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At least 1,117 records · Page 62Linked to original sources
PubMed2006

Minimum sample size requirements for bone density precision assessment produce inconsistency in clinical monitoring.

INTRODUCTION: Detection of change during bone mineral density (BMD) monitoring is affected by test precision. The International Society of Clinical Densitometry (ISCD) recommends that each center determine precision error using repeat measurements in 30 subjects (or an equivalent method providing 30 degrees of freedom). METHODS: We hypothesized that this sample size may be too small for a robust precision estimate, which could affect the performance of BMD monitoring in clinical practice. Replicate measurements of the spine and total hip (198 spine and 193 hip scan pairs) were obtained (interval 6+/-5 days). The sample was randomly divided into six groups of 30 patients each. Root mean square standard deviation (RMS-SD in g/cm(2)) and coefficient of variation (RMS-CV in %) precision errors and corresponding 95% least significant change (LSC) were calculated for each group and the pooled sample. LSC cutoffs were applied to 1,420 individuals from the Manitoba Bone Density Program who had follow-up measurements on the same instrument (interval 21+/-9 months). While the pooled spine RMS-SD was 0.017 and pooled hip RMS-SD was 0.009 g/cm(2), sample sizes of 30 gave a range of RMS-SD point estimates from 0.012 to 0.021 for the spine and from 0.008 to 0.012 for the hip. RESULTS: When the respective LSC cutoffs were applied to the 1,420 follow-up scan pairs, the fraction of patients categorized with significant change in the spine varied from 20.7% to 46.0%; four of the six LSCs based upon 30 subjects gave fractions significantly different from the pooled LSC of 30.7%. Significant change fractions for the hip varied from 31.1% to 51.1%; two of the six LSCs based upon 30 subjects gave fractions significantly different from the pooled LSC of 40.1%. Similar results were obtained using relative precision errors. CONCLUSION: BMD precision studies using a sample size of 30 are insufficient to reliably characterize precision error or change during clinical monitoring.

Absorptiometry, Photon↗
PubMedDate not supplied

Small sample estimation of log odds ratios from logistic regression and fourfold tables.

Schaefer has proposed a method to correct the maximum likelihood logistic regression coefficients for bias in small samples. We show here that this reduces, in the special case of a single dichotomous regression variable, to an earlier result of Haldane, for the estimation of a single log odds ratio. This paper reviews various estimators for the log odds ratio in a fourfold table, and compares the properties of two by complete enumeration in sets of tables with small sample sizes. The first of these, also due to Haldane, is based on the addition of 1/2 to each cell of the table; the second is where 1/2 is added to all cells of the table only if a zero frequency arises. We evaluate the bias and mean squared error of both of these estimators in sets of tables with various sample sizes and odds ratios. Haldane's estimator usually has lower bias and MSE, and so we do not in general recommend the practice of adding 1/2 only as necessary. Exceptions might occur if one has good a priori estimates of the outcome probabilities in the two samples under comparison.

Regression Analysis↗
PubMed2005

Adaptive design and estimation in randomized clinical trials with correlated observations.

Clinical trial designs involving correlated data often arise in biomedical research. The intracluster correlation needs to be taken into account to ensure the validity of sample size and power calculations. In contrast to the fixed-sample designs, we propose a flexible trial design with adaptive monitoring and inference procedures. The total sample size is not predetermined, but adaptively re-estimated using observed data via a systematic mechanism. The final inference is based on a weighted average of the block-wise test statistics using generalized estimating equations, where the weight for each block depends on cumulated data from the ongoing trial. When there are no significant treatment effects, the devised stopping rule allows for early termination of the trial and acceptance of the null hypothesis. The proposed design updates information regarding both the effect size and within-cluster correlation based on the cumulated data in order to achieve a desired power. Estimation of the parameter of interest and its confidence interval are proposed. We conduct simulation studies to examine the operating characteristics and illustrate the proposed method with an example.

Biometry↗
PubMed2001

Gene expression analysis with the parametric bootstrap.

