[P2–333]: CAVEATS WHEN SUBTRACTING TWO SERIAL MEASUREMENTS TO ESTIMATE THE NUMBER OF PARTICIPANTS NEEDED FOR CLINICAL TRIALS THAT ARE LONGER OR SHORTER THAN THE OBSERVED MEASUREMENT INTERVAL
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One approach to estimate the number of participants needed to detect a treatment effect in Alzheimer's disease randomized clinical trials (RCTs) involves the subtraction of measurements acquired at two times over an observed time interval (ΔTo). While this approach may be suitable for RCT in which the proposed treatment time interval (ΔTt) is equal to ΔTo, its use need some cautions when a) ΔTt is longer or shorter than ΔTo or b) there are substantial individual variations in ΔTo. We considered the case in which each individual j had two observed serial measurements, xj1 and xj2, before and after time interval ΔToj for total of N subjects in an existing data set. The subtraction method multiplies the annualized subject group's mean change μ=(1/N)(∑(xj1 - xj2)/ΔToj) and its standard deviation σ by ΔTt to form ΔTt × μ and ΔTt × σ and use them to estimate the number of subjects needed to detect a particular treatment effect with a pre-defined statistical power and type-I error. As is known, the sample size estimate would then depend entirely on the std/mean ratio, with no additional consideration of the impact of longer or shorter ΔTt rather than serving as a common multiplier. 1), Using the simple subtraction method, sample size estimates would be the same regardless of RCT duration due to the common std/mean ratio and without additional models or assumptions. 2, The reason for this limitation is the misuse of the linear assumption (common multiplier) and the overlook of the measurement errors in forming the subtraction. 3, The simple subtraction approach works if one of several conditions holds. For example, a) the measurement error is ignorable or linearly related to trial duration; b) the proposed RCT duration ΔTt and the individualized ΔToj satisfy ∑Nj=1(1/ΔToj2)=N/ΔTt2; or c) if the between-subject variability of the annualized change is low, the std/mean ratio will be proportional to 1/ΔTt and the corresponding sample size decreases for longer ΔTt duration. The subtraction procedure should be used with caution. Importantly, this approach would require assumptions about the impact of treatment interval or use of an alternative (e.g., mixed model) approach.Keywords:
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The approval of local ethics committees is required for clinical researches. In order to obtain approval, how the sample size is determined, whether power analysis is done or not and under what assumptions these analyses are made, are important questions/problems. In hypothesis tests, it is possible two types of errors (type 1 error denoted by α and type 2 error denoted by β), of which α is the probability of rejecting the null hypothesis that is actually true and is the probability of accepting the actually false null hypothesis. These errors also determine the reliability of the test (1-α) and the power of test (1-β). While α is directly determined by the researchers and generally as taken 0.05 (in some cases 0.01), β cannot be determined directly. Because β, hence the power of test (1-β) depends on the α (negatively correlated with β) the variation in the population (positively correlated with β) and sample size (n; negatively correlated with β). In clinical researches, it is required that β does not exceed 0.10 (in some cases 0.05) so the power of test should be at least 0.90 and above. In this study, the sample sizes required for some statistical tests (independent sample t-test, one-way ANOVA and Chi-square) which are widely used in clinical research, were calculated with the G*Power program and some evaluations were made. As a result, as expected in the statistical tests, it was observed that decreasing both α and effect size and increasing the power of the test significantly increased the required sample size. However, it was also observed that increasing effect on the sample size of increasing the power of test decreased (5-11%) in the smaller values of α in the independent sample t-test, decreased (nearly 5%) when increasing the number of compared groups in one-way ANOVA and decreased (10-15%) when increasing degree of freedom of Chi-square test.
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Before conducting a scientific study, a power analysis is performed to determine the sample size required to test an effect within allowable probabilities of Type I error (α) or Type II error (β). The power of a study is related to Type II error by 1-β. Most scientific studies set α=0.05 and power=0.80 as minimums. More conservative study designs will decrease α or increase power, which will require a larger sample size. The third and final parameter required for a power analysis is the effect size (ES). ES is a measure of the strength of the observation in the outcome of interest (ie, the dependent variable). ES must be estimated from pilot studies or published values. A small ES will require a larger sample size than a large ES. It is possible to detect statistically significant findings even for very small ES, if the sample size is sufficiently large. Therefore, it is also essential to evaluate whether ES is sufficiently large to be clinically meaningful.
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In historical control trials (HCTs), the experimental therapy is compared with a control therapy that has been evaluated in a previously conducted trial. Makuch and Simon developed a sample size formula where the observations from the HC group were considered not subject to sampling variability. Many researchers have pointed out that the Makuch–Simon sample size formula does not preserve the nominal power and type I error. We develop a sample size calculation approach that properly accounts for the uncertainty in the true response rate of the HC group. We demonstrate that the empirical power and type I error, obtained over the simulated HC data, have extremely skewed distributions. We then derive a closed‐form sample size formula that enables researchers to control percentiles, instead of means, of the power and type I error accounting for the skewness of the distributions. A simulation study demonstrates that this approach preserves the operational characteristics in a more realistic scenario where the true response rate of the HC group is unknown. We also show that the controlling percentiles can be used to describe the joint behavior of the power and type I error. It provides a new perspective on the assessment of HCTs.
