Group sequential designs using a family of type I error probability spending functions

1990 ◽  
Vol 9 (12) ◽  
pp. 1439-1445 ◽  
Author(s):  
Irving K. Hwang ◽  
Weichung J. Shih ◽  
John S. De Cani
Keyword(s):  
Error Probability ◽  
Type I Error ◽  
Type I ◽  
Sequential Designs ◽  
Group Sequential ◽  
Group Sequential Designs ◽  
Type I Error Probability

Group sequential designs with robust semiparametric recurrent event models

2018 ◽  
Vol 28 (8) ◽  
pp. 2385-2403 ◽  
Author(s):  
Tobias Mütze ◽  
Ekkehard Glimm ◽  
Heinz Schmidli ◽  
Tim Friede
Keyword(s):  
Error Rate ◽  
Joint Distribution ◽  
Recurrent Events ◽  
Type I Error ◽  
Type I ◽  
Sequential Designs ◽  
Group Sequential ◽  
Type I Error Rate ◽  
Sequential Procedures ◽  
Group Sequential Designs

Robust semiparametric models for recurrent events have received increasing attention in the analysis of clinical trials in a variety of diseases including chronic heart failure. In comparison to parametric recurrent event models, robust semiparametric models are more flexible in that neither the baseline event rate nor the process inducing between-patient heterogeneity needs to be specified in terms of a specific parametric statistical model. However, implementing group sequential designs in the robust semiparametric model is complicated by the fact that the sequence of Wald statistics does not follow asymptotically the canonical joint distribution. In this manuscript, we propose two types of group sequential procedures for a robust semiparametric analysis of recurrent events. The first group sequential procedure is based on the asymptotic covariance of the sequence of Wald statistics and it guarantees asymptotic control of the type I error rate. The second procedure is based on the canonical joint distribution and does not guarantee asymptotic type I error rate control but is easy to implement and corresponds to the well-known standard approach for group sequential designs. Moreover, we describe how to determine the maximum information when planning a clinical trial with a group sequential design and a robust semiparametric analysis of recurrent events. We contrast the operating characteristics of the proposed group sequential procedures in a simulation study motivated by the ongoing phase 3 PARAGON-HF trial (ClinicalTrials.gov identifier: NCT01920711) in more than 4600 patients with chronic heart failure and a preserved ejection fraction. We found that both group sequential procedures have similar operating characteristics and that for some practically relevant scenarios, the group sequential procedure based on the canonical joint distribution has advantages with respect to the control of the type I error rate. The proposed method for calculating the maximum information results in appropriately powered trials for both procedures.

scholarly journals Evaluation by simulation of clinical trial designs for evaluation of treatment during a viral haemorrhagic fever outbreak

2020 ◽  
Author(s):  
Pauline Manchon ◽  
Drifa Belhadi ◽  
France Mentré ◽  
Cédric Laouénan
Keyword(s):  
Clinical Trial ◽  
Survival Rate ◽  
Type I Error ◽  
Experimental Treatment ◽  
Type I ◽  
Sequential Designs ◽  
Group Sequential ◽  
Standard Case ◽  
Group Sequential Designs ◽  
Over Time

Abstract Background Viral haemorrhagic fevers are characterized by irregular outbreaks with high mortality rate. Difficulties arise when implementing therapeutic trials in this context. The outbreak duration is hard to predict and can be short compared to delays of trial launch and number of subject needed (NSN) recruitment. Our objectives were to compare, using clinical trial simulation, different trial designs for experimental treatment evaluation in various outbreak scenarios. Methods Four type of designs were compared: fixed or group-sequential, each being single- or two-arm. The primary outcome was 14-day survival rate. For single-arm designs, results were compared to a pre-trial historical survival rate pH. Treatments efficacy was evaluated by one-sided tests of proportion (fixed designs) and Whitehead triangular tests (group-sequential designs) with type-I-error = 0.025. Both survival rates in the control arm pC and survival rate differences Δ (including 0) varied. Three specific cases were considered: “standard” (fixed pC, reaching NSN for fixed designs and maximum sample size NMax for group-sequential designs); “changing with time” (increased pC\(\text{ }\)over time); “stopping of recruitment” (epidemic ends). We calculated the proportion of simulated trials showing treatment efficacy, with K = 93,639 simulated trials to get a type-I-error PI95% of [0.024;0.026]. Results Under H0 (Δ = 0), for the “standard” case, the type-I-error was maintained regardless of trial designs. For “changing with time” case, when pC>pH, type-I-error was inflated, and when pC<pH it decreased. Wrong conclusions were more often observed for single-arm designs due to an increase of Δ over time. Under H1 (Δ=+0.2), for the “standard” case, the power was similar between single- and two-arm designs when pC=pH. For “stopping of recruitment” case, single-arm performed better than two-arm designs, and fixed designs reported higher power than group-sequential designs. A web R-Shiny application was developed. Conclusions At an outbreak beginning, group-sequential two-arm trials should be preferred, as the infected cases number increases allowing to conduct a strong randomized control trial. Group-sequential designs allow early termination of trials in cases of harmful experimental treatment. After the epidemic peak, fixed single-arm design should be preferred, as the cases number decreases but this assumes a high level of confidence on the pre-trial historical survival rate.

