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PubMed2004

[Sample size determination given data of preliminary experiment for student's t-test, ANOVA and Tukey's multiple comparison].

The purpose of this article is to calculate the probability that a null hypothesis is rejected using data of preliminary experiment, and to determine an appropriate sample size based on that probability. The procedure to calculate that probability is as follows: (a)generate parameters from the posterior distribution of parameters given data of preliminary experiment; (b) generate test statistics from the conditional distribution given those parameters; (c) count how many of the generated test statistics exceed a critical value. Once the probability of rejecting null hypothesis is estimated, researchers can decide sample size corresponding to the desirable probability. Examples of the procedure are provided and compared with the traditional methods in the case of Student's t-test.

Analysis of Variance↗
PubMed1986

The impact of recent stereological advances on quantitative studies of the nervous system.

The usefulness of a number of new stereological principles for unbiased estimation of particle number and sizes and sampling of particles is illustrated together with a novel principle for unbiased estimation of anisotropic surfaces. The examples include descriptions of estimators of neurone and synapse number and sizes, synapse gradients, neurone point patterns in three-dimensional space, capillary surface area, and perikarya volumes. A major advantage of the methods is the possibility to carry out the estimation procedures in specified, well-characterized regions or layers of the brain. Some general statistical and stereological problems are briefly discussed.

Animals↗
PubMed2005

A simple hybrid variance estimator for the Kaplan-Meier survival function.

In this paper, we propose a hybrid variance estimator for the Kaplan-Meier survival function. This new estimator approximates the true variance by a Binomial variance formula, where the proportion parameter is a piecewise non-increasing function of the Kaplan-Meier survival function and its upper bound, as described below. Also, the effective sample size equals the number of subjects not censored prior to that time. In addition, we consider an adjusted hybrid variance estimator that modifies the regular estimator for small sample sizes. We present a simulation study to compare the performance of the regular and adjusted hybrid variance estimators to the Greenwood and Peto variance estimators for small sample sizes. We show that on average these hybrid variance estimators give closer variance estimates to the true values than the traditional variance estimators, and hence confidence intervals constructed with these hybrid variance estimators have more nominal coverage rates. Indeed, the Greenwood and Peto variance estimators can substantially underestimate the true variance in the left and right tails of the survival distribution, even with moderately censored data. Finally, we illustrate the use of these hybrid and traditional variance estimators on a data set from a leukaemia clinical trial.

Analysis of Variance↗
PubMed1989

Estimation of prevalence on the basis of screening tests.

Estimates of disease prevalence based on screening tests can be severely biased unless adjusted for the sensitivity and specificity of the screening test. One such adjusted estimate, the maximum likelihood estimator proposed by Levy and Kass, can yield an extreme estimate of zero or one that has undesirable characteristics such as a standard error of zero. We develop here a Bayesian estimator which always falls between zero and one. Users without specialized software can use the maximum likelihood estimate for most circumstances and, in special cases, such as a zero estimate of prevalence, turn to the Bayesian estimate. Others can use software to carry out a complete Bayesian solution. We have provided a method to obtain numerical values for the Bayesian estimate for those ranges of sample size (20-100), sensitivity (0.7-0.9) and specificity (0.7-0.9) for which the use of this estimator seems most practical.

Algorithms↗
PubMed1982

A two stage design for the study of the relationship between a rare exposure and a rare disease.

Studies of the relationship between a rare disease and a rare exposure to a risk factor require a very large sample size to obtain reasonable estimates of risk. The cost of such studies is often prohibitive. This paper presents a less costly, two stage approach. Disease and exposure status are ascertained on a large sample in the first stage, but covariate data are collected on only a subsample in the second stage. This subsample is chosen by separately sampling from the four groups based on disease and exposure status (the diseased and exposed, the diseased and unexposed, etc.). The efficiency of this design is achieved by sampling a large proportion (or all) of the subjects from the small groups and a smaller proportion of those from the large groups. An example of a method of analyzing data from this study design, based on weighted least squares techniques, is given. Application of this new design to studies not involving a rare disease and rare exposure are discussed.

Epidemiologic Methods↗
PubMed1997

Bayesian design for dose-response curves with penalized risk.

This paper considers some Bayesian design problems in quantal response analysis. An experimenter must choose a set of dose levels and number of independent observations to take at these levels, subject to a total sample size, in order to estimate some characteristic phi, e.g., ED50, of a tolerance distribution F theta, where theta is the vector of unknown parameters. It is shown for the logistic model that the sampling variability of the posterior variance of phi is such that the predicted posterior variance alone is an undesirable criterion for design selection. A family of penalty functions is introduced that penalizes any excess in the posterior variance over the expected or predicted variance and protects against unexpected outcomes. The goal is to find a design that avoids experimental results with little information, at the expense of a small sacrifice in the Bayes risk. Numerical results indicate that the chance of an extreme posterior variance can be reduced by sacrificing a small amount of posterior risk.

