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[Practical aspects regarding sample size in clinical research].

BACKGROUND: The knowledge of the right sample size let us to be sure if the published results in medical papers had a suitable design and a proper conclusion according to the statistics analysis. To estimate the sample size we must consider the type I error, type II error, variance, the size of the effect, significance and power of the test. To decide what kind of mathematics formula will be used, we must define what kind of study we have, it means if its a prevalence study, a means values one or a comparative one. In this paper we explain some basic topics of statistics and we describe four simple samples of estimation of sample size.

Sample Size↗

The numbers game: sample-size determination.

Sample-size determination is a crucial component of study design. Estimates of sample size are influenced by the amount of change that must occur between study groups and the degree of risk that the investigator is willing to accept in evaluating the null hypothesis. A complete understanding of the impact of sample size on the interpretation of study data is therefore a prerequisite for quality, innovative, valid research.

Epidemiologic Factors↗

Multiplicity-adjusted sample size requirements: a strategy to maintain statistical power with Bonferroni adjustments.

BACKGROUND: 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.

Clinical Protocols↗

Sample size calculations for disease freedom and prevalence estimation surveys.

We developed a Bayesian approach to sample size calculations for studies designed to estimate disease prevalence that uses a hierarchical model for estimating the proportion of infected clusters (cluster-level prevalence) within a country or region. The clusters may, for instance, be villages within a region, cities within a state, or herds within a country. Our model allows for clusters with zero prevalence and for variability in prevalences among infected clusters. Moreover, uncertainty about diagnostic test accuracy and within-cluster prevalences is accounted for in the model. A predictive approach is used to address the issue of sample size selection in human and animal health surveys. We present sample size calculations for surveys designed to substantiate freedom of a region from an infectious agent (disease freedom surveys) and for surveys designed to estimate cluster-level prevalence of an endemic disease (prevalence estimation surveys). In disease freedom surveys, for instance, assuming the cluster-level prevalence for a particular infectious agent in the region is greater than a maximum acceptable threshold, a sample size combination consisting of the number of clusters sampled and number of subjects sampled per cluster can be determined for which authorities conducting the survey detect this excessive cluster-level prevalence with high predictive probability. The method is straightforward to implement using the Splus/R library emBedBUGS together with WinBUGS.

Animals↗

Statistical power in psychiatric research.

Statistical power is neglected in much psychiatric research, with the consequence that many studies do not provide a reasonable chance of detecting differences between groups if they exist in the population. This paper attempts to improve current practice by providing an introduction to the essential quantities required for performing a power analysis (sample size, effect size, type 1 and type 2 error rates). We provide simplified tables for estimating the sample size required to detect a specified size of effect with a type 1 error rate of alpha and a type 2 error rate of beta, and for estimating the power provided by a given sample size for detecting a specified size of effect with a type 1 error rate of alpha. We show how to modify these tables to perform power analyses for multiple comparisons in univariate and some multivariate designs. Power analyses for each of these types of design are illustrated by examples.

Clinical Trials as Topic↗

Spatial distribution of neurons in tissue culture wells: implications for sampling methods to estimate population size.

Many laboratory procedures require the counting of cells in culture. While many cultured cells may be counted by automated methods, neuronal cultures often require manual cell counting methods that are prohibitively time-consuming. This paper examines methods of sampling from tissue culture wells for estimating total cell counts. Performance of sampling and estimation schemes will depend in part on how the cells distribute themselves within a well. Spatial statistical analysis techniques are applied to the known total number and distribution of neurons in two wells counted in a grid scheme to demonstrate some important features of the neuron distributional patterns. Based on these two wells and simulated realizations from other point processes, a new sampling and estimation technique using open wedge-shaped sampling regions radiating from the centre of the well is proposed. This method is shown to result in more accurate estimates of the total number of neurons in the well than standard methods.

Animals↗

Estimating the mean and variance from the median, range, and the size of a sample.

