A note on stopping rules for iterative regularisation methods and filtered SVD

"This volume contains the proceedings of a meeting held at Montpellier from December 1st to December 5th 1986 .sponsored by the Centre national de la recherche scientifique ."--Preface.

An analysis of protocols and publications suggested that most discontinuations of clinical trials were not based on preplanned interim analyses or stopping rules.

OBJECTIVES: To investigate the frequency of interim analyses, stopping rules, and data safety and monitoring boards (DSMBs) in protocols of randomized controlled trials (RCTs); to examine these features across different reasons for trial discontinuation; and to identify discrepancies in reporting between protocols and publications. STUDY DESIGN AND SETTING: We used data from a cohort of RCT protocols approved between 2000 and 2003 by six research ethics committees in Switzerland, Germany, and Canada. RESULTS: Of 894 RCT protocols, 289 prespecified interim analyses (32.3%), 153 stopping rules (17.1%), and 257 DSMBs (28.7%). Overall, 249 of 894 RCTs (27.9%) were prematurely discontinued; mostly due to reasons such as poor recruitment, administrative reasons, or unexpected harm. Forty-six of 249 RCTs (18.4%) were discontinued due to early benefit or futility; of those, 37 (80.4%) were stopped outside a formal interim analysis or stopping rule. Of 515 published RCTs, there were discrepancies between protocols and publications for interim analyses (21.1%), stopping rules (14.4%), and DSMBs (19.6%). CONCLUSION: Two-thirds of RCT protocols did not consider interim analyses, stopping rules, or DSMBs. Most RCTs discontinued for early benefit or futility were stopped without a prespecified mechanism. When assessing trial manuscripts, journals should require access to the protocol.

Stopping rules for phase II studies

This paper, the second in a series of three papers concerned with the statistical aspects of interim analyses in clinical trials, is concerned with stopping rules in phase II clinical trials. Phase II trials are generally small-scale studies, and may include one or more experimental treatments with or without a control. A common feature is that the results primarily determine the course of further clinical evaluation of a treatment rather than providing definitive evidence of treatment efficacy. This means that there is more flexibility available in the design and analysis of such studies than in phase III trials. This has led to a range of different approaches being taken to the statistical design of stopping rules for such trials. This paper briefly describes and compares the different approaches. In most cases the stopping rules can be described and implemented easily without knowledge of the detailed statistical and computational methods used to obtain the rules.

An analysis of protocols and publications suggested that most discontinuations of clinical trials were not based on preplanned interim analyses or stopping rules.

OBJECTIVES To investigate the frequency of interim analyses, stopping rules, and data safety and monitoring boards (DSMBs) in protocols of randomized controlled trials (RCTs); to examine these features across different reasons for trial discontinuation; and to identify discrepancies in reporting between protocols and publications. STUDY DESIGN AND SETTING We used data from a cohort of RCT protocols approved between 2000 and 2003 by six research ethics committees in Switzerland, Germany, and Canada. RESULTS Of 894 RCT protocols, 289 prespecified interim analyses (32.3%), 153 stopping rules (17.1%), and 257 DSMBs (28.7%). Overall, 249 of 894 RCTs (27.9%) were prematurely discontinued; mostly due to reasons such as poor recruitment, administrative reasons, or unexpected harm. Forty-six of 249 RCTs (18.4%) were discontinued due to early benefit or futility; of those, 37 (80.4%) were stopped outside a formal interim analysis or stopping rule. Of 515 published RCTs, there were discrepancies between protocols and publications for interim analyses (21.1%), stopping rules (14.4%), and DSMBs (19.6%). CONCLUSION Two-thirds of RCT protocols did not consider interim analyses, stopping rules, or DSMBs. Most RCTs discontinued for early benefit or futility were stopped without a prespecified mechanism. When assessing trial manuscripts, journals should require access to the protocol.

Stopping rules in Bayesian adaptive threshold estimation

Threshold estimation with sequential procedures is justifiable on the surmise that the index used in the so-called dynamic stopping rule has diagnostic value for identifying when an accurate estimate has been obtained. The performance of five types of Bayesian sequential procedure was compared here to that of an analogous fixed-length procedure. Indices for use in sequential procedures were: (1) the width of the Bayesian probability interval, (2) the posterior standard deviation, (3) the absolute change, (4) the average change, and (5) the number of sign fluctuations. A simulation study was carried out to evaluate which index renders estimates with less bias and smaller standard error at lower cost (i.e. lower average number of trials to completion), in both yes–no and two-alternative forced-choice (2AFC) tasks. We also considered the effect of the form and parameters of the psychometric function and its similarity with themodel function assumed in the procedure. Our results show that sequential procedures do not outperform fixed-length procedures in yes–no tasks. However, in 2AFC tasks, sequential procedures not based on sign fluctuations all yield minimally better estimates than fixed-length procedures, although most of the improvement occurs with short runs that render undependable estimates and the differences vanish when the procedures run for a number of trials (around 70) that ensures dependability. Thus, none of the indices considered here (some of which are widespread) has the diagnostic value that would justify its use. In addition, difficulties of implementation make sequential procedures unfit as alternatives to fixed-length procedures.