scholarly journals Group Sequential Designs: A Tutorial

2021 ◽  
Author(s):  
Daniel Lakens ◽  
Friedrich Pahlke ◽  
Gernot Wassmer
Keyword(s):  
Sample Size ◽  
Type I Error ◽  
A Priori ◽  
R Package ◽  
Error Rates ◽  
Type I ◽  
Sequential Designs ◽  
Group Sequential ◽  
Shiny App ◽  
Group Sequential Designs

This tutorial illustrates how to design, analyze, and report group sequential designs. In these designs, groups of observations are collected and repeatedly analyzed, while controlling error rates. Compared to a fixed sample size design, where data is analyzed only once, group sequential designs offer the possibility to stop the study at interim looks at the data either for efficacy or futility. Hence, they provide greater flexibility and are more efficient in the sense that due to early stopping the expected sample size is smaller as compared to the sample size in the design with no interim look. In this tutorial we illustrate how to use the R package 'rpact' and the associated Shiny app to design studies that control the Type I error rate when repeatedly analyzing data, even when neither the number of looks at the data, nor the exact timing of looks at the data, is specified. Specifically for *t*-tests, we illustrate how to perform an a-priori power analysis for group sequential designs, and explain how to stop the data collection for futility by rejecting the presence of an effect of interest based on a beta-spending function. Finally, we discuss how to report adjusted effect size estimates and confidence intervals. The recent availability of accessible software such as 'rpact' makes it possible for psychologists to benefit from the efficiency gains provided by group sequential designs.

scholarly journals On the Performances of Trend and Change-Point Detection Methods for Remote Sensing Data

2020 ◽  
Vol 12 (6) ◽  
pp. 1008 ◽  
Author(s):  
Ana Militino ◽  
Mehdi Moradi ◽  
M. Ugarte
Keyword(s):  
Error Probability ◽  
Type I Error ◽  
Remote Sensing Data ◽  
Change Point Detection ◽  
Change Points ◽  
Detection Methods ◽  
Type I ◽  
Power Of The Test ◽  
Type I Error Probability ◽  
Point Detection

Detecting change-points and trends are common tasks in the analysis of remote sensing data. Over the years, many different methods have been proposed for those purposes, including (modified) Mann–Kendall and Cox–Stuart tests for detecting trends; and Pettitt, Buishand range, Buishand U, standard normal homogeneity (Snh), Meanvar, structure change (Strucchange), breaks for additive season and trend (BFAST), and hierarchical divisive (E.divisive) for detecting change-points. In this paper, we describe a simulation study based on including different artificial, abrupt changes at different time-periods of image time series to assess the performances of such methods. The power of the test, type I error probability, and mean absolute error (MAE) were used as performance criteria, although MAE was only calculated for change-point detection methods. The study reveals that if the magnitude of change (or trend slope) is high, and/or the change does not occur in the first or last time-periods, the methods generally have a high power and a low MAE. However, in the presence of temporal autocorrelation, MAE raises, and the probability of introducing false positives increases noticeably. The modified versions of the Mann–Kendall method for autocorrelated data reduce/moderate its type I error probability, but this reduction comes with an important power diminution. In conclusion, taking a trade-off between the power of the test and type I error probability, we conclude that the original Mann–Kendall test is generally the preferable choice. Although Mann–Kendall is not able to identify the time-period of abrupt changes, it is more reliable than other methods when detecting the existence of such changes. Finally, we look for trend/change-points in land surface temperature (LST), day and night, via monthly MODIS images in Navarre, Spain, from January 2001 to December 2018.

scholarly journals Locally adaptive change-point detection (LACPD) with applications to environmental changes