Recent developments in microarray technology make it possible to capture the gene expression profiles for thousands of genes at once. With this data researchers are tackling problems ranging from the identification of 'cancer genes' to the formidable task of adding functional annotations to our rapidly growing gene databases. Specific research questions suggest patterns of gene expression that are interesting and informative: for instance, genes with large variance or groups of genes that are highly correlated. Cluster analysis and related techniques are proving to be very useful. However, such exploratory methods alone do not provide the opportunity to engage in statistical inference. Given the high dimensionality (thousands of genes) and small sample sizes (often <30) encountered in these datasets, an honest assessment of sampling variability is crucial and can prevent the over-interpretation of spurious results. We describe a statistical framework that encompasses many of the analytical goals in gene expression analysis; our framework is completely compatible with many of the current approaches and, in fact, can increase their utility. We propose the use of a deterministic rule, applied to the parameters of the gene expression distribution, to select a target subset of genes that are of biological interest. In addition to subset membership, the target subset can include information about relationships between genes, such as clustering. This target subset presents an interesting parameter that we can estimate by applying the rule to the sample statistics of microarray data. The parametric bootstrap, based on a multivariate normal model, is used to estimate the distribution of these estimated subsets and relevant summary measures of this sampling distribution are proposed. We focus on rules that operate on the mean and covariance. Using Bernstein's Inequality, we obtain consistency of the subset estimates, under the assumption that the sample size converges faster to infinity than the logarithm of the number of genes. We also provide a conservative sample size formula guaranteeing that the sample mean and sample covariance matrix are uniformly within a distance epsilon > 0 of the population mean and covariance. The practical performance of the method using a cluster-based subset rule is illustrated with a simulation study. The method is illustrated with an analysis of a publicly available leukemia data set.

Journal Article↗
PubMed1975

Sequential Estimation of p with Squared Relative Error Loss.

We consider the sequential estimation of p, the probability of success in an infinite sequence of Bernoulli trials, when the loss incurred in stopping after n trials and estimating p by some function delta(n) of the first n outcomes is taken to be [Formula: see text] The loss due to error of estimation is thus the symmetrized relative squared error, which is appropriate in applications when p may be near 0 or 1.We begin by finding a heuristic procedure for sequentially determining the sample size n which, with the usual terminal estimator of p, performs well for any fixed 0 < p < 1 as the cost per observation c --> 0. For any fixed c > 0, however, this procedure is poor as p --> 0 or 1. To remedy this defect, the uniform prior on p is introduced. The corresponding Bayes procedure is found and is shown to have a Bayes risk approximately 2pi radicalc as c --> 0.

Journal Article↗
PubMedDate not supplied

Intraclass correlation among measures related to tobacco use by adolescents: estimates, correlates, and applications in intervention studies.

Tobacco intervention studies that employ a community trial design require adjustment to the usual analytic methods to account for the allocation of intact social groups to study conditions and the positive intraclass correlation (p) that is inevitable in such a design. In the absence of valid estimates of the relevant p, investigators seeking to establish an appropriate sample size could only guess about the magnitude of the problem. We recently published estimates of p for common measures of adolescent tobacco use, but those estimates were unadjusted for potential covariates and so represented an upper limit on the magnitude of p. This report demonstrates how estimates of intraclass correlation may be substantially reduced through regression adjustment for easily measured covariates. Results show that both the p and the residual variance can be reduced, by an average of 20 and 11%, respectively, offering greater efficiency for investigators who plan future studies and who are able to measure those covariates in their studies. Future work should seek both to replicate this work and to extend it; for example, to cohort designs where the improvements might be even greater.

Adolescent↗
PubMed2007

Sizing a trial to alter the trajectory of health behaviours: methods, parameter estimates, and their application.

Group-randomized trials often involve repeat observations on the same participants. When there are no more than two observations from each participant, standard mixed-model regression methods for a pretest-posttest design can be used. When there are more than two observations from each participant, random coefficients models may be useful. This paper describes the random coefficients analysis appropriate to data from an extended nested cohort design and presents the methods for power analysis and sample size calculations based on that analysis. We provide estimates for the parameters required for those calculations for a number of adolescent health behaviours. We also show how the estimates can be used to plan a future trial.

Adolescent↗
PubMedDate not supplied

Rural hospital costs: an analysis with policy implications.

The 1977 National Guidelines for Health Planning suggest a maximum of 4 hospital beds per 1,000 population and a minimum occupancy rate of 80 percent for those beds as desirable for an efficient local hospital system. Rural areas often have more than 4 hospital beds per 1,000 population and generally exhibit occupancy rates well below the rate specified by the Guidelines. Hence, there appears to be an opportunity for reducing the cost of hospital services in rural areas by providing care with fewer beds concentrated in larger, better utilized facilities. This paper presents estimates of the annual savings that would result from following such a policy in rural areas. The statistically estimated cost curves are based on data from a sample of 116 rural hospitals for the years 1971-77. With a quadratic specification for the cost function, the hospital size that minimizes average costs is estimated to be 113 beds, and the occupancy rate that minimizes costs is 73 percent. Hospitals with 113 beds are estimated to have average costs per patient day that are from $6.51 (logarithmic specification) to $15.15 (quadratic specification) below the average cost per patient day of a 41-bed hospital, the average size of the hospitals in the sample. Hospitals with a 73 percent occupancy rate are estimated to have average costs that are $5.96 logarithmic specification to $11.75 (quadratic specification) lower than the average costs in hospitals with 51 percent occupancy rates, the average in the sample, if other factors are held constant. These benefits can be weighed by health policy analysts against the increased cost of travel and ambulance service, and the accompanying increase in risk to patients, to determine if the present structure for the delivery of acute care in rural areas warrants change.