Apply response adaptive randomization to group sequential with early stopping

Group sequential methods and response adaptive randomization (RAR) procedures have been applied in clinical trials due to economical and ethical considerations. Group sequential methods are able to reduce the average sample size by inducing early stopping, but patients are equally allocated with half of chance to inferior arm. RAR procedures incline to allocate more patients to better arm; however it requires more sample size to obtain a certain power. This study intended to combine these two procedures. We applied the Bayesian decision theory approach to define our group sequential stopping rules and evaluated the operating characteristics under RAR setting. The results showed that Bayesian decision theory method was able to preserve the type I error rate as well as achieve a favorable power; further by comparing with the error spending function method, we concluded that Bayesian decision theory approach was more effective on reducing average sample size.^

An evaluation of a Bayesian method of dose escalation based on bivariate binary responses

Recently, various approaches have been suggested for dose escalation studies based on observations of both undesirable events and evidence of therapeutic benefit. This article concerns a Bayesian approach to dose escalation that requires the user to make numerous design decisions relating to the number of doses to make available, the choice of the prior distribution, the imposition of safety constraints and stopping rules, and the criteria by which the design is to be optimized. Results are presented of a substantial simulation study conducted to investigate the influence of some of these factors on the safety and the accuracy of the procedure with a view toward providing general guidance for investigators conducting such studies. The Bayesian procedures evaluated use logistic regression to model the two responses, which are both assumed to be binary. The simulation study is based on features of a recently completed study of a compound with potential benefit to patients suffering from inflammatory diseases of the lung.

Iterative regularization methods for ill-posed problems

This Ph.D thesis focuses on iterative regularization methods for regularizing linear and nonlinear ill-posed problems. Regarding linear problems, three new stopping rules for the Conjugate Gradient method applied to the normal equations are proposed and tested in many numerical simulations, including some tomographic images reconstruction problems. Regarding nonlinear problems, convergence and convergence rate results are provided for a Newton-type method with a modified version of Landweber iteration as an inner iteration in a Banach space setting.

Continuous safety screens for randomized controlled clinical trials with blinded treatment information

Standard methods for testing safety data are needed to ensure the safe conduct of clinical trials. In particular, objective rules for reliably identifying unsafe treatments need to be put into place to help protect patients from unnecessary harm. DMCs are uniquely qualified to evaluate accumulating unblinded data and make recommendations about the continuing safe conduct of a trial. However, it is the trial leadership who must make the tough ethical decision about stopping a trial, and they could benefit from objective statistical rules that help them judge the strength of evidence contained in the blinded data. We design early stopping rules for harm that act as continuous safety screens for randomized controlled clinical trials with blinded treatment information, which could be used by anyone, including trial investigators (and trial leadership). A Bayesian framework, with emphasis on the likelihood function, is used to allow for continuous monitoring without adjusting for multiple comparisons. Close collaboration between the statistician and the clinical investigators will be needed in order to design safety screens with good operating characteristics. Though the math underlying this procedure may be computationally intensive, implementation of the statistical rules will be easy and the continuous screening provided will give suitably early warning when real problems were to emerge. Trial investigators and trial leadership need these safety screens to help them to effectively monitor the ongoing safe conduct of clinical trials with blinded data.^

Selection bias and the cross-validation of regression models for prediction

Strategies are compared for the development of a linear regression model with stochastic (multivariate normal) regressor variables and the subsequent assessment of its predictive ability. Bias and mean squared error of four estimators of predictive performance are evaluated in simulated samples of 32 population correlation matrices. Models including all of the available predictors are compared with those obtained using selected subsets. The subset selection procedures investigated include two stopping rules, C$\sb{\rm p}$ and S$\sb{\rm p}$, each combined with an 'all possible subsets' or 'forward selection' of variables. The estimators of performance utilized include parametric (MSEP$\sb{\rm m}$) and non-parametric (PRESS) assessments in the entire sample, and two data splitting estimates restricted to a random or balanced (Snee's DUPLEX) 'validation' half sample. The simulations were performed as a designed experiment, with population correlation matrices representing a broad range of data structures.^ The techniques examined for subset selection do not generally result in improved predictions relative to the full model. Approaches using 'forward selection' result in slightly smaller prediction errors and less biased estimators of predictive accuracy than 'all possible subsets' approaches but no differences are detected between the performances of C$\sb{\rm p}$ and S$\sb{\rm p}$. In every case, prediction errors of models obtained by subset selection in either of the half splits exceed those obtained using all predictors and the entire sample.^ Only the random split estimator is conditionally (on $\\beta$) unbiased, however MSEP$\sb{\rm m}$ is unbiased on average and PRESS is nearly so in unselected (fixed form) models. When subset selection techniques are used, MSEP$\sb{\rm m}$ and PRESS always underestimate prediction errors, by as much as 27 percent (on average) in small samples. Despite their bias, the mean squared errors (MSE) of these estimators are at least 30 percent less than that of the unbiased random split estimator. The DUPLEX split estimator suffers from large MSE as well as bias, and seems of little value within the context of stochastic regressor variables.^ To maximize predictive accuracy while retaining a reliable estimate of that accuracy, it is recommended that the entire sample be used for model development, and a leave-one-out statistic (e.g. PRESS) be used for assessment. ^

