100 research outputs found
Treatment Effect Quantification for Time-to-event Endpoints -- Estimands, Analysis Strategies, and beyond
A draft addendum to ICH E9 has been released for public consultation in
August 2017. The addendum focuses on two topics particularly relevant for
randomized confirmatory clinical trials: estimands and sensitivity analyses.
The need to amend ICH E9 grew out of the realization of a lack of alignment
between the objectives of a clinical trial stated in the protocol and the
accompanying quantification of the "treatment effect" reported in a regulatory
submission. We embed time-to-event endpoints in the estimand framework, and
discuss how the four estimand attributes described in the addendum apply to
time-to-event endpoints. We point out that if the proportional hazards
assumption is not met, the estimand targeted by the most prevalent methods used
to analyze time-to-event endpoints, logrank test and Cox regression, depends on
the censoring distribution. We discuss for a large randomized clinical trial
how the analyses for the primary and secondary endpoints as well as the
sensitivity analyses actually performed in the trial can be seen in the context
of the addendum. To the best of our knowledge, this is the first attempt to do
so for a trial with a time-to-event endpoint. Questions that remain open with
the addendum for time-to-event endpoints and beyond are formulated, and
recommendations for planning of future trials are given. We hope that this will
provide a contribution to developing a common framework based on the final
version of the addendum that can be applied to design, protocols, statistical
analysis plans, and clinical study reports in the future.Comment: 37 page
Maximum likelihood estimation of a log-concave density and its distribution function: Basic properties and uniform consistency
We study nonparametric maximum likelihood estimation of a log-concave
probability density and its distribution and hazard function. Some general
properties of these estimators are derived from two characterizations. It is
shown that the rate of convergence with respect to supremum norm on a compact
interval for the density and hazard rate estimator is at least
and typically , whereas the difference
between the empirical and estimated distribution function vanishes with rate
under certain regularity assumptions.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ141 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm), Version 3 is
the extended technical report cited in version
logcondens: Computations Related to Univariate Log-Concave Density Estimation
Maximum likelihood estimation of a log-concave density has attracted considerable attention over the last few years. Several algorithms have been proposed to estimate such a density. Two of those algorithms, an iterative convex minorant and an active set algorithm, are implemented in the R package logcondens. While these algorithms are discussed elsewhere, we describe in this paper the use of the logcondens package and discuss functions and datasets related to log-concave density estimation contained in the package. In particular, we provide functions to (1) compute the maximum likelihood estimate (MLE) as well as a smoothed log-concave density estimator derived from the MLE, (2) evaluate the estimated density, distribution and quantile functions at arbitrary points, (3) compute the characterizing functions of the MLE, (4) sample from the estimated distribution, and finally (5) perform a two-sample permutation test using a modified Kolmogorov-Smirnov test statistic. In addition, logcondens makes two datasets available that have been used to illustrate log-concave density estimation.
Integrating Phase 2 into Phase 3 based on an Intermediate Endpoint While Accounting for a Cure Proportion -- with an Application to the Design of a Clinical Trial in Acute Myeloid Leukemia
For a trial with primary endpoint overall survival for a molecule with
curative potential, statistical methods that rely on the proportional hazards
assumption may underestimate the power and the time to final analysis. We show
how a cure proportion model can be used to get the necessary number of events
and appropriate timing via simulation. If Phase 1 results for the new drug are
exceptional and/or the medical need in the target population is high, a Phase 3
trial might be initiated after Phase 1. Building in a futility interim analysis
into such a pivotal trial may mitigate the uncertainty of moving directly to
Phase 3. However, if cure is possible, overall survival might not be mature
enough at the interim to support a futility decision. We propose to base this
decision on an intermediate endpoint that is sufficiently associated with
survival. Planning for such an interim can be interpreted as making a
randomized Phase 2 trial a part of the pivotal trial: if stopped at the
interim, the trial data would be analyzed and a decision on a subsequent Phase
3 trial would be made. If the trial continues at the interim then the Phase 3
trial is already underway. To select a futility boundary, a mechanistic
simulation model that connects the intermediate endpoint and survival is
proposed. We illustrate how this approach was used to design a pivotal
randomized trial in acute myeloid leukemia, discuss historical data that
informed the simulation model, and operational challenges when implementing it.Comment: 23 pages, 3 figures, 3 tables. All code is available on github:
https://github.com/numbersman77/integratePhase2.gi
Marshall's lemma for convex density estimation
Marshall's [Nonparametric Techniques in Statistical Inference (1970)
174--176] lemma is an analytical result which implies --consistency
of the distribution function corresponding to the Grenander [Skand.
Aktuarietidskr. 39 (1956) 125--153] estimator of a non-decreasing probability
density. The present paper derives analogous results for the setting of convex
densities on .Comment: Published at http://dx.doi.org/10.1214/074921707000000292 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
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