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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↗
PubMed2001

A comparison of methods for adaptive sample size adjustment.

In fixed sample size designs, precise knowledge about the magnitude of the outcome variable's variance in the planning phase of a clinical trial is mandatory for an adequate sample size determination. Wittes and Brittain introduced the internal pilot study design that allows recalculation of the sample size during an ongoing trial using the estimated variance obtained from an interim analysis. However, this procedure requires the unblinding of the treatment code. Since unblinding of an ongoing trial should be avoided whenever possible, there should be some benefit of this design compared with blinded sample size recalculation procedures to justify the unveiling of the treatment code. In this paper, we compare several sample size recalculation procedures with and without unblinding. The simulation results indicate that the procedures behave similarly. In particular, breaking of the blind is not required for an efficient sample size adjustment. We also compare these pure sample size adaptation procedures with study designs which additionally allow for early stopping. Evaluation of the cumulative distribution function of the resulting sample sizes shows that the option for early stopping may lead to lower expectation but generally to a higher variability. The procedures are illustrated by an example of a trial in the treatment of depression.

Computer Simulation↗
PubMed1994

Application of optimal sampling theory to the determination of metacycline pharmacokinetic parameters: effect of model misspecification.

Use of optimal sampling theory (OST) in pharmacokinetic studies allows the number of sampling times to be greatly reduced without loss in parameter estimation precision. OST has been applied to the determination of the bioavailability parameters (area under the curve (AUC), maximal concentration (Cmax), time to reach maximal concentration (Tmax), elimination half-life (T1/2), of metacycline in 16 healthy volunteers. Five different models were used to fit the data and to define the optimal sampling times: one-compartment first-order, two-compartment first-order, two-compartment zero-order, two-compartment with Michaelis-Menten absorption kinetics, and a stochastic model. The adequacy of these models was first evaluated in a 6-subject pilot study. Only the stochastic model with zero-order absorption kinetics was adequate. Then, bioavailability parameters were estimated in a group of 16 subjects by means of noncompartmental analysis (with 19 samples per subject) using each optimal sampling schedule based procedure (with 6 to 9 samples depending on the model). Bias (PE) and precision (RMSE) of each bioavailability parameter estimation were calculated by reference to noncompartmental analysis, and were satisfactory for the 3 adequate models. The most relevant criteria for discrimination of the best model were the coefficient of determination, the standard deviation, and the mean residual error vs. time plot. Additional criteria were the number of required sampling times and the coefficient of variation of the estimates. In this context, the stochastic model was superior and yielded very good estimates of the bioavailability parameters with only 8 samples per subject.

Adult↗
PubMed2005

Development of a PLS based method for determination of the quality of beers by use of NIR: spectral ranges and sample-introduction considerations.

Near infrared spectroscopy (NIR) has been used to determine important indicators of the quality of beers, for example original and real extract and alcohol content, using a partial least squares (PLS) calibration approach. A population of 43 samples, obtained commercially in Spain and including different types of beer, was used. Cluster hierarchical analysis was used to select calibration and validation data sets. Absorbance sample spectra, in transmission mode, were obtained in triplicate by using a 1-mm pathlength quartz flow cell and glass chromatography vials of 6.5 mm internal diameter. The two methods of sample introduction were compared critically, on the basis of spectral reproducibility for triplicate measurements and after careful selection of the best spectral pre-processing and the spectral range for building the PLS model, to obtain the best predictive capability. For each mode of sample introduction two calibration sets were assayed, one based on the use of 15 samples and a second extended based on use of 30 samples, thus leaving 28 and 13 samples, respectively, for validation. The best results were obtained for 1 mm flow cell measurements. For this method original zero-order spectra data in the ranges 2220-2221 and 2250-2350 nm were chosen. For the real extract, original extract, and alcohol d(x-y) and s(x-y) values of -0.04 and 0.07% w/w, -0.01 and 0.13% w/w, and -0.01 and 0.1% v/v, respectively, were obtained. The maximum errors in the prediction of any of these three indicators for a new sample were 2.2, 1.2, and 1.9%, respectively. This method compares favorably with the automatic reference method in terms of speed, reagent consumed, and waste generated.

Beer↗
PubMed2006

Methods to recruit hard-to-reach groups: comparing two chain referral sampling methods of recruiting injecting drug users across nine studies in Russia and Estonia.

