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PubMed1998

Sample size calculations based on slopes and other summary statistics.

Sample size calculations based on two-sample comparisons of slopes have been reported by many. This paper extends such discussions to include summary statistics other than slopes, such as post-baseline means, change scores, and final observations. Specifically, sample size formulas for analyses based on a broad class of summary statistics are presented, with modifications proposed to allow for missing data caused by staggered entry and random dropouts. The formulas developed are used to illustrate how required sample size is affected by summary statistic choice, variance parameters, the type of treatment difference of interest, and the manner in which incomplete observations are used in the analysis. An example based on longitudinal data from the Muscatine Study is presented.

Adolescent↗
PubMed1999

Sample size calculations in studies using the EuroQol 5D.

Health-related quality of life (HRQoL) instruments are increasingly used as outcome variables in clinical trials, leading to a requirement for sample size calculations based on these variables. This paper aims to provide a guide to sample size calculations for use with the EuroQol-5D. The paper focuses on sample sizes required for comparative studies, and uses scores from two reference groups of general population and critically ill patients to determine sample sizes using the three parts of the EQ-5D (descriptive system, visual analogue scale (VAS), and EQ-5D index). The effect on sample sizes of different methods of categorising the three variables are compared, and comparisons are also made between sample sizes using parametric and non-parametric methods. Sample sizes required when the EQ-5D descriptive system is used as a binary variable (problems/no problems) are higher than or equal to those required when each dimension is categorised in three levels of severity (no problems, moderate problems, extreme problems). The use of three categories is appropriate in ill populations, though in more healthy populations two categories should be used. Due to the slight skewness of VAS data, and the equality of results using parametric and non-parametric methods, sample size calculations using the VAS should be based on a parametric approach. Sample sizes were considerably higher for the EQ-5D index when predefined intervals, as opposed to a score frequency based categorisation, were used with the general population reference group. Using the EQ-5D index in ill populations, it is recommended that sample size calculations are based on parametric methods, whilst in healthier populations non-parametric methods should be used.

Critical Illness↗
PubMed1999

Modification of sample size in group sequential clinical trials.

In group sequential clinical trials, sample size reestimation can be a complicated issue when it allows for change of sample size to be influenced by an observed sample path. Our simulation studies show that increasing sample size based on an interim estimate of the treatment difference can substantially inflate the probability of type I error in most practical situations. A new group sequential test procedure is developed by modifying the weights used in the traditional repeated significance two-sample mean test. The new test has the type I error probability preserved at the target level and can provide a substantial gain in power with the increase of sample size. Generalization of the new procedure is discussed.

Biometry↗
PubMed1995

More reliable outcome measures can reduce sample size requirements.

In the design of a clinical trial, considerations of statistical power primarily involve the evaluation of prospective sample sizes. Another strategy for increasing statistical power that is rarely used focuses on the selection of the outcome measure. When an outcome measure is selected, its reliability and validity must be carefully evaluated. Here the relationship between reliability and statistical power is explored empirically. We show that as the number of related items in an outcome scale increases, the internal consistency reliability of the scale also increases. As a consequence, the within-group variability decreases and, in turn, the between-group effect size increases and sample size requirements decrease. As a result, sample size requirements can be reduced and research costs decreased. We recommend careful consideration of the psychometric properties of outcome measures prior to sample size determination in any statistical power analyses.

Alprazolam↗
PubMed2006

Sample size recalculation in internal pilot study designs: a review.

The adequacy of sample size is important to clinical trials. In the planning phase of a trial, however, the investigators are often quite uncertain about the sizes of parameters which are needed for sample size calculations. A solution to this problem is mid-course recalculation of the sample size during the ongoing trial. In internal pilot study designs, nuisance parameters are estimated on the basis of interim data and the sample size is adjusted accordingly. This review attempts to give an overview on the available methods. It is written not only for biometricians who are already familar with the the topic and wish to update their knowledge but also for users new to the subject.

Clinical Trials as Topic↗
PubMed1989

Multiple correlation: exact power and sample size calculations.

