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PubMed2005

Limitations of mRNA amplification from small-size cell samples.

BACKGROUND: Global mRNA amplification has become a widely used approach to obtain gene expression profiles from limited material. An important concern is the reliable reflection of the starting material in the results obtained. This is especially important with extremely low quantities of input RNA where stochastic effects due to template dilution may be present. This aspect remains under-documented in the literature, as quantitative measures of data reliability are most often lacking. To address this issue, we examined the sensitivity levels of each transcript in 3 different cell sample sizes. ANOVA analysis was used to estimate the overall effects of reduced input RNA in our experimental design. In order to estimate the validity of decreasing sample sizes, we examined the sensitivity levels of each transcript by applying a novel model-based method, TransCount. RESULTS: From expression data, TransCount provided estimates of absolute transcript concentrations in each examined sample. The results from TransCount were used to calculate the Pearson correlation coefficient between transcript concentrations for different sample sizes. The correlations were clearly transcript copy number dependent. A critical level was observed where stochastic fluctuations became significant. The analysis allowed us to pinpoint the gene specific number of transcript templates that defined the limit of reliability with respect to number of cells from that particular source. In the sample amplifying from 1000 cells, transcripts expressed with at least 121 transcripts/cell were statistically reliable and for 250 cells, the limit was 1806 transcripts/cell. Above these thresholds, correlation between our data sets was at acceptable values for reliable interpretation. CONCLUSION: These results imply that the reliability of any amplification experiment must be validated empirically to justify that any gene exists in sufficient quantity in the input material. This finding has important implications for any experiment where only extremely small samples such as single cell analyses or laser captured microdissected cells are available.

Analysis of Variance↗

PubMed1988

Sample size for comparison of changes in the presence of right censoring caused by death, withdrawal, and staggered entry.

In estimating and comparing the rates of change of a continuous variable between two groups, the unweighted averages of individual simple least-square estimates from each group are often used. Under the linear random effects model, these statistics are maximum likelihood estimates for the expected rates of change when all individuals have complete observations. However, death and withdrawal often cause observations on the variable of interest to be right censored for some participants, which makes any subsequent measurements impossible (to be referred to as right censoring). In this situation, the unweighted averages are no longer efficient in comparison with the generalized least-square estimates. Relationship between sample size, frequency of measurement, and right censoring are described for the different estimation procedures. Using realistic estimates of the random effect parameters, we illustrate that if there were 8% right censored observations each year due to participants' death or loss to follow-up, the sample size requirements for a proposed 3-year controlled clinical trial of alpha 1-protease inhibitor replacement therapy could be more than doubled if the unweighed rather than the generalized least-square estimates were used.

Clinical Trials as Topic↗

PubMed2002

Determination of minimum sample size and discriminatory expression patterns in microarray data.

MOTIVATION: Transcriptional profiling using microarrays can reveal important information about cellular and tissue expression phenotypes, but these measurements are costly and time consuming. Additionally, tissue sample availability poses further constraints on the number of arrays that can be analyzed in connection with a particular disease or state of interest. It is therefore important to provide a method for the determination of the minimum number of microarrays required to separate, with statistical reliability, distinct disease states or other physiological differences. RESULTS: Power analysis was applied to estimate the minimum sample size required for two-class and multi-class discrimination. The power analysis algorithm calculates the appropriate sample size for discrimination of phenotypic subtypes in a reduced dimensional space obtained by Fisher discriminant analysis (FDA). This approach was tested by applying the algorithm to existing data sets for estimation of the minimum sample size required for drawing certain conclusions on multi-class distinction with statistical reliability. It was confirmed that when the minimum number of samples estimated from power analysis is used, group means in the FDA discrimination space are statistically different. CONTACT: gregstep@mit.edu

Acute Disease↗

PubMed1985

An initial test of a method for the estimation of real mean particle size from shadowed samples.

During shadowing, a "cap" of metal develops on small particles. This cap increases apparent particle with (measured normal to the shadowing direction) by an extent which cannot be predetermined. The extent of this increase in particle size (here defined as the "cap," X) is estimated in the present method by using opposite (180 degrees sample rotation) bidirectional shadowing. It is argued that the bidirectional cap is the sum of the two unidirectional caps, and therefore that X = 2A - (B + C), where A is the mean bidirectionally shadowed particle size, and B and C are the two mean unidirectionally shadowed particle sizes. As a validation of the method, the mean diameter of air-dried ferritin was estimated and the results appear to confirm the hypothesis (mean diameter by present method, 10.7 +/- 0.2 nm; mean diameter by previous methods, 10.89 nm).

Carbon↗

PubMedDate not supplied

Methodological issues with adaptation of clinical trial design.