Evidence suggests rapid diffusion of injecting drug use and associated outbreaks of HIV among injecting drug users (IDUs) in the Russian Federation and Eastern Europe. There remains a need for research among non-treatment and community-recruited samples of IDUs to better estimate the dynamics of HIV transmission and to improve treatment and health services access. We compare two sampling methodologies "respondent-driven sampling" (RDS) and chain referral sampling using "indigenous field workers" (IFS) to investigate the relative effectiveness of RDS to reach more marginal and hard-to-reach groups and perhaps to include those with the riskiest behaviour around HIV transmission. We evaluate the relative efficiency of RDS to recruit a lower cost sample in comparison to IFS. We also provide a theoretical comparison of the two approaches. We draw upon nine community-recruited surveys of IDUs undertaken in the Russian Federation and Estonia between 2001 and 2005 that used either IFS or RDS. Sampling effects on the demographic composition and injecting risk behaviours of the samples generated are compared using multivariate analysis. Our findings suggest that RDS does not appear to recruit more marginalised sections of the IDU community nor those engaging in riskier injecting behaviours in comparison with IFS. RDS appears to have practical advantages over IFS in the implementation of fieldwork in terms of greater recruitment efficiency and safety of field workers, but at a greater cost. Further research is needed to assess how the practicalities of implementing RDS in the field compromises the requirements mandated by the theoretical guidelines of RDS for adjusting the sample estimates to obtain estimates of the wider IDU population.

Data Collection↗
PubMed1990

Fetomaternal transfusion depends on amount of chorionic villi aspirated but not on method of chorionic villus sampling.

Transcervical and transabdominal chorionic villus sampling are believed, on the basis of indirect evidence, to result in fetomaternal transfusion. We sought to measure this phenomenon by devising a simple method that would allow us to identify variables that influence fetomaternal transfusion. We investigated patients undergoing transcervical-chorionic villus sampling (n = 15) and transabdominal-chorionic villus sampling (n = 15), restricting the sample to subjects who required only a single catheter passage or needle insertion to obtain villi. Maternal serum alpha-fetoprotein was measured before and after the procedure along with alpha-fetoprotein concentration of the transport medium into which the villi had been aspirated. We first confirmed that the change in maternal serum alpha-fetoprotein levels after chorionic villus sampling, an indirect measure of fetomaternal transfusion, was indeed correlated with the alpha-fetoprotein concentration of transport medium into which the villi were aspirated (p = 0.0350). Fetomaternal transfusion next proved to be correlated with the amount of villi obtained (p = 0.0279). However, when adjusted for the amount of villi obtained, no significant difference was observed between transcervical and transabdominal-chorionic villus sampling with respect to the change in maternal serum alpha-fetoprotein levels after chorionic villus sampling (p = 0.8512). These data suggest that the magnitude of fetomaternal transfusion depends on the amount of villi obtained but not on the chorionic villus sampling method used.

Adult↗
PubMed1991

Sample size and dimensionality in multivariate classification: implications for body surface potential mapping.

This paper presents empirically determined guidelines for specifying the number of features appropriate for multivariate classification studies for given sample sizes. Sample size was considered adequate if the mean distance between two sample sets, taken from the same continuous multivariate distribution and projected onto the best separating direction, remained below a prescribed level. To quantitate the sample size requirement, homogeneity of sample set pairs of equal size. N, taken from the same continuous multivariate distribution was studied as a function of dimensionality. M. Homogeneity was characterized by the maximum absolute distances (Dmax) between the corresponding pairs of empirical cumulative probability distributions on the best separating projection. Computer generated data sets were used to estimate the cumulative probability distribution, P(D)M.N, for sample sizes, N, ranging from 5 to 100 and the dimensionality, M, ranging from 1 to 4. An empirical relationship between the estimated step-polygons and the Kolmogorov type one dimensional limiting distribution L(z) has been established. Based on the sample size data of 34 key papers on clinical body surface potential mapping (BSPM) it is noted that in 30% of the cases only one, and in 6% of the cases only two parameters could be used for statistical group representation to ensure a reasonable reliability (Dmax less than 0.2). In 56% of the published cases the sample sizes could not guarantee this reliability even for one feature or parameter.

Computer Simulation↗
PubMed1996

Random selection algorithms for spatial and temporal sampling.