Bed Occupancy↗
PubMed1999

Estimation of the average correlation coefficient for stratified bivariate data.

If the relationship between two ordered categorical variables X and Y is influenced by a third categorical variable with K levels, the Cochran-Mantel-Haenszel (CMH) correlation statistic QC is a useful stratum-adjusted summary statistic for testing the null hypothesis of no association between X and Y. Although motivated by and developed for the case of K I x J contingency tables, the correlation statistic QC is also applicable when X and Y are continuous variables. In this paper we derive a corresponding estimator of the average correlation coefficient for K I x J tables. We also study two estimates of the variance of the average correlation coefficient. The first is a restricted variance based on the variances of the observed cell frequencies under the null hypothesis of no association. The second is an unrestricted variance based on an asymptotic variance derived by Brown and Benedetti. The estimator of the average correlation coefficient works well in tables with balanced and unbalanced margins, for equal and unequal stratum-specific sample sizes, when correlation coefficients are constant over strata, and when correlation coefficients vary across strata. When the correlation coefficients are zero, close to zero, or the cell frequencies are small, the confidence intervals based on the restricted variance are preferred. For larger correlations and larger cell frequencies, the unrestricted confidence intervals give superior performance. We also apply the CMH statistic and proposed estimators to continuous non-normal data sampled from bivariate gamma distributions. We compare our methods to statistics for data sampled from normal distributions. The size and power of the CMH and normal theory statistics are comparable. When the stratum-specific sample sizes are small and the distributions are skewed, the proposed estimator is superior to the normal theory estimator. When the correlation coefficient is zero or close to zero, the restricted confidence intervals provide the best performance. None of the confidence intervals studied provides acceptable performances across all correlation coefficients, sample sizes and non-normal distributions.

Aged↗
PubMed1994

Gestational age correlates with immunosuppressive properties of hydatidiform mole pregnancies.

PROBLEM: Soluble trophoblast extracts (HME) from some human hydatidiform mole pregnancies suppress IL-2-dependent T-cell proliferation, while others express no immunosuppressive bioactivity. This study was designed to determine if suppression by HME was correlated with gestational age, uterine size, or hCG secretion. METHOD: Soluble extracts were prepared from nine hydatidiform mole trophoblast samples and screened for immunosuppressive activity using a murine cytotoxic T-cell proliferation assay (CTLL-2). Gestational ages were determined from last menstrual cycle and uterine size was estimated at the time of surgery. Serum samples were collected prior to uterine evacuation and were assayed for human chorionic gonadotropin (hCG). RESULTS: Four of nine HME samples significantly (P < 0.05) suppressed CTLL2 proliferation, while five exhibited no suppressive activity. A strong positive correlation (r = 0.639) was noted for the relationship between gestational age of the molar pregnancies and interleukin-2 (IL-2)-stimulated CTLL2 proliferation (expressed as % of control) in the presence of HME (500 micrograms/mL). This indicates that HME suppression of CTLL2 proliferation is highest in early gestation and then declines with increasing gestational age. A similar correlation was observed between estimated uterine size at surgery and CTLL2 proliferation with added HME, although the association was not as strong (r = 0.359). No association was noted between hCG levels and CTLL2 proliferative responses (r = -0.091). CONCLUSIONS: The results of this study suggest that production of immunosuppressive factors by hydatidiform mole trophoblast is developmentally regulated, and decreases with advancing gestation.

Cells, Cultured↗
PubMedDate not supplied

Approaches to sample size calculation in comparative studies.

The questions 'what should be the minimum study subjects' and 'how these subjects should be enrolled in the study' are two aspects that are considered at the design stage. Regardless of research question and the study design adopted, these two questions are an integral part of any research proposal. No matter how well a study is conducted and statistically analysed using sophisticated statistical methods/softwares, if the study size is inadequate, concluding statements will have inadequate power and such statements may be misleading and harmful to both target population and the scientific community. There is no substitute/shortcut to an adequate study size as no statistical methods are available to adjust for an inadequate study size. Though a larger sample size will result in higher precision in estimates, however, it may not be desirable in terms of cost, time and the efforts. In medical sciences, majority of research questions pertain to comparing outcome measures in two or more than two groups. Focus of this article is on the number of study subjects required in a study and an attempt is made to review the ingredients required to calculate the sample size in situations commonly encountered by researchers in medical sciences. Formulae for the specific situations are provided with worked out examples.