BACKGROUND: Usually the researchers performing meta-analysis of continuous outcomes from clinical trials need their mean value and the variance (or standard deviation) in order to pool data. However, sometimes the published reports of clinical trials only report the median, range and the size of the trial. METHODS: In this article we use simple and elementary inequalities and approximations in order to estimate the mean and the variance for such trials. Our estimation is distribution-free, i.e., it makes no assumption on the distribution of the underlying data. RESULTS: We found two simple formulas that estimate the mean using the values of the median (m), low and high end of the range (a and b, respectively), and n (the sample size). Using simulations, we show that median can be used to estimate mean when the sample size is larger than 25. For smaller samples our new formula, devised in this paper, should be used. We also estimated the variance of an unknown sample using the median, low and high end of the range, and the sample size. Our estimate is performing as the best estimate in our simulations for very small samples (n < or = 15). For moderately sized samples (15 < n < or = 70), our simulations show that the formula range/4 is the best estimator for the standard deviation (variance). For large samples (n > 70), the formula range/6 gives the best estimator for the standard deviation (variance). We also include an illustrative example of the potential value of our method using reports from the Cochrane review on the role of erythropoietin in anemia due to malignancy. CONCLUSION: Using these formulas, we hope to help meta-analysts use clinical trials in their analysis even when not all of the information is available and/or reported.

Analysis of Variance↗

Behavioral sampling techniques for feedlot cattle.

Continuous observations are an accurate method for behavioral measurements but are difficult to conduct on large numbers of animals because of extensive labor requirements. Thus, we sought to develop methods of behavioral data collection in feedlot cattle production systems that reasonably approximated continuous sampling. Standing, lying, feeding, drinking, and walking behaviors were examined from 224 h of continuous video from 64 heifers. Experiment 1 (n = 24 heifers) compared continuous behavioral sampling techniques (Continuous) with scan sampling using intervals of 1, 5, 10, 15, 30, and 60 min and time sampling (a technique for the periodic recording of behavior) for the first 10 min out of every 60 min. Means for each scan sampling method did not differ in estimated percentage of duration of behaviors (P > 0.05) from continuous sampling, except for scan sampling with a 60-min interval. Scan sampling with a 60-min interval differed from more frequent scan sampling intervals for all behaviors except lying. Scan sampling with short intervals (1 and 5 min) was correlated highly with Continuous for all behaviors. The longer the scan interval, the lower the correlations, especially for behaviors with short duration. Time sampling was not an accurate technique for measuring the sampled behaviors. Focal animal sampling (using continuous sampling of individuals) indicated that one heifer was representative of the entire pen of 10 animals (Continuous) for all maintenance behaviors except drinking. Scan sampling methods (1-, 5-, 10-, and 15-min intervals) were accurate methods of behavioral sampling for feedlot cattle, but scan intervals of 30 or 60 min were less accurate and less precise. Time sampling was not an accurate method because it overestimated standing and underestimated lying behaviors. Experiment 2 (n = 40 heifers) investigated the number of focal animals required to accurately represent continuous behavioral sampling for all animals. Focal animal sampling was accurate for most behaviors using as few as 1 animal out of 10 but was not an accurate method for drinking behavior unless 40% of the animals in the pen were observed. Estimates of sample sizes needed for experimental protocols are provided. Behavioral means, standard deviations, and coefficients of variation are presented along with estimates of required sample sizes. These results validate accurate, precise, and efficient methods for quantifying feedlot cattle behavior.

Animals↗

Exact conditional and unconditional sample size for pair-matched studies with binary outcome: a practical guide.

Tables of sample sizes for pair-matched studies with binary outcome are presented. They are based on conditional and unconditional approaches using the 'exact' (binomial) test. An approximate procedure is suggested to estimate the sample size for parameter values that do not correspond exactly with table entries. The procedure utilizes a minor modification of the large-sample formula given by Connett et al. A practical strategy for estimating the overall sample size in the presence of a nuisance parameter (the proportion of discordant pairs) is recommended. An example from a proposed clinical trial is given.

Binomial Distribution↗

Enumerative and binomial sampling plans for armored scale (Homoptera: Diaspididae) on kiwifruit leaves.