This article discusses power and sample size calculations for observational studies in which the values of the independent variables cannot be fixed in advance but are themselves outcomes of the study. It reviews the mathematical framework applicable when a multivariate normal distribution can be assumed and describes a method for calculating exact power and sample sizes using a series expansion for the distribution of the multiple correlation coefficient. A table of exact sample sizes for level .05 tests is provided. Approximations to the exact power are discussed, most notably those of Cohen (1977). A rigorous justification of Cohen's approximations is given. Comparisons with exact answers show that the approximations are quite accurate in many situations of practical interest. More extensive tables and a computer program for exact calculations can be obtained from the authors.

Computer Simulation↗
PubMed2005

Sample size determination in microarray experiments for class comparison and prognostic classification.

Determining sample sizes for microarray experiments is important but the complexity of these experiments, and the large amounts of data they produce, can make the sample size issue seem daunting, and tempt researchers to use rules of thumb in place of formal calculations based on the goals of the experiment. Here we present formulae for determining sample sizes to achieve a variety of experimental goals, including class comparison and the development of prognostic markers. Results are derived which describe the impact of pooling, technical replicates and dye-swap arrays on sample size requirements. These results are shown to depend on the relative sizes of different sources of variability. A variety of common types of experimental situations and designs used with single-label and dual-label microarrays are considered. We discuss procedures for controlling the false discovery rate. Our calculations are based on relatively simple yet realistic statistical models for the data, and provide straightforward sample size calculation formulae.

Biomarkers↗
PubMed2001

Sample size calculations for clustered binary data.

In this paper we propose a sample size calculation method for testing on a binomial proportion when binary observations are dependent within clusters. In estimating the binomial proportion in clustered binary data, two weighting systems have been popular: equal weights to clusters and equal weights to units within clusters. When the number of units varies cluster by cluster, performance of these two weighting systems depends on the extent of correlation among units within each cluster. In addition to them, we will also use an optimal weighting method that minimizes the variance of the estimator. A sample size formula is derived for each of the estimators with different weighting schemes. We apply these methods to the sample size calculation for the sensitivity of a periodontal diagnostic test. Simulation studies are conducted to evaluate a finite sample performance of the three estimators. We also assess the influence of misspecified input parameter values on the calculated sample size. The optimal estimator requires equal or smaller sample sizes and is more robust to the misspecification of an input parameter than those assigning equal weights to units or clusters.

Bacteroides Infections↗
PubMed1998

Application of GEE procedures for sample size calculations in repeated measures experiments.

Derivation of the minimum sample size is an important consideration in an applied research effort. When the outcome is measured at a single time point, sample size procedures are well known and widely applied. The corresponding situation for longitudinal designs, however, is less well developed. In this paper, we adapt the generalized estimating equation (GEE) approach of Liang and Zeger to sample size calculations for discrete and continuous outcome variables. The non-central version of the Wald Chi 2 test is considered. We use the damped exponential family of correlation structures described in Muñoz et al. for the 'working' correlation matrix among the repeated measures. We present a table of minimum sample sizes for binary outcomes, and discuss extensions that account for unequal allocation, staggered entry and loss to follow-up.

Bias↗
PubMed2006

Evaluation of fixed sample-size plans for Plutella xylostella (Lepidoptera: Plutellidae) on broccoli crops in Australia.

Fixed sample-size plans for monitoring Plutella xylostella (L.) (Lepidoptera: Plutellidae) on broccoli and other Brassica vegetable crops are popular in Australia for their simplicity and ease of application. But the sample sizes used are often small, approximately 10-25 plants per crop, and it may be that they fail to provide sufficient information upon which to base pest control decisions. We tested the performance of seven fixed sample-size plans (10, 15, 20, 30, 35, 40, and 45 plants) by resampling a large data set on P. xylostella in commercial broccoli crops. For each sample size, enumerative and presence-absence plans were assessed. The precision of the plans was assessed in terms of the ratio of the standard error to the mean; and at least 45 and 35 samples were necessary for the enumerative and presence-absence plans, respectively, to attain the generally accepted benchmark of < or = 0.3. Sample sizes of 10-20 were highly imprecise. We also assessed the consequences of classifications based on action thresholds (ATs) of 0.2 and 0.8 larvae per plant for the enumerative case, and 0.15 and 0.45 proportion of plants of infested for the presence-absence case. Operating characteristic curves and investigations of the frequency of correct decisions suggest improvements in the performance of plans with increased sample size. In both the enumerative and presence-absence cases, the proportion of incorrect decisions was much higher for the lower of the two ATs assessed, and type II errors (i.e., failure to suggest pest control upon the AT is exceeded) generally accounted for the majority of this error. Type II errors are the most significant from a producer's standpoint. Further consideration is necessary to determine what is an acceptable type II error rate.