Seven BASIC programs are presented that use algorithms for selection of treatments and samples in spatial and temporal contexts. Program (1) takes a natural sequence of samples (such as logs cut from a tree trunk) and divides them into groups (equal to the number of samples divided by treatments), and then selects non-redundantly from each group a sample at random for each treatment. Program (2) matches items from different categories equally to any number of treatments in proportion to the numbers of items of each category. Program (3) selects sampling times or segment lengths of specified interval and number from within a time period or perimeter distance. These samples can be spaced apart by at least a specified amount of time or distance but otherwise are chosen at random. In program (4), a series of sample coordinates (x,y) are chosen at random from a rectangular area so that no points are closer than a specified minimum distance to any other. For each of the sample points, the Cartesian and polar coordinates are given. Program (5) generates any possible Latin square, while program (6) generates Latin cubes, and program (7) makes Graeco-Latin cubes. Examples of program use and output are presented for experiments with bark beetles (Coleoptera: Scolytidae) responding to pheromone blends and colonizing host trees.

Animals↗
PubMed1994

Preferences of pregnant women for amniocentesis or chorionic villus sampling for prenatal testing: comparison of patients' choices and those of a decision-analytic model.

Decision analytic models have suggested that the choice of amniocentesis or chorionic villus sampling for prenatal genetic testing is a utility-driven decision. We compared preferences for prenatal testing among 156 pregnant women who had chosen either amniocentesis (n = 82) or chorionic villus sampling (n = 74) for the indication of maternal age. We also compared their choices with those of a decision-analytic model based on their preferences, and age-specific rates of spontaneous abortion and chromosomal abnormalities. Preferences were assessed using written scenarios describing potential outcomes of prenatal testing, and were recorded on linear rating scales. The differences in preference ratings for first- vs second-trimester prenatal diagnosis of a normal child (4.2 vs -1.6, p = 0.0004), and for first- vs second-trimester abortion of an abnormal fetus (4.4 vs -1.6, p = 0.01), were significantly greater among women choosing chorionic villus sampling than among women choosing amniocentesis. There were no significant differences between chorionic villus sampling and amniocentesis patients in their preference ratings for test-related miscarriage, disconfirmed results at pregnancy termination, or maternal morbidity from therapeutic abortion. After adjusting for demographic and obstetric factors, the difference in preferences for early vs late prenatal diagnosis was an independent predictor of the choice of chorionic villus sampling in a multivariate model. Among women whose decision analyses selected amniocentesis, 56.8% had chosen amniocentesis, and among women whose analyses selected chorionic villus sampling, 63.2% had chosen chorionic villus sampling (p = 0.05). We conclude that the preferences of pregnant women for the outcomes of prenatal testing were associated with their choice of amniocentesis or chorionic villus sampling. In addition, the choice of prenatal test made by the majority of women was concordant with that of a decision-analytic model that incorporated their preferences. Nevertheless, because many women made choices that were discordant with their decision-analytic results, further research into the bases for their choices is warranted.

Abortion, Induced↗
PubMed2005

Effect of sample geometry on the apparent biaxial mechanical behaviour of planar connective tissues.

Mechanical testing methodologies developed for engineering materials may result in artifactual material properties if applied to soft planar connective tissues. The use of uniaxial tissue samples with high aspect ratios or biaxial samples with slender cruciform arms could lead to preferential loading of only the discrete subset of extracellular fibres that fully extend between the grips. To test this hypothesis, cruciform biaxial connective tissue samples that display distinctly different material properties (bovine pericardium, fish skin), as well as model textile laminates with predefined fibrous orientations, were repeatedly tested with decreasing sample arm lengths. With mechanical properties determined at the sample centre, results demonstrated that the materials appeared to become stiffer and less extensible with less slender sample geometries, suggesting that fibre recruitment increases with decreasing sample arm length. Alterations in the observed shear behaviour and rigid body rotation were also noted. The only truly reliable method to determine material properties is through in vivo testing, but this is not always convenient and is typically experimentally demanding. For the in vitro determination of the biaxial material properties, appropriate sample geometry should be employed in which all of the fibres contribute to the mechanical response.

Animals↗
PubMed2005

Optimisation of sampling for the temporal monitoring of technetium-99 in the Arctic marine environment.