Animals↗
PubMed1994

The robustness of recombination frequency estimates in intercrosses with dominant markers.

The robustness of the maximum likelihood estimates of recombination frequencies has been investigated in double intercrosses with complete dominance at both loci. The robustness was investigated with respect to bias in the recombination frequency estimates due to: (1) limited sample sizes, (2) heterogeneity in recombination frequencies between sexes or among meioses and (3) factors that distort the segregation-misclassification or differential viability. In the coupling phase, the recombination frequency estimates are quite robust with respect to most of the investigated factors. Potentially, the most serious cause of a bias is misclassifications, which tend to increase the recombination frequency estimates. In the repulsion phase, misclassifications are particularly serious, leading to extreme discrepancies between true and observed values. In addition, limited sample size and sex differences in recombination can also bias recombination frequency estimates in repulsion. These effects may pose serious problem in genetic mapping with random amplified polymorphic DNA (RAPD) markers.

Animals↗
PubMed1982

Application of digital filtering and automatic peak detection to brain stem auditory evoked potential.

A method to establish optimal parameters for automatic analysis of the BAEP was proposed. Spectral analysis of a set of BAEP trial averages yields criteria for the selection of the optimal bandwidth for digital filtering, establishes a lower limit for the number of averaged responses required for accurate determination of BAEP wave shape and permits accurate estimation of the amplitude and latency of BAEP peaks. Estimation of phase variance proved to be an effective procedure for selection of the optimal frequency band for automatic peak detection. Complete representation of the BAEP should include unfiltered and digitally filtered signals, an accuracy estimate of the filtered signal, and computer peak detection. High stability of detected peak latency values, as a result of using a digital filter with optimal parameters, will allow a reduction in the number of responses which must be averaged to obtain an accurate estimate of BAEP morphology. This should be of particular value where closely spaced serial observations are desirable, as in intra-operative monitoring. Procedures analogous to those described herein should permit reduction of the sample size required for accurate estimation of the morphology of far-field somatosensory evoked potentials, and for cortical potentials evoked by any stimulus modality. The consequent increase in the speed with which reliable measurements can be obtained can be expected to increase the practical application of all evoked potential techniques.

Brain Stem↗
PubMed2005

Determinants of the intracluster correlation coefficient in cluster randomized trials: the case of implementation research.

The objective of this research was to identify determinants of the magnitude of intracluster correlation coefficients (ICCs) in cluster randomized trials from the field of implementation research. A survey of experts was conducted to generate a priori hypotheses of factors that might affect ICC size. Hypotheses were tested on empirical estimates of ICCs calculated from 21 implementation research datasets, mainly from the UK. Effects of setting (primary or secondary care), type of variable (process or outcome), type of measurement (objective or subjective), prevalence of outcome and size of cluster were tested. In total, 220 ICCs were available (range 0 to 0.415). Significant differences in ICC magnitude were found. The ICCs were significantly higher for process than for outcome variables, and for secondary care outcomes compared with primary care outcomes. The effects of prevalence and size were less clear cut. There was no evidence to suggest that type of measurement affected ICC size. In conclusion, accurate estimates of ICCs are essential for sample size calculations for cluster randomized trials of professional behaviour change interventions. This study demonstrates that ICCs are sensitive to a number of trial factors, particularly setting and outcome type. These factors must be considered when planning such cluster randomized trials.

Biomedical Research↗
PubMed1992

The impact of automated blood pressure devices on the efficiency of clinical trials.

By reducing measurement error, automated blood pressure (BP) devices should enhance the precision of BP estimation and thereby decrease sample size requirements in clinical trials of BP-lowering therapy. Enhanced precision would be particularly relevant to clinical trials assessing the efficacy of nonpharmacological therapies. In the present investigation, resting (clinic) BPs by the Dinamap 8100 (a stationary device) and the Accutracker II (an ambulatory device) were as precise as manual BPs given an equal number of observations by each method. However, both the Dinamap and Accutracker devices underestimated resting diastolic BP in comparison to the manual observers. Estimates of average daytime and 24-hour ambulatory BP, based on large numbers of observations over an extended period of time, were extremely precise. These findings suggest that the use of automated devices to measure resting BP may not reduce samples sizes, whereas use of ambulatory BP devices should reduce samples sizes considerably.

Bias↗
PubMed1999

Parameter recovery for the rating scale model using PARSCALE.