Animals↗
PubMed1998

Power and sample size calculations for studies involving linear regression.

This article presents methods for sample size and power calculations for studies involving linear regression. These approaches are applicable to clinical trials designed to detect a regression slope of a given magnitude or to studies that test whether the slopes or intercepts of two independent regression lines differ by a given amount. The investigator may either specify the values of the independent (x) variable(s) of the regression line(s) or determine them observationally when the study is performed. In the latter case, the investigator must estimate the standard deviation(s) of the independent variable(s). This study gives examples using this method for both experimental and observational study designs. Cohen's method of power calculations for multiple linear regression models is also discussed and contrasted with the methods of this study. We have posted a computer program to perform these and other sample size calculations on the Internet (see http://www.mc.vanderbilt.edu/prevmed/psintro+ ++.htm). This program can determine the sample size needed to detect a specified alternative hypothesis with the required power, the power with which a specific alternative hypothesis can be detected with a given sample size, or the specific alternative hypotheses that can be detected with a given power and sample size. Context-specific help messages available on request make the use of this software largely self-explanatory.

Bacterial Vaccines↗
PubMed2003

Sample size estimation for GEE method for comparing slopes in repeated measurements data.

Sample size calculation is an important component at the design stage of clinical trials. Controlled clinical trials often use a repeated measurement design in which individuals are randomly assigned to treatment groups and followed-up for measurements at intervals across a treatment period of fixed duration. In studies with repeated measurements, one of the popular primary interests is the comparison of the rates of change in a response variable between groups. Statistical models for calculating sample sizes for repeated measurement designs often fail to take into account the impact of missing data correctly. In this paper we propose to use the generalized estimating equation (GEE) method in comparing the rates of change in repeated measurements and introduce closed form formulae for sample size and power that can be calculated using a scientific calculator. Since the sample size formula is based on asymptotic theory, we investigate the performance of the estimated sample size in practical settings through simulations.

Data Interpretation, Statistical↗
PubMed1998

The quantitative LOD score: test statistic and sample size for exclusion and linkage of quantitative traits in human sibships.

We present a test statistic, the quantitative LOD (QLOD) score, for the testing of both linkage and exclusion of quantitative-trait loci in randomly selected human sibships. As with the traditional LOD score, the boundary values of 3, for linkage, and -2, for exclusion, can be used for the QLOD score. We investigated the sample sizes required for inferring exclusion and linkage, for various combinations of linked genetic variance, total heritability, recombination distance, and sibship size, using fixed-size sampling. The sample sizes required for both linkage and exclusion were not qualitatively different and depended on the percentage of variance being linked or excluded and on the total genetic variance. Information regarding linkage and exclusion in sibships larger than size 2 increased as approximately all possible pairs n(n-1)/2 up to sibships of size 6. Increasing the recombination (theta) distance between the marker and the trait loci reduced empirically the power for both linkage and exclusion, as a function of approximately (1-2theta)4.

Chromosome Mapping↗
PubMedDate not supplied

Sample size re-estimation: recent developments and practical considerations.

Interim findings of a clinical trial often will be useful for increasing the sample size if necessary to provide the required power against the null hypothesis when the alternative hypothesis is true. Strategies for carrying out the interim examination that have been described over the past several years include "internal pilot studies", blinded interim sample size adjustment and conditional power. Simulation studies show that the alternative methods generally control the type I error rate satisfactorily, although the power properties are more variable. The important issues associated with sample size re-estimation are strategic, not numeric. Clearly expressed regulatory preferences suggest that methods not requiring unblinding the data before completion of the trial would be most appropriate. Extending a trial has its risks. The investigators/patients enrolled later in the course of a trial are not necessarily the same as those recruited/entered early. Re-activating the enrollment process may be sufficiently complicated and expensive to justify enrolling more investigators/patients at the outset. Since sample size re-estimation adjusts the sample size on the basis of variability while efficacy interim analysis adjusts the sample size based on the basis of estimated effect size, both principles can be used in the same trial. Sample size re-estimation may not be advisable for trials involving extended follow-up of individual patients or, more generally, when the follow-up time is long relative to the recruitment time. In such cases, it may be better to estimate the sample size conservatively and introduce an interim efficacy evaluation.