Monitoring of the marine environment for radioactivity, for both radiological protection and oceanographic purposes, remains an expensive and labour intensive activity due to the large sample volumes needed and the complex and lengthy analytical procedures required to measure low levels of contamination. Because of this, some consideration must be given to the design of sampling plans to ensure effective and efficient sampling that can be defended on the basis of scientific rationale. This article tests the hypothesis that geostatistical techniques may prove of use in the optimisation and design of sampling regimes for the monitoring of temporal fluctuations in the levels of technetium at a location in the Norwegian Arctic marine environment. The level of temporal correlation exhibited by two relevant time series was investigated and the information used to observe the effect of sampling frequency on the production of monthly estimates of activity of technetium in both seawater and seaweed. The results indicate that reduced sampling frequency allows production of estimates that acceptably replicate the actual data and that use of geostatistical procedures may offer advantages in the planning of monitoring systems for marine radioactivity. The use of an oceanographic model was also investigated as a means of assessing the temporal correlation prior to actual sampling, an approach that may offer significant advantages by reducing the need to have lengthy time series prior to designing sampling regimes.

Arctic Regions↗
PubMed1998

Two-stage sampling in surveys to substantiate freedom from disease.

Disease in livestock populations tends to cluster at the herd level. In order to account for this--and to overcome the problems of simple random sampling from a very large population--large-scale livestock surveys usually involve two-stage sampling. However, the use of two-stage sampling presents particular problems for sample-size calculation and analysis. We developed a probability formula for two-stage sampling, initially based on the assumption of a perfect test. We used this formula to demonstrate how combinations of first-stage (number of herds) and second-stage (number of animals in selected herds) sample sizes can be altered to achieve a least-cost survey, and used simulation to validate the formula. To overcome the unrealistic assumption of a perfect test, we then applied an exact-probability formula (which takes imperfect tests and finite population sizes into account) to the two-stage sampling design. An example is given which shows how implementing the formula with the FreeCalc computer program allows least-cost first and second-stage sample sizes to be calculated.

Animal Diseases↗
PubMed1998

Threats to the validity of clinical trials employing enrichment strategies for sample selection.

Subject selection and exclusion criteria employed in typical clinical effectiveness trials of investigational new drugs have two fundamental aims: (1) to ensure that patients entering a study are truly suffering from the condition the drug is intended to treat and (2) to maximize the likelihood that the study will detect an effect of the drug if, in fact, one exists. Typical protocol selection criteria not only specify exacting procedures for establishing and documenting the diagnosis of those recruited for a study but also seek to increase, relative to the prevalence in the general population, the proportion of individuals in the sample likely to respond to pharmacological treatment. Because it is ordinarily impossible to learn prior to extensive clinical experience with a new drug which, if any, patient characteristics reliably predict a consistent treatment response, strategies for sample "enrichment" typically operate by excluding patients (for example, those with very advanced and/or complicated illness, those with serious concomitant illness, those at the extremes of age, those with very mild illness, and so forth) in whom a dependable response to treatment seems unlikely on logical and/or generic grounds. Some studies use positive strategies for sample "enrichment." In studies evaluating drugs intended to treat recurrent episodes of psychiatric illnesses, many protocols recommend selective recruitment of patients with a history of meaningful positive responses to antipsychotic treatment during prior episodes. Sample selection procedures of these kinds impose limits on the generalizability of a study's results (i.e., external validity), but the use of nonrandom patient samples is ordinarily held to have no effect on the internal validity of the results. In short, studies employing highly selected patient samples are, despite their limited external validity, regularly accepted as valid sources of evidence bearing on a drug's effectiveness. There are exceptions, however; this paper describes one in which the use of a seemingly innocuous sample enrichment maneuver proved highly damaging to the ultimate credibility of an important multicenter trial. In particular, exposure to an experimental treatment during an open qualification phase may invalidate drug-placebo comparisons made during a later randomized, blinded, controlled phase. Our review of the trial also reveals that the enrichment maneuver employed probably failed to accomplish its intended aims, selecting patients whose improvements on the outcome variable may be as reasonably ascribed to chance as to drug effect. This is all the more surprising because the method of sample enrichment employed has much in common with those long recommended in the clinical trial literature.

Aged↗
PubMed2001

Sampling optimization, at site scale, in contamination monitoring with moss, pine and oak.

With the aim of optimizing protocols for sampling moss, pine and oak for biomonitoring of atmospheric contamination and also for inclusion in an Environmental Specimen Bank, 50 sampling units of each species were collected from the study area for individual analysis. Levels of Ca, Cu, Fe, Hg, Ni, and Zn in the plants were determined and the distributions of the concentrations studied. In moss samples, the concentrations of Cu, Ni and Zn, considered to be trace pollutants in this species, showed highly variable long-normal distributions; in pine and oak samples only Ni concentrations were log-normally distributed. In addition to analytical error, the two main source of error found to be associated with making a collective sample were: (1) not carrying out measurements on individual sampling units; and (2) the number of sampling units collected and the corresponding sources of variation (microspatial, age and interindividual). We recommend that a minimum of 30 sampling units are collected when contamination is suspected.