2021 ◽  
Author(s):  
Mehdi Moradi ◽  
Manuel Montesino-SanMartin ◽  
M. Dolores Ugarte ◽  
Ana F. Militino
Keyword(s):  
Time Series ◽  
Change Point ◽  
Error Probability ◽  
Type I Error ◽  
Change Point Detection ◽  
Alternative Methods ◽  
Change Points ◽  
Type I ◽  
Type I Error Probability ◽  
Point Detection

AbstractWe propose an adaptive-sliding-window approach (LACPD) for the problem of change-point detection in a set of time-ordered observations. The proposed method is combined with sub-sampling techniques to compensate for the lack of enough data near the time series’ tails. Through a simulation study, we analyse its behaviour in the presence of an early/middle/late change-point in the mean, and compare its performance with some of the frequently used and recently developed change-point detection methods in terms of power, type I error probability, area under the ROC curves (AUC), absolute bias, variance, and root-mean-square error (RMSE). We conclude that LACPD outperforms other methods by maintaining a low type I error probability. Unlike some other methods, the performance of LACPD does not depend on the time index of change-points, and it generally has lower bias than other alternative methods. Moreover, in terms of variance and RMSE, it outperforms other methods when change-points are close to the time series’ tails, whereas it shows a similar (sometimes slightly poorer) performance as other methods when change-points are close to the middle of time series. Finally, we apply our proposal to two sets of real data: the well-known example of annual flow of the Nile river in Awsan, Egypt, from 1871 to 1970, and a novel remote sensing data application consisting of a 34-year time-series of satellite images of the Normalised Difference Vegetation Index in Wadi As-Sirham valley, Saudi Arabia, from 1986 to 2019. We conclude that LACPD shows a good performance in detecting the presence of a change as well as the time and magnitude of change in real conditions.

Hypothesis Testing in Business Administration

2020 ◽  
Author(s):  
Rand R. Wilcox
Keyword(s):  
Hypothesis Testing ◽  
Empirical Evidence ◽  
Confidence Intervals ◽  
Error Probability ◽  
Type I Error ◽  
Type I ◽  
Type Ii ◽  
Practical Concern ◽  
Type I Error Probability ◽  
The Difference

Hypothesis testing is an approach to statistical inference that is routinely taught and used. It is based on a simple idea: develop some relevant speculation about the population of individuals or things under study and determine whether data provide reasonably strong empirical evidence that the hypothesis is wrong. Consider, for example, two approaches to advertising a product. A study might be conducted to determine whether it is reasonable to assume that both approaches are equally effective. A Type I error is rejecting this speculation when in fact it is true. A Type II error is failing to reject when the speculation is false. A common practice is to test hypotheses with the type I error probability set to 0.05 and to declare that there is a statistically significant result if the hypothesis is rejected. There are various concerns about, limitations to, and criticisms of this approach. One criticism is the use of the term significant. Consider the goal of comparing the means of two populations of individuals. Saying that a result is significant suggests that the difference between the means is large and important. But in the context of hypothesis testing it merely means that there is empirical evidence that the means are not equal. Situations can and do arise where a result is declared significant, but the difference between the means is trivial and unimportant. Indeed, the goal of testing the hypothesis that two means are equal has been criticized based on the argument that surely the means differ at some decimal place. A simple way of dealing with this issue is to reformulate the goal. Rather than testing for equality, determine whether it is reasonable to make a decision about which group has the larger mean. The components of hypothesis-testing techniques can be used to address this issue with the understanding that the goal of testing some hypothesis has been replaced by the goal of determining whether a decision can be made about which group has the larger mean. Another aspect of hypothesis testing that has seen considerable criticism is the notion of a p-value. Suppose some hypothesis is rejected with the Type I error probability set to 0.05. This leaves open the issue of whether the hypothesis would be rejected with Type I error probability set to 0.025 or 0.01. A p-value is the smallest Type I error probability for which the hypothesis is rejected. When comparing means, a p-value reflects the strength of the empirical evidence that a decision can be made about which has the larger mean. A concern about p-values is that they are often misinterpreted. For example, a small p-value does not necessarily mean that a large or important difference exists. Another common mistake is to conclude that if the p-value is close to zero, there is a high probability of rejecting the hypothesis again if the study is replicated. The probability of rejecting again is a function of the extent that the hypothesis is not true, among other things. Because a p-value does not directly reflect the extent the hypothesis is false, it does not provide a good indication of whether a second study will provide evidence to reject it. Confidence intervals are closely related to hypothesis-testing methods. Basically, they are intervals that contain unknown quantities with some specified probability. For example, a goal might be to compute an interval that contains the difference between two population means with probability 0.95. Confidence intervals can be used to determine whether some hypothesis should be rejected. Clearly, confidence intervals provide useful information not provided by testing hypotheses and computing a p-value. But an argument for a p-value is that it provides a perspective on the strength of the empirical evidence that a decision can be made about the relative magnitude of the parameters of interest. For example, to what extent is it reasonable to decide whether the first of two groups has the larger mean? Even if a compelling argument can be made that p-values should be completely abandoned in favor of confidence intervals, there are situations where p-values provide a convenient way of developing reasonably accurate confidence intervals. Another argument against p-values is that because they are misinterpreted by some, they should not be used. But if this argument is accepted, it follows that confidence intervals should be abandoned because they are often misinterpreted as well. Classic hypothesis-testing methods for comparing means and studying associations assume sampling is from a normal distribution. A fundamental issue is whether nonnormality can be a source of practical concern. Based on hundreds of papers published during the last 50 years, the answer is an unequivocal Yes. Granted, there are situations where nonnormality is not a practical concern, but nonnormality can have a substantial negative impact on both Type I and Type II errors. Fortunately, there is a vast literature describing how to deal with known concerns. Results based solely on some hypothesis-testing approach have clear implications about methods aimed at computing confidence intervals. Nonnormal distributions that tend to generate outliers are one source for concern. There are effective methods for dealing with outliers, but technically sound techniques are not obvious based on standard training. Skewed distributions are another concern. The combination of what are called bootstrap methods and robust estimators provides techniques that are particularly effective for dealing with nonnormality and outliers. Classic methods for comparing means and studying associations also assume homoscedasticity. When comparing means, this means that groups are assumed to have the same amount of variance even when the means of the groups differ. Violating this assumption can have serious negative consequences in terms of both Type I and Type II errors, particularly when the normality assumption is violated as well. There is vast literature describing how to deal with this issue in a technically sound manner.