The spatial dispersion of armored scale insects; greedy scale, Hemiberlesia rapax (Comstock); and latania scale, Hemiberlesia lataniae (Signoret), was investigated on kiwifruit, Actinidia deliciosa (A. Chevalier) C. F. Liang et A. R. Ferguson, leaves in New Zealand. A universal description for dispersion was determined using Taylor's power law, which encompassed a wide range of different orchards, blocks, block sizes, sampling times, scale control practices, regions and seasons. Scale density significantly altered dispersion, especially at the high densities found on unsprayed kiwifruit. Most commercially managed kiwifruit blocks had low densities of <0.5 scale per leaf and had a slightly aggregated scale dispersion. Wilson and Room's binomial model, which incorporates a clumping pattern as a function of density, gave a significant relationship between the proportion of infested leaves and scale density. The optimal leaf sample sizes were estimated for predetermined levels of sampling reliability. Where population estimates require a high degree of precision and enumerative sampling methods are used, 2,500 leaves should be sampled when scale densities are near the current spray threshold of 4% infested leaves and 500 leaves at 20% infested leaves. For management-decision sampling, where a lower level of precision was acceptable, enumerative sampling would require that 400 leaves be sampled at 4%; or 85 leaves at 20% infested leaves. With binomial sampling to achieve an equivalent level of precision an increased sample size of 6-11% is required.

Animals↗

Variance estimation, design effects, and sample size calculations for respondent-driven sampling.

Hidden populations, such as injection drug users and sex workers, are central to a number of public health problems. However, because of the nature of these groups, it is difficult to collect accurate information about them, and this difficulty complicates disease prevention efforts. A recently developed statistical approach called respondent-driven sampling improves our ability to study hidden populations by allowing researchers to make unbiased estimates of the prevalence of certain traits in these populations. Yet, not enough is known about the sample-to-sample variability of these prevalence estimates. In this paper, we present a bootstrap method for constructing confidence intervals around respondent-driven sampling estimates and demonstrate in simulations that it outperforms the naive method currently in use. We also use simulations and real data to estimate the design effects for respondent-driven sampling in a number of situations. We conclude with practical advice about the power calculations that are needed to determine the appropriate sample size for a study using respondent-driven sampling. In general, we recommend a sample size twice as large as would be needed under simple random sampling.

Analysis of Variance↗

Sample size computations for PK/PD population models.

We describe an accurate, yet simple and fast sample size computation method for hypothesis testing in population PK/PD studies. We use a first order approximation to the nonlinear mixed effects model and chi-square distributed Wald statistic to compute the minimum sample size to achieve given degree of power in rejecting a null hypothesis in population PK/PD studies. The method is an extension of Rochon's sample size computation method for repeated measurement experiments. We compute sample sizes for PK and PK/PD models with different conditions, and use Monte Carlo simulation to show that the computed sample size retrieves the required power. We also show the effect of different sampling strategies, such as minimal, i.e., as many observations per individual as parameters in the model, and intensive on sample size. The proposed sample size computation method can produce estimates of minimum sample size to achieve the desired power in hypothesis testing in a greatly reduced time than currently available simulation-based methods. The method is rapid and efficient for sample size computation in population PK/PD study using nonlinear mixed effect models. The method is general and can accommodate any type of hierarchical models. Simulation results suggest that intensive sampling allows the reduction of the number of patients enrolled in a clinical study.

Algorithms↗

Analysis, sample size, and power for estimating incremental net health benefit from clinical trial data.

Stinnett and Mullahy recently introduced the concept of net health benefit as an alternative to cost-effectiveness ratios for the statistical analysis of patient-level data on the costs and health effects of competing interventions. Net health benefit addresses a number of problems associated with cost-effectiveness ratios by assuming a value for the willingness-to-pay for a unit of effectiveness. We extend the concept of net health benefit to demonstrate that standard statistical procedures can be used for the analysis, power, and sample size determinations of cost-effectiveness data. We also show that by varying the value of the willingness-to-pay, the point estimate and confidence interval for the incremental cost-effectiveness ratio can be determined. An example is provided.

Biometry↗

Statistics for nonparametric linkage analysis of X-linked traits in general pedigrees.