Adaptation of clinical trial design generates many issues that have not been resolved for practical applications, though statistical methodology has advanced greatly. This paper focuses on some methodological issues. In one type of adaptation such as sample size re-estimation, only the postulated value of a parameter for planning the trial size may be altered. In another type, the originally intended hypothesis for testing may be modified using the internal data accumulated at an interim time of the trial, such as changing the primary endpoint and dropping a treatment arm. For sample size re-estimation, we make a contrast between an adaptive test weighting the two-stage test statistics with the statistical information given by the original design and the original sample mean test with a properly corrected critical value. We point out the difficulty in planning a confirmatory trial based on the crude information generated by exploratory trials. In regards to selecting a primary endpoint, we argue that the selection process that allows switching from one endpoint to the other with the internal data of the trial is not very likely to gain a power advantage over the simple process of selecting one from the two endpoints by testing them with an equal split of alpha (Bonferroni adjustment). For dropping a treatment arm, distributing the remaining sample size of the discontinued arm to other treatment arms can substantially improve the statistical power of identifying a superior treatment arm in the design. A common difficult methodological issue is that of how to select an adaptation rule in the trial planning stage. Pre-specification of the adaptation rule is important for the practicality consideration. Changing the originally intended hypothesis for testing with the internal data generates great concerns to clinical trial researchers.

Clinical Trials as Topic↗

PubMed2004

Sample-size requirements for comparisons of two groups on repeated observations of a binary outcome.

When preparing a research protocol, an investigator must be as careful in projecting sample-size requirements as in specifying hypotheses. In this article, tables are presented that provide estimates of sample-size requirements for statistical power of 0.80 with two-tailed alpha-levels of 0.05 in studies with a balanced design that plan to compare two groups on time-averaged, repeated observations of a binary outcome. The estimates, which are based on the algorithm of Diggle, Heagerty, Liang, and Zeger, are a function of several features of the study, including the response rates for each group, the number of repeated observations per participant, and the strength of the association among observations within participants as quantified with an intraclass correlation coefficient.

Algorithms↗

PubMedDate not supplied

Design and analysis of controlled trials in naturally clustered environments: implications for medical informatics.

In medical informatics research, study questions frequently involve individuals who are grouped into clusters. For example, an intervention may be aimed at a clinician (who treats a cluster of patients) with the intention of improving the health of individual patients. Correlation among individuals within a cluster can lead to incorrect estimates of the sample size required to detect an effect and inappropriate estimates of the confidence intervals and the statistical significance of the intervention effects. Contamination, which is the spread of the effect of an intervention or control treatment to the opposite group, often occurs between individuals within clusters. It leads to an attenuation of the effect of the intervention and reduced power to detect a difference. If individuals are randomized in a clinical trial (individual-randomized trial), then correlation must be taken into account in the analysis, and the sample size may need to be increased to compensate for contamination. Randomizing clusters rather than individuals (cluster-randomized trials) can eliminate contamination and may be preferred for logistical reasons. Cluster-randomized trials are generally less efficient than individual-randomized trials, so the tradeoffs must be assessed. Correlation must be taken into account in the analysis and in the sample-size calculations for cluster-randomized trials.

Cluster Analysis↗

PubMed2003

Statistics and sample design in epidemiological studies of Echinococcus multilocularis in fox populations.

In this paper possible sampling strategies for estimating the prevalence of Echinococcus multilocularis infections in foxes are discussed. To draw valid conclusions from the analysis of fractions of a total fox population, each member of the total population must have the same chance of being selected for the investigation (random sampling), the sample must be representative with respect to all epidemiologically relevant conditions in the population (e.g. age, endemic status, seasonal effects, population density), and it must be large enough to obtain results with the required precision. For detection/exclusion of infections at a pre-specified prevalence threshold and confidence level (e.g. 99%), the required sample is rather small, but the information obtained from the data is limited. For prevalence estimates, the required sample sizes depend on the expected prevalence, the desired precision of the estimate and the chosen confidence level (e.g. 90, 95, or 99%). The samples need to be taken in spatial units where the variation of the conditions potentially influencing the infection can be neglected. A first impression of the spatial distribution of E. multilocularis infections in foxes can also be obtained by mapping the investigated sample (infected and uninfected animals) using the municipalities where they were shot or found as a spatial grid. To analyse the local influence of environmental factors, data on the geographical positions where the animals were sampled need to be collected and analysed in the context of a Geographic Information System (GIS).

Age Factors↗

PubMed1980

An easy and reliable estimation of acute myocardial infarct size from serum CK-MB measurements.

