecified fraction of the active-control effect. The size of the active-control effect may be based on previous trials comparing this active-control with a placebo--for example, through a meta-analysis. Delta-method 95% confidence interval procedures are among the testing procedures that have been proposed to test a non-inferiority hypothesis that an experimental treatment retains more than some prespecified fraction of the active-control effect. For time-to-event endpoints using hazard ratios, we will examine the type I error probability of such testing procedures under the assumption that the current active-control effect has been correctly modeled. Conditions are discussed for when such testing procedures maintain a desired approximate type I error rate and when such testing procedures will not. Two applications (one in Cardiorenalogy and one in Oncology) are given--one maintains the desired approximate type I error probability and the other does not. The delta-method 95% confidence interval procedures will also be contrasted with Fieller 95% confidence intervals. Testing based on Fieller 95% confidence intervals will maintain a desired approximate type I error rate.

Confidence Intervals↗