We have compared the power of several allele-sharing statistics for "nonparametric" linkage analysis of X-linked traits in nuclear families and extended pedigrees. Our rationale was that, although several of these statistics have been implemented in popular software packages, there has been no formal evaluation of their relative power. Here, we evaluate the relative performance of five test statistics, including two new test statistics. We considered sibships of sizes two through four, four different extended pedigrees, 15 different genetic models (12 single-locus models and 3 two-locus models), and varying recombination fractions between the marker and the trait locus. We analytically estimated the sample sizes required for 80% power at a significance level of.001 and also used simulation methods to estimate power for a sample size of 10 families. We tried to identify statistics whose power was robust over a wide variety of models, with the idea that such statistics would be particularly useful for detection of X-linked loci associated with complex traits. We found that a commonly used statistic, S(all), generally performed well under various conditions and had close to the optimal sample sizes in most cases but that there were certain cases in which it performed quite poorly. Our two new statistics did not perform any better than those already in the literature. We also note that, under dominant and additive models, regardless of the statistic used, pedigrees with all-female siblings have very little power to detect X-linked loci.

Alleles↗

Cardiac arrest research in humans--insights into failure.

Cardiac arrest research in humans has failed to fulfil expectations generated by laboratory studies. This reflects a number of factors. It is difficult to perform clinical research in the setting of emergency cardiac resuscitation. Both the epidemiology and pathophysiology of sudden death present special problems to the clinical researcher. Laboratory studies and clinical trials have failed to faithfully mimic each other. Estimation of sample size and application of inclusion/exclusion criteria present special problems in methodology. Our focus on improving long term survival by changing one component of therapy may have been premature and obscured the utility of extant data. Many of these problems can be addressed through refinements in: laboratory models, our understanding of the underlying pathophysiology, estimation of sample size, the application of inclusion/exclusion criteria, the identification of the primary dependent variables and subgroups of interest, the overall quality of therapy. Clinical studies will not generate useful data until these issues, among others, have been addressed.

Clinical Trials as Topic↗

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↗

Sample size-based indication of normality in lognormally distributed populations.

Occupational and environmental hygiene sampling strategies are usually dictated by factors that limit sample sizes to relatively small numbers. Often, parameters estimated from small sample sizes are then used to make further estimates of the occurrence of extreme events, which are governed by the underlying exposure distribution. We investigated the limitations superimposed by the number of samples in distinguishing an asymmetric (Lognormal) distribution through the rejection of a hypothesized symmetric (Normal) distribution. Sets of 5 to 250 synthetic samples from underlying Lognormal distributions with unit median were generated for 24 separate geometric standard deviations (GSDs), ranging from 1.25 to 7.00. Each simulated combination was repeated in blocks of 200 and each block was repeated tenfold. The synthetic samples were then tested for goodness of fit for Normality by using the Shapiro and Wilk's W Test. Results indicated that the number of samples required to distinguish between Normal and Lognormal distributions was inversely related to GSD. When GSD = 1.25, 169 samples were required for 90 percent distinction at alpha = 0.05. The criteria for success for GSD of 2.00 and 4.00 were 25 and 15 samples, respectively. These results led to the conclusion that the general inability to distinguish an underlying distribution may impose serious difficulties in the estimation of extreme events associated with occupational and environmental hygiene-related sampling.

Environmental Monitoring↗

Estimating morbidity risks with variable age of onset: review of methods and a maximum likelihood approach.

Various methods for the estimation of morbidity risk in a disease with late variable onset are described, along with a maximum likelihood approach. It is shown that the Strömgren estimator is nearly as efficient as the maximum likelihood estimator when the true risk is low, but may be significantly less efficient for high morbidity risks. The maximum likelihood estimator offers greater protection against risk estimates greater than or equal to 1, and for small samples, may also be less biased than the Strömgren estimator, especially when risk is high. For reasonable sample sizes both estimates are nearly unbiased. The modified Strömgren estimator is too biased, in general, to be practical. Methods for comparing morbidity risks are also described. If an age-of-onset distribution is estimated from the same sample as morbidity risk, a single maximum likelihood procedure is advocated. The methods are applied to a data set on major affective disorder. The sensitivity of morbidity-risk estimates and tests of hypotheses to the form of onset function assumed is examined.

Age Factors↗