The purpose of this study was to determine a simple and reliable procedure of estimating acute myocardial infarct (AMI) size by measuring serum creatine kinase MB (CK-MB) in few daily blood samples. In 13 patients with AMI blood samples were drawn every second hour for 60 h for determination of serum CK-MB activity. Infarct size was calculated using the CK-MB values of all samples and compared to the size calculated according to various models based on enzyme levels in few samples. Two models, using 3 daily samples, showed very high correlations and satisfactory standard errors of estimate when compared to the infarct size calculated from all samples. One of the 2 models was based on a computerized log-normal curve fit programme and one on accumulation of serum activities of CK-MB. The coefficient of variation of infarct size estimated from thrice-daily sampling was 7.4 and 9.4 for the 2 models. Considering the twenty-fold variation in infarct size a satisfactory quantitation is achieved from 3 daily samples.

Aged↗

PubMed2006

Frequentist model-averaged estimators and tests for univariate twin models.

Parameter estimates from analyses of univariate twin data usually do not reflect the uncertainty due to the model selection phase of the data analysis. To address the effect of model selection uncertainty on parameter estimates, we introduce frequentist model-averaged estimators for univariate twin data analysis that use information-theoretic criteria to assign model weights. We conduct simulation studies to examine the performance of model-averaged estimators of additive genetic variance, and for tests for additive genetic variance based on model-averaged estimators. In simulation studies with small or moderate sample sizes, model-averaged estimators of additive genetic variance typically have lower mean-squared error than either (i) estimators from individual twin models, or (ii) estimators obtained from a decision procedure where the best-fitting model from likelihood-ratio testing is used to estimate additive genetic variance. For each sample size simulated, bootstrap tests based on model-averaged estimators have higher power to detect additive genetic variance than currently-used tests in most cases.

Analysis of Variance↗

PubMedDate not supplied

Confidence intervals and sample-size calculations for the sisterhood method of estimating maternal mortality.

The sisterhood method is an indirect method of estimating maternal mortality that has, in comparison with conventional direct methods, the dual advantages of ease of use in the field and smaller sample-size requirements. This report describes how to calculate a standard error to quantify the sampling variability for this method. This standard error can be used to construct confidence intervals and statistical tests and to plan the size of a sample survey that employs the sisterhood method. Statistical assumptions are discussed, particularly in relation to the effective sample size and to effects of extrabinomial variation. In a worked example of data from urban Pakistan, a maternal mortality ratio of 153 (95 percent confidence interval between 96 and 212) deaths per 100,000 live births is estimated.

Age Factors↗

PubMed1991

Sample sizes and power computation for clinical intervention trials.

The purpose of this article was to describe basic concepts of sample size and power estimation for planning nursing intervention trials and interpreting their results. Simple mathematical calculations, using the formulas presented here, can be used to estimate the number of subjects required to conduct a study with a designated effect size and level of power. These methods are of great importance, since most funding agencies require sample size and power estimations before a grant is awarded. In general, studies with power lower than .7 or .8 need careful consideration before they are implemented. In these situations, it may be wise to consider various alternatives for obtaining study subjects or deleting treatment groups for investigations involving more than two groups. The formulas presented here can also be useful in estimating the power of published research findings. Through a quick calculation, the consumer of nursing research can critically evaluate the meaning of a negative trial and draw appropriate conclusions for future research and practice.

Clinical Nursing Research↗

PubMed2006

A general approach for sample size and statistical power calculations assessing of interventions using a mixture model in the presence of detection limits.

A zero-inflated log-normal mixture model (which assumes that the data has a probability mass at zero and a continuous response for values greater than zero) with left censoring due to assay measurements falling below detection limits has been applied to compare treatment groups in randomized clinical trials and observational cohort studies. The sample size calculation (for a given type I error rate and a desired statistical power) has not been studied for this type of data under the assumption of equal proportions of true zeros in the treatment and control groups. In this article, we derive the sample sizes based on the expected differences between the non-zero values of individuals in treatment and control groups. Methods for calculation of statistical power are also presented. When computing the sample sizes, caution is needed as some irregularities occur, namely that the location parameter is sometimes underestimated due to the mixture distribution and left censoring. In such cases, the aforementioned methods fail. We calculated the required sample size for a recent randomized chemoprevention trial estimating the effect of oltipraz on reducing aflatoxin. A Monte Carlo simulation study was also conducted to investigate the performance of the proposed methods. The simulation results illustrate that the proposed methods provide adequate sample size estimates. However, when the aforementioned irregularity occurs, our methods are restricted and further research is needed.

Anticarcinogenic Agents↗

PubMed2004

A sample size computation method for non-linear mixed effects models with applications to pharmacokinetics models.