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This chapter addresses the questions why a low-powered study has a high probability of failing to detect genuine effects. It highlights how low power makes drawing useful inferences from failure to reject the null hypothesis more difficult. It shows that the risk that a significant result is a Type I error increases if an experiment is low-powered and analyses why low power inflates the effect sizes associated with statistical significance. The chapter clarifies that the statistical power of an experiment is one minus the probability of making a Type II error based on the outcome of that experiment. It confirms that low power is undesirable because it means an increased risk of a Type II error, emphasizing that the lower the power, the less likely it is that a significant result is actually triggered by a real underlying effect.
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Background: adaptive clinical trial design has been proposed as a promising new approach to improve the drug discovery process. Among the many options available, adaptive sample size re-estimation is of great interest mainly because of its ability to avoid a large ‘up-front’ commitment of resources. In this simulation study, we investigate the statistical properties of two-stage sample size re-estimation designs in terms of type I error control, study power and sample size, in comparison with the fixed-sample study.
Methods: we simulated a balanced two-arm trial aimed at comparing two means of normally distributed data, using the inverse normal method to combine the results of each stage, and considering scenarios jointly defined by the following factors: the sample size re-estimation method, the information fraction, the type of group sequential boundaries and the use of futility stopping. Calculations were performed using the statistical software SAS™ (version 9.2).
Results: under the null hypothesis, any type of adaptive design considered maintained the prefixed type I error rate, but futility stopping was required to avoid the unwanted increase in sample size. When deviating from the null hypothesis, the gain in power usually achieved with the adaptive design and its performance in terms of sample size were influenced by the specific design options considered.
Conclusions: we show that adaptive designs incorporating futility stopping, a sufficiently high information fraction (50-70%) and the conditional power method for sample size re-estimation have good statistical properties, which include a gain in power when trial results are less favourable than anticipated.
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Poslovna izvrsnost : znanstveni časopis za promicanje kulture kvalitete i poslovne izvrsnosti (2013)
Selection of an appropriate sample size is one of the most important aspects of any quality inspection. The right sample size enables making valid conclusions about the quality of the product with minimum necessary resources. The choice of sample size and the probability of Type II error (s) are closely connected. The purpose of this paper is to examine how usage of statistical power analysis can improve researcher’s decision about choosing an appropriate sample size for experimental purposes and quality inspection. Besides sample size, the power of a study (1- s) or the probability that the study yield significant results is determined by the magnitude of the treatment effect and by level of statistical significance required (α). Goal of power analysis is to balance values of these three factors to get an appropriate power. Impact of individual changes of each factor on the power was observed through a hypothetical statistical example based on significance test in which the difference between proportions of two independent samples was estimated. Power and Precision software is used for calculations. Results of power analysis have shown that increase of effect size, sample size and/or level of statistical significance leads to increase of power. That means if power increase and/or effect size and/or level of statistical significance would decrease, a larger sample size would be required. This paper demonstrates usefulness of using statistical power analysis in determining appropriate sample size and warns on possible consequences of erroneously selected sample size.
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Article AbstractBackground: A researcher must carefully balance the risk of 2 undesirable outcomes when designing a clinical trial: false-positive results (type I error) and false-negative results (type II error). In planning the study, careful attention is routinely paid to statistical power (i.e., the complement of type II error) and corresponding sample size requirements. However, Bonferroni-type alpha adjustments to protect against type I error for multiple tests are often resisted. Here, a simple strategy is described that adjusts alpha for multiple primary efficacy measures, yet maintains statistical power for each test. Method: To illustrate the approach, multiplicity-adjusted sample size requirements were estimated for effects of various magnitude with statistical power analyses for 2-tailed comparisons of 2 groups using chi2 tests and t tests. These analyses estimated the required sample size for hypothetical clinical trial protocols in which the prespecified number of primary efficacy measures ranged from 1 to 5. Corresponding Bonferroni-adjusted alpha levels were used for these calculations. Results: Relative to that required for 1 test, the sample size increased by about 20% for 2 dependent variables and 30% for 3 dependent variables. Conclusion: The strategy described adjusts alpha for multiple primary efficacy measures and, in turn, modifies the sample size to maintain statistical power. Although the strategy is not novel, it is typically overlooked in psychopharmacology trials. The number of primary efficacy measures must be prespecified and carefully limited when a clinical trial protocol is prepared. If multiple tests are designated in the protocol, the alpha-level adjustment should be anticipated and incorporated in sample size calculations.
Bonferroni correction
Statistical power
Multiple comparisons problem
Nominal level
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Censoring (clinical trials)
Statistical power
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Analysis of covariance (ANCOVA) is widely applied in practice and its use is recommended by regulatory guidelines. However, the required sample size for ANCOVA depends on parameters that are usually uncertain in the planning phase of a study. Sample size recalculation within the internal pilot study design allows to cope with this problem. From a regulatory viewpoint it is preferable that the treatment group allocation remains masked and that the type I error is controlled at the specified significance level. The characteristics of blinded sample size reassessment for ANCOVA in non-inferiority studies have not been investigated yet. We propose an appropriate method and evaluate its performance.In a simulation study, the characteristics of the proposed method with respect to type I error rate, power and sample size are investigated. It is illustrated by a clinical trial example how strict control of the significance level can be achieved.A slight excess of the type I error rate beyond the nominal significance level was observed. The extent of exceedance increases with increasing non-inferiority margin and increasing correlation between outcome and covariate. The procedure assures the desired power over a wide range of scenarios even if nuisance parameters affecting the sample size are initially mis-specified.The proposed blinded sample size recalculation procedure protects from insufficient sample sizes due to incorrect assumptions about nuisance parameters in the planning phase. The original procedure may lead to an elevated type I error rate, but methods are available to control the nominal significance level.
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