The purpose of the present study was to investigate item and trait parameter recovery for Andrich's rating scale model using the PARSCALE computer program. The four factors upon which the simulated data matrices varied were (a) the distribution of the scale values for the items (skewed or uniform), (b) the number of category response options (4 or 5), (c) the distribution of known trait levels (normal or skewed), and (d) the sample size (60, 125, 250, 500, or 1,000). Each condition was replicated 10 times resulting in 400 data matrices. Accurate item and trait parameter estimates were obtained for all sample sizes examined. As expected, sample size seemed to have little influence on the recovery of trait parameters but did influence item parameter recovery. The distribution of known trait levels did not seriously impact the item parameter recovery. It was concluded that Andrich's rating scale model allows for the use of considerably smaller calibration samples than are typically recommended for other polytomous IRT models.

Attitude↗
PubMed2003

Catching up on health outcomes: the Texas Medication Algorithm Project.

OBJECTIVE: To develop a statistic measuring the impact of algorithm-driven disease management programs on outcomes for patients with chronic mental illness that allowed for treatment-as-usual controls to "catch up" to early gains of treated patients. DATA SOURCES/STUDY SETTING: Statistical power was estimated from simulated samples representing effect sizes that grew, remained constant, or declined following an initial improvement. Estimates were based on the Texas Medication Algorithm Project on adult patients (age > or = 18) with bipolar disorder (n = 267) who received care between 1998 and 2000 at 1 of 11 clinics across Texas. STUDY DESIGN: Study patients were assessed at baseline and three-month follow-up for a minimum of one year. Program tracks were assigned by clinic. DATA COLLECTION/EXTRACTION METHODS: Hierarchical linear modeling was modified to account for declining-effects. Outcomes were based on 30-item Inventory for Depression Symptomatology-Clinician Version. PRINCIPAL FINDINGS: Declining-effect analyses had significantly greater power detecting program differences than traditional growth models in constant and declining-effects cases. Bipolar patients with severe depressive symptoms in an algorithm-driven, disease management program reported fewer symptoms after three months, with treatment-as-usual controls "catching up" within one year. CONCLUSIONS: In addition to psychometric properties, data collection design, and power, investigators should consider how outcomes unfold over time when selecting an appropriate statistic to evaluate service interventions. Declining-effect analyses may be applicable to a wide range of treatment and intervention trials.

Adult↗
PubMed2002

Adverse effects of observational studies when examining adverse outcomes of drugs: case-control studies with low prevalence of exposure.

OBJECTIVES: The case-control study is commonly used to examine adverse drug events, in which prevalence of exposure in the source population is frequently very low. The objective of the current study was to examine the bias inherent in the odds ratio assessing the association between exposure and an adverse outcome when prevalence of exposure in the source population is extremely low. DESIGN: Monte Carlo simulations examined the effect of sample size, exposure prevalence, and magnitude of the underlying odds ratio on the bias of the estimated risk ratio, and the power to detect a non-zero risk ratio. RESULTS: Once the underlying odds ratio was at least four, the adverse effects of low prevalence of exposure was minimal. Studies with small sample sizes and low prevalence of exposure, coupled with small to moderate effect sizes, can result in biased estimates of association between exposure and disease status. With a sample size of 200 and an exposure prevalence of 0.5% in the control population, the bias in the estimated odds ratio can be as large as 115%. However, bias becomes negligible as sample size becomes large (n > or = 2000), even when prevalence of exposure is very low. Once the expected number of exposed controls is at least eight, the bias in the estimated odds ratio was no more than 5%. CONCLUSIONS: Studies with small sample sizes and low prevalence of exposure, coupled with small to moderate effect sizes can result in biased estimates of association between exposure status and adverse drug effects. However, bias becomes negligible as sample size becomes large.

Bias↗
PubMed1999

Necessary sample size for method comparison studies based on regression analysis.

BACKGROUND: In method comparison studies, it is of importance to assure that the presence of a difference of medical importance is detected. For a given difference, the necessary number of samples depends on the range of values and the analytical standard deviations of the methods involved. For typical examples, the present study evaluates the statistical power of least-squares and Deming regression analyses applied to the method comparison data. METHODS: Theoretical calculations and simulations were used to consider the statistical power for detection of slope deviations from unity and intercept deviations from zero. For situations with proportional analytical standard deviations, weighted forms of regression analysis were evaluated. RESULTS: In general, sample sizes of 40-100 samples conventionally used in method comparison studies often must be reconsidered. A main factor is the range of values, which should be as wide as possible for the given analyte. For a range ratio (maximum value divided by minimum value) of 2, 544 samples are required to detect one standardized slope deviation; the number of required samples decreases to 64 at a range ratio of 10 (proportional analytical error). For electrolytes having very narrow ranges of values, very large sample sizes usually are necessary. In case of proportional analytical error, application of a weighted approach is important to assure an efficient analysis; e.g., for a range ratio of 10, the weighted approach reduces the requirement of samples by >50%. CONCLUSIONS: Estimation of the necessary sample size for a method comparison study assures a valid result; either no difference is found or the existence of a relevant difference is confirmed.