Air Pollutants↗
PubMed2003

Underpowering in randomized trials reporting a sample size calculation.

OBJECTIVE: The objective of this study was to determine whether standard deviations (SDs) used in sample size calculations are smaller than those found in the resulting study sample, thereby leading to underpowered studies. METHOD: The predicted SD used in the sample size calculation and the actual SD of the study sample were recorded for randomized trials recently published in one of four major journals. RESULTS: Sample SD was greater than predicted SD for 80% of endpoints. About one quarter of trials required five times as many patients as specified in the sample size calculation. CONCLUSION: Trials reporting sample size calculations for continuous endpoints published in the most reputable medical journals are often underpowered. There seems to be insufficient understanding that the SD of a sample of patients is a random variable, associated with imprecision, that cannot easily be extrapolated from one population to another.

Data Interpretation, Statistical↗
PubMed2001

Study sampling in the Canadian Study of Health and Aging.

The Canadian Study of Health and Aging drew representative samples of people aged 65 or over from the community and institutions across Canada. The sample was designed to provide regional and national prevalence estimates for dementia by age and sex. Thirty-six sampling areas were used in a stratified cluster design with optimal allocation; sampling weights were developed to provide population estimates. The sample included 9,008 people aged 65 or over from the community, and 1,255 from institutions. This report describes the sampling procedures, the methods used to recruit people to the study and participation rates, the characteristics of the resulting sample, and the way in which sample weights should be used.

Aged↗
PubMed2006

Estimating sampling frequency in pollen exposure assessment over time.

A time series model was fitted to the pollen concentration data collected in the Greater Cincinnati area for the Cincinnati Childhood Allergy and Air Pollution Study (CCAAPS). A traditional time series analysis and temporal variogram approach were applied to the regularly spaced databases (collected in 2003) and irregularly spaced ones (collected in 2002), respectively. The aim was to evaluate the effect of the sampling frequency on the sampling precision in terms of inverse of standard error of the overall level of mean value across time. The presence of high autocorrelation in the data was confirmed and indicated some degree of temporal redundancy in the pollen concentration data. Therefore, it was suggested that sampling frequency could be reduced from once a day to once every several days without a major loss of sampling precision of the overall mean over time. Considering the trade-offs between sampling frequency and the possibility of sampling bias increasing with larger sampling interval, we recommend that the sampling interval should take values from 3 to 5 days for the pollen monitoring program, if the goal is to track the long-term average.

Air Pollution↗
PubMedDate not supplied

Sampling frequency of the RR interval time series for spectral analysis of heart rate variability.

Spectral analysis of heart rate variability (HRV) is an accepted method for assessment of cardiac autonomic function and its relationship to numerous disorders and diseases. Various non-parametric methods for HRV estimation have been developed and extensive literature on their respective properties is available. The RR interval time series can be seen as a series of non-uniformly spaced samples. To analyse the power spectra of this series using the discrete Fourier transform (DFT), we need to interpolate the series for obtaining uniformly spaced intervals. The selection of sampling period plays a critical role in obtaining the power spectra in terms of computational efficiency and accuracy. In this paper, we shall analyse the RR interval time series from selected subjects for different sampling frequencies to compare the error introduced in selected frequency-domain measures of HRV at a constant frequency resolution for a specific duration of electrocardiogram (ECG) data. It should be pointed out that, although many other error causes are possible in the frequency-domain measures, our attention will be confined only to the performance comparison due to the different sampling frequencies. While the choice of RR interval sampling frequency (f(s)) is arbitrary, the sampling rate of RR interval series must be selected with due consideration to mean and minimum RR interval; f(s = )4 Hz was proposed for a majority of cases. This is an appropriate sampling rate for the study of autonomic regulation, since it enables us to compute reliable spectral estimates between dc and 1 Hz, which represents the frequency band within which the autonomic nervous system has significant response. Furthermore, resampled RR intervals are evenly spaced in time and are synchronized with the samples of the other physiologic signals, enabling cross-spectral estimates with these signals.

Algorithms↗