Reporting on data monitoring committees in neonatal randomised controlled trials is inconsistent

Aim: To evaluate the reported use of Data Monitoring Committees (DMCs), the frequency of interim analysis, pre-specified stopping rules and early trial termination in neonatal randomised controlled trials (RCTs). Methods: We reviewed neonatal RCTs published in four high impact general medical journals, specifically looking at safety issues including documented involvement of a DMC, stated interim analysis, stopping rules and early trial termination. We searched all journal issues over an 11-year period (2003-2013) and recorded predefined parameters on each item for RCTs meeting inclusion criteria. Results: Seventy neonatal trials were identified in four general medical journals: Lancet, New England Journal of Medicine (NEJM), British Medical Journal and Journal of American Medical Association (JAMA). 43 (61.4%) studies reported the presence of a DMC, 36 (51.4%) explicitly mentioned interim analysis; stopping rules were reported in 15 (21.4%) RCTs and 7 (10%) trials were terminated early. The NEJM most frequently reported these parameters compared to the other three journals reviewed. Conclusion: While the majority of neonatal RCTs report on DMC involvement and interim analysis there is still scope for improvement. Clear documentation of safety related issues should be a central component of reporting in neonatal trials involving newborn infants.

An account of the stopping of Daggenham Breach ... Containing also proper rules for performing any the like work: and proposals for rendering the ports of Dover and Dublin ... commodious for entertaining large ships. To which is prefix'd, a plan of the levels which were over-flow'd by the breach.

Bound in old sprinkled calf.

Young, inexperienced and on the road : do novice drivers comply with road rules?

The graduated driver licensing (GDL) program in Queensland, Australia, was considerably enhanced in July 2007. This paper explores the compliance of young Learner and Provisional (intermediate) drivers with current GDL requirements and general road rules. Unsupervised driving, Learner logbook accuracy, and experiences of punishment avoidance were explored, along with speeding as a Provisional driver. Participants (609 females; M = 17.43 years) self-reported sociodemographic characteristics, driving behaviours and licensing experiences as Learners. A subset of participants (238 females, 105 males) completed another survey six months later exploring their Provisional behaviours and experiences. While the majority of the participants reported compliance with both the GDL requirements and general road rules such as stopping at red lights on their Learner licence; a considerable proportion reported speeding. Furthermore, they reported becoming less compliant during the Provisional phase, particularly with speed limits. Self-reported speeding was predicted by younger age at licensure, being in a relationship, driving unsupervised, submitting inaccurate Learner logbooks, and speeding as a Learner. Enforcement and education countermeasures should focus upon curtailing noncompliance, targeting speeding in particular. Novice drivers should be encouraged to comply with all road rules, including speed limits, and safe driving behaviours should be developed and reinforced during the Learner and early Provisional periods. Novice drivers have been found to model their parents’ driving, and parents are pivotal in regulating novice driving. It is vital young novice drivers and parents alike are encouraged to comply with all road rules, including GDL requirements.

Forcing Usage Rules in PublicWireless LANs

Langattomien lähiverkkojen yleistyessä nopeasti suurten verkkojen teknologiana käyttösääntöjen valvonta tulee tarpeelliseksi. Tässä työssä kuvataan, kuinka käyttäjät voidaan pakottaa noudattamaan käyttösääntöjä julkisissa WLAN-verkoissa. Työssä käsiteltävät ongelmat koskevat menetelmiä epäluotettavien DHCP-palvelinten paljastamiseksi sekä omia IP-osoitteita käyttävien käyttäjien paljastamiseksi tilanteissa, jolloin IP-osoite ei ole virallisen DHCP-palvelimen myöntämä. Jokaisen menetelmän kohdalla pohditaan, kuinka tällaisia käyttäjiä voidaan estää rikkomasta käyttösääntöjä. Lisäksi pohditaan keskitetyn tietojen keruun hyödyntämistä kuvattujen tehtävien suorittamiseksi. Esitetyt ratkaisut on erityisesti suunniteltu testiverkkoa varten, mutta yleiset ideat ovat toimivia missä tahansa langattomassa verkossa.