Child↗
PubMed2005

On the use of beta coefficients in meta-analysis.

This research reports an investigation of the use of standardized regression (beta) coefficients in meta-analyses that use correlation coefficients as the effect-size metric. The investigation consisted of analyzing more than 1,700 corresponding beta coefficients and correlation coefficients harvested from published studies. Results indicate that, under certain conditions, using knowledge of corresponding beta coefficients to input missing correlations (effect sizes) generally produces relatively accurate and precise population effect-size estimates. Potential benefits from applying this knowledge include smaller sampling errors because of increased numbers of effect sizes and smaller non-sampling errors because of the inclusion of a broader array of research designs.

Humans↗
PubMed2003

Improved up-and-down designs for phase I trials.

We consider several designs from the family of up-and-down rules for the sequential allocation of dose levels to subjects in a dose-response study. We show that an up-and-down design can be improved by using more information than the most recent response. For example, the k-in-a-row rule uses up to the k most recent responses. We introduce a new design, the Narayana rule, which uses a local estimate of the probability of toxicity calculated from all previous responses. For the Narayana rule, as the sample size gets large, the probability of assignment goes to zero for dose levels not among the two (or three) closest to the target. Different estimators of the target dose are compared. We find that the isotonic regression estimator is superior to other estimators for small to moderate sample sizes.

Clinical Trials, Phase I as Topic↗
PubMed2003

Pooled fecal culture sampling for Mycobacterium avium subsp. paratuberculosis at different herd sizes and prevalence.

A stochastic spreadsheet model was developed to obtain estimates of the costs of whole herd testing on dairy farms for Mycobacterium avium subsp. paratuberculosis (Map) with pooled fecal samples. The optimal pool size was investigated for 2 scenarios, prevalence (a low-prevalence herd [< or = 5%] and a high-prevalence herd [> 5%]) and for different herd sizes (100-, 250-, 500- and 1,000-cow herds). All adult animals in the herd were sampled, and the samples of the individuals were divided into equal sized pools. When a pool tested positive, the manure samples of the animals in the pool were tested individually. The individual samples from a negative pool were assumed negative and not tested individually. Distributions were used to model the uncertainty about the sensitivity of the fecal culture at farm level and Map prevalence. The model randomly allocated a disease status to the cows (not shedding, low Map shedder, moderate Map shedder, and heavy Map shedder) on the basis of the expected prevalence in the herd. Pooling was not efficient in 100-cow and 250-cow herds with low prevalence because the probability to detect a map infection in these herds became poor (53% and 88%) when samples were pooled. When samples were pooled in larger herds, the probability to detect at least 1 (moderate to heavy) shedder was > 90%. The cost reduction as a result of pooling varied from 43% in a 100-cow herd with a high prevalence to 71% in a 1,000-cow herd with a low prevalence. The optimal pool size increased with increasing herd size and varied from 3 for a 500-cow herd with a low prevalence to 5 for a 1,000-cow herd with a high prevalence.

Animals↗
PubMed2000

A method for estimating the intensity of overdominant selection from the distribution of allele frequencies.

A method is proposed for estimating the intensity of overdominant selection scaled by the effective population size, S = 2Ns, from allele frequencies. The method is based on the assumption that, with strong overdominant selection, allele frequencies are nearly at their deterministic equilibrium values and that, to a first approximation, deviations depend only on S. Simulations verify that reasonably accurate estimates of S can be obtained for realistic sample sizes. The method is applied to data from several loci in the major histocompatibility complex (Mhc) in numerous human populations. For alleles distinguished by both serological typing and the sequence of the peptide-binding region, our estimates of S are comparable to those obtained by analysis of DNA sequences in showing that selection is strongest on HLA-B and weaker on HLA-A, HLA-DRB1, and HLA-DQA1. The intensity of selection on HLA-B varied considerably among populations. Two populations, Native American and Inuit, showed an excess rather than a deficiency in homozygosity. Comparable estimates of S were obtained for alleles at Mhc class II loci distinguished by serological reactions (serotyping) and by differences in the amino acid sequences of the peptide-binding region (molecular typing). A comparison of two types of data for DQA1 and DRB1 showed that serotyping led to generally lower estimates of S.

Algorithms↗
PubMed2006

Estimation in flexible two stage designs.

Adaptive test designs for clinical trials allow for a wide range of