Fixed sized samples for type-specific surveillance of human papillomavirus in genital warts

Sexual Health ◽  
2013 ◽  
Vol 10 (1) ◽  
pp. 95
Author(s):  
Edward K. Waters ◽  
Andrew J. Hamilton ◽  
Anthony M. A. Smith ◽  
David J. Philp ◽  
Basil Donovan ◽  
...  
Keyword(s):  
Human Papillomavirus ◽  
Sample Size ◽  
Error Probability ◽  
Type I Error ◽  
Hpv Vaccination ◽  
Genital Warts ◽  
Type I ◽  
Post Vaccination ◽  
Hpv Types ◽  
Type I Error Probability

Surveillance data suggest that human papillomavirus (HPV) vaccination in Australia is reducing the incidence of genital warts. However, existing surveillance measures do not assess the proportion of the remaining cases of warts that are caused by HPV types other than 6 or 11, against which the vaccine has no demonstrated effectiveness. Using computer simulation rather than sample size formulae, we established that genotyping at least 60 warts can accurately test whether the proportion of warts due to HPV types not targeted by the vaccine has increased (Type I error probability ≤0.05, Type II error probability <0.07). Standard formulae for calculating sample size, in contrast, suggest that a sample size of more than 130 would be required for this task, but using these formulae entails making several strong assumptions. Our methods require fewer assumptions and demonstrate that a smaller sample size than anticipated could be used to address the question of what proportion of post-vaccination cases of warts are due to nonvaccine types. In conjunction with indications of incidence and prevalence provided by existing surveillance measures, this could indicate the number of cases of post-vaccination warts due to nonvaccine types and hence whether type replacement is occurring.

Effects of Differential Genotyping Error Rate on the Type I Error Probability of Case-Control Studies

2006 ◽  
Vol 61 (1) ◽  
pp. 55-64 ◽  
Author(s):  
Valentina Moskvina ◽  
Nick Craddock ◽  
Peter Holmans ◽  
Michael J. Owen ◽  
Michael C. O’Donovan
Keyword(s):  
Error Rate ◽  
Error Probability ◽  
Type I Error ◽  
Case Control ◽  
Type I ◽  
Genotyping Error ◽  
Case Control Studies ◽  
Genotyping Error Rate ◽  
Type I Error Probability
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