Early stopping

When started with a smooth image, iterative maximum likelihood algorithms can achieve some level of regularization by early stopping of the iterations before convergence (see e.g. Lanteri et al., 1999). In this case, the regularized solution is not the maximum fikelihood one and it also depends on the initial solution and the number of performed iterations. A better solution is to explicitly account for additional regularization constraints in the penalty criterion. This is explained in the next section. 

Gebski V, McNeil D, Coates A, Forbes J. Monitoring distributional assumptions and early stopping for a prospective clinical trial using Monte Carlo simulation. StatMed 1987 Sep 6(6) 667-78. 

The principal reason that a test set is necessary for validation is that empirical model-building methods cannot readily distinguish between noise and information in data sets, so the methods are prone to adjusting the model parameters to reduce error beyond the point warranted by the information contained in the data. This problem is called overtraining and can be countered by a variety of techniques such as descriptor reduction and early stopping, and readers interested in those topics are referred to the more detailed reviews of numerical methods cited in each of the following sections. 

Some of the early stopped-flow work concentrated on the oxidations of iron(II) complexes shown in Eqs. 7-9 [9, 10]. 

The consequence of the one-base deletions was that all bases down.stream of the deletion were out of frame, thus producing a garbled series of amino acids during the process of translation. The garbling of codons downstream of the one-base deletion also resulted in generation of an early stop codon, which produced a tnmeafed APC protein. 

It is suggested that in Drosophila, the DSCAM gene may produce more than 38,000 mRNAs encoding different proteins. Among an array of mRNA, not all mRNAs are translatable for a variety of reasons, including the presence of an early stop codon. Alternate splicing may be tissue specific and... 

It is of interest to compare the rate constants determined for intramolecular ET in Ps-NiR (23 s at 298 K, pH 7.0) with the corresponding ones reported for Pa- and Pp-NiRs (cf. Table V). An early stopped-flow study of the reduction kinetics of Pa-NiR by an excess of reduced azurin yielded a rate constant of... 

It is the case for many indications that the number of patients needed to prove efficacy is actually less than the number who must be exposed to the new treatment to assess its safety. Furthermore, for most treatments under study, once the trial is finished, if it is successful, there will be a period of time before the drug will be generally available. The first reason makes stopping boundaries for efficacy irrelevant. The second reason means that there is no good reason for stopping because the experimental treatment has proved itself more effective than the control treatment since it will not be possible to switch all future patients onto this treatment. The second reason does, of course, leave the door open for stopping trials for lack of efficacy of an experimental treatment but this, in any case, does not raise quite the same number of issues which are attendant upon early stopping for proven efficacy. 

So, if there is a place for sequential analysis of drug-development trials, monitoring and so forth, it is either for safety and/or lack of efficacy reasons, or for economic reasons. The latter can be important for some indications. There may be cases where the sponsor realizes that the number of patients needed to prove efficacy may, for a fixed trial, exceed those which need to be studied for registration. Under such circumstance, the possibility of early stopping, either for proven efficacy or lack of efficacy (what was referred to in section 19.1 as futility), may be attractive. The expected run length will be less than the fixed sample size required, the costs of the trial may be less, and the time to registration if the trial is successful will probably be reduced. 

Souhami RL (1994) The clinical importance of early stopping of randomized trials in cancer treatments. Statistics in Medicine 13 1293-1295. 

Adaptive methodologies, such as sample size or outcome re-estimations and early stopping decision rules, could be specified in the statistical analysis plans for cardiovascular safety outcome trials, potentially to reduce study duration, increase the chances of success, and facilitate earlier submissions. Many different types of adaptive designs are in use. The most common adaptation is to increase the sample size if the rate at which outcomes are accruing is slow. This modification raises no statistical issues if done in a blinded manner. 

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