Clinical Trials as Topic↗
PubMed2000

Effects of sample size on the noise floor and distortion product otoacoustic emissions.

This study investigated the effects of sample size on the noise floor and distortion product otoacoustic emissions (DPOAEs) in 55 normal-hearing subjects as a function of intensity. More specifically, we investigated the effects of sample size (12-400 sweeps) as a function of intensity (L1 = L2 = 35, 45 and 55 dB SPL), firstly, on the identifiability of DPOAEs (2F1-F2), secondly, on the noise floor adjacent to DPOAEs, and thirdly, on the magnitude of DPOAEs centred around geometric means of 531 Hz, 1,000 Hz, 2,000 Hz and 4,000 Hz. Testing was conducted with a commercially available system for measuring DPOAEs (Grason-Stadler, GSI-60). A constant F2:F1 ratio of 1.21 was used. As sample size increased from 12 to 400 sweeps, the noise floors decreased by about 13 dB; this closely corresponds to the expected 15 dB reduction based on the square root rule of noise reduction. The highest noise floors were measured at 531 Hz and the lowest noise floors at 2,000 Hz and 4,000 Hz. Identifiability increased as intensity increased from 35 to 55 dB SPL and as sample size increased from 12 to 400 sweeps for all stimulus conditions. Mean DPOAEs for all frequencies (531-4,000 Hz) appeared to decrease as sample size increased, particularly at stimulus levels of 35 dB and 45 dB SPL. These results may be explained by a reduction in the noise levels within the bandwidth of the DPOAE bin. That is, the DPOAE bin is comprised of the DPOAE plus background noise and these two quantities are not separated within the measured bin. Because the magnitude of bin containing DPOAEs is critically dependent on sample size, clinicians should carefully document this variable when collecting normative data. Similarly, clinicians who compare the magnitude of their DPOAEs to published data should note the sample size employed.

Acoustic Stimulation↗
PubMed1994

Sample size for repeated measures studies with binary responses.

We consider the sample size required for repeated measures studies when the response variable is binary. We propose the use of weighted least squares (WLS) for calculating the minimum sample size required to detect some minimum clinically important treatment effect. We provide tabulated values of the estimated sample sizes for a simple example and we discuss some practical considerations in determination of sample size with repeated binary responses.

Bias↗
PubMed1999

Sample size considerations for superiority trials in systemic lupus erythematosus (SLE).

For reasons of efficiency and ethics, sample size calculations are an important part of the design of all clinical trials. This paper highlights the statistical issues inherent to the estimation of sample size requirements in superiority trials particular to SLE. Calculations based on statistical power for testing hypotheses have historically been the method of choice for sample size determination in clinical trials. The advantages of using confidence intervals (CI's) rather than P-values in reporting results of clinical trials is now well established. Since the design of a trial should match the analysis that will eventually be performed, sample size methods based on ensuring accurate estimation of important parameters via sufficiently narrow CI widths should be preferred to methods based on hypothesis testing. Methods and examples are given for sample size calculations for continuous and dichotomous outcomes from both a power and confidence interval width viewpoint. An understanding of sample size calculations in association with expert statistical consultation will result in better designed clinical trials that accurately estimate clinically relevant differences between treatment outcomes, thereby furthering the treatment of patients with SLE.

Confidence Intervals↗
PubMed2001

Sample size determination for a t test given a t value from a previous study: A FORTRAN 77 program.

When uncertain about the magnitude of an effect, researchers commonly substitute in the standard sample-size-determination formula an estimate of effect size derived from a previous experiment. A problem with this approach is that the traditional sample-size-determination formula was not designed to deal with the uncertainty inherent in an effect-size estimate. Consequently, estimate-substitution in the traditional sample-size-determination formula can lead to a substantial loss of power. A method of sample-size determination designed to handle uncertainty in effect-size estimates is described. The procedure uses the t value and sample size from a previous study, which might be a pilot study or a related study in the same area, to establish a distribution of probable effect sizes. The sample size to be employed in the new study is that which supplies an expected power of the desired amount over the distribution of probable effect sizes. A FORTRAN 77 program is presented that permits swift calculation of sample size for a variety of t tests, including independent t tests, related t tests, t tests of correlation coefficients, and t tests of multiple regression b coefficients.

Data Interpretation, Statistical↗