Clinical Laboratory Techniques↗
PubMed1990

Sample size and power in psychiatric research.

The conclusions drawn by study are susceptible to two types of errors. The more familiar one occurs when it is believed that there was a true difference between the groups or an association between two variables, when in fact this observation was due to chance (a Type I error). The second potential error consists of falsely concluding that there was no difference or association when indeed there was one (a Type II error). Most researchers know that the probability of a Type I error can be controlled by the setting of alpha level of statistical significance; however, many are unaware of methods to control or estimate Type II errors, based on estimates of an appropriate sample size. This paper discusses techniques researchers can use to calculate the sample sizes required for studies, and the effects of sample sizes which are too small or too large. If it is too small, there is an increased risk of a Type II error, whereas if it is too large, there may be a needless waste of time, money, and effort. The paper also discusses how readers of research articles can determine whether or not negative findings reported by a study are a true reflection of the lack of any difference between groups, or a result of insufficient sample size.

Canada↗
PubMed1997

End-of-life decisions in Australian medical practice.

OBJECTIVE: To estimate the proportion of medical end-of-life decisions in Australia, describe the characteristics of such decisions and compare these data with medical end-of-life decisions in the Netherlands, where euthanasia is openly practised. DESIGN: Postal survey, conducted between May and July 1996, using a self-administered questionnaire based on the questionnaire used to determine medical end-of-life decisions in the Netherlands in 1995. PARTICIPANTS: A random sample of active medical practitioners from all Australian States and Territories selected from medical disciplines in which there were opportunities to be the attending doctor at non-acute patient deaths, and hence to make medical end-of-life decisions. MAIN OUTCOME MEASURE: Proportion of Australian deaths that involved a medical end-of-life decision, using ratio-to-size estimation based on the sampled doctors' responses to the questionnaire. The response rate was 64%. RESULTS: The proportion of all Australian deaths that involved a medical end-of-life decision were: euthanasia, 1.8% (including physician-assisted suicide, 0.1%); ending of patient's life without patient's concurrent explicit request, 3.5%; withholding or withdrawing of potentially life-prolonging treatment, 28.6%; alleviation of pain with opioids in doses large enough that there was a probable life-shortening effect, 30.9%. In 30% of all Australian deaths, a medical end-of-life decision was made with the explicit intention of ending the patient's life, of which 4% were in response to a direct request from the patient. Overall, Australia had a higher rate of intentional ending of life without the patient's request than the Netherlands. CONCLUSIONS: Australian law has not prevented doctors from practising euthanasia or making medical end-of-life decisions explicitly intended to hasten the patient's death without the patient's request.

Adult↗
PubMed1993

Quantification of parasite aggregation: a simulation study.

A simulation study is used to examine the statistical behaviour of estimators of parameters of parasite infection in relation to variation in sample size, the degree of parasite aggregation, and mean parasite burden. The most important patterns to emerge are the associations between estimates of parameters and sample size (= number of host individuals). As sample size decreases values of sample mean parasite burden, its associated variance, and the level of parasite aggregation are all systematically underestimated. The geometric mean of parasite burden and the prevalence of infection appear to be independent of associations with other parasite parameters. Estimates of parameter values may also depend on the underlying frequency distribution, but appear insensitive to variation in the population mean parasite burden. Results are discussed in relation to the interpretation of data derived from field-based studies. In particular, establishing the form of the relationship between host age and mean parasite burden and/or the degree of parasite aggregation. It is typical for sample size to decline as a function of host age within cross-sectional field data. This may give rise to artefactual patterns in the shape of age-aggregation curves in which sample sizes are unequal among host age classes.

Animals↗
PubMed2001

Article 5. An introduction to estimation--2: from z to t.

Provided the sample size is large enough (that is, n greater than 100), the z statistic can be used to determine the confidence interval estimation of the population mean even when the sigma is not known. In these cases the estimation of the standard error of the mean is used. The z statistic is also valid when determining the population's proportion based upon a large sample. However, when dealing with smaller samples, the z statistic is replaced by the t statistic. This makes it possible to estimate, in a population with an unknown standard deviation: The probability of getting a sample mean greater than or equal to a particular value The value of a sample mean with a particular probability of occurring The probability of getting a sample mean between two particular values The confidence interval for the estimation of the population mean can also be determined using the t statistic.

Bias↗