We propose a simple method to compute sample size for an arbitrary test hypothesis in population pharmacokinetics (PK) studies analysed with non-linear mixed effects models. Sample size procedures exist for linear mixed effects model, and have been recently extended by Rochon using the generalized estimating equation of Liang and Zeger. Thus, full model based inference in sample size computation has been possible. The method we propose extends the approach using a first-order linearization of the non-linear mixed effects model and use of the Wald chi(2) test statistic. The proposed method is general. It allows an arbitrary non-linear model as well as arbitrary distribution of random effects characterizing both inter- and intra-individual variability of the mixed effects model. To illustrate possible uses of the method we present tables of minimum sample sizes, in particular, with an illustration of the effect of sampling design on sample size. We demonstrate how (D-)optimal or frequent sampling requires fewer subjects in comparison to a sparse sampling design. We also present results from Monte Carlo simulations showing that the computed sample size can produce the desired power. The proposed method greatly reduces computing times compared with simulation-based methods of estimating sample sizes for population PK studies.

Black People↗

PubMed2000

Survey and surveillance development in settings with low human immunodeficiency virus prevalence.

In most countries, during the early phases of a human immunodeficiency virus epidemic, independently initiated surveys of perceived high-risk groups tend to precede the development of formal surveillance systems. Unfortunately, in low-prevalence settings, small sample sizes produce unreliable estimates of prevalence and trends, with an inevitable tendency towards positive results. In our study, we present sample size calculations and typical samples used in actual surveys, with Pakistan as our example. More useful data on risk behaviour and potential for spread can be derived from the study of commoner sexually transmitted diseases and associated risk behaviours, including assessments of knowledge, attitudes, beliefs and practices.

Bias↗

PubMed2005

Minimum sample size and sampling time requirements for assessment of rifampicin bioequivalence from FDC formulations.

SETTING: The WHO- and IUATLD-recommended protocol for rifampicin (RMP) bioequivalence utilises 20-22 volunteers and 8 h, whereas the requirement of other regulatory authorities is 12 volunteers with a 24 h sampling schedule. Differing sampling size and time requirements may change the outcome of RMP bioequivalence. OBJECTIVE: To determine the minimal sample size and time required to assess RMP bioequivalence from FDC formulations. DESIGN: Bioequivalence studies were conducted that fulfilled the criteria of the WHO and Indian regulatory protocols. From earlier studies, retrospective pharmacokinetic evaluation, power of the test and bioequivalence limits were also calculated using 8-22 volunteers and sampling points of 8-24 h. Pharmacokinetic and statistical evaluations from three representative studies showing low, moderate and high intra-subject variability are given to determine minimum requirements for RMP bioequivalence. RESULT: It was found that a sampling schedule up to 8 h was sufficient to compare the absorption process of RMP. There was no influence of reduced sample size on bioequivalence estimates of RMP that showed low or moderate variability. However, in a study showing higher variation, a sample size of 14-16 subjects was found to be optimal. CONCLUSION: It is possible to reduce the sample size requirement for determination of RMP bioequivalence using the WHO protocol.

Antibiotics, Antitubercular↗

PubMed2006

Survey and surveillance development in settings with low human immunodeficiency virus prevalence.

Journal Article↗

PubMed2005

Mixed effects versus fixed effects modelling of binary data with inter-subject variability.

The question of whether or not a mixed effects model is required when modelling binary data with inter-subject variability and within subject correlation was reported in this journal by Yano et al. (J. Pharmacokin. Pharmacodyn. 28:389-412 [2001]). That report used simulation experiments to demonstrate that, under certain circumstances, the use of a fixed effects model produced more accurate estimates of the fixed effect parameters than those produced by a mixed effects model. The Laplace approximation to the likelihood was used when fitting the mixed effects model. This paper repeats one of those simulation experiments, with two binary observations recorded for every subject, and uses both the Laplace and the adaptive Gaussian quadrature approximations to the likelihood when fitting the mixed effects model. The results show that the estimates produced using the Laplace approximation include a small number of extreme outliers. This was not the case when using the adaptive Gaussian quadrature approximation. Further examination of these outliers shows that they arise in situations in which the Laplace approximation seriously overestimates the likelihood in an extreme region of the parameter space. It is also demonstrated that when the number of observations per subject is increased from two to three, the estimates based on the Laplace approximation no longer include any extreme outliers. The root mean squared error is a combination of the bias and the variability of the estimates. Increasing the sample size is known to reduce the variability of an estimator with a consequent reduction in its root mean squared error. The estimates based on the fixed effects model are inherently biased and this bias acts as a lower bound for the root mean squared error of these estimates. Consequently, it might be expected that for data sets with a greater number of subjects the estimates based on the mixed effects model would be more accurate than those based on the fixed effects model. This is borne out by the results of a further simulation experiment with an increased number of subjects in each set of data. The difference in the interpretation of the parameters of the fixed and mixed effects models is discussed. It is demonstrated that the mixed effects model and parameter estimates can be used to estimate the parameters of the fixed effects model but not vice versa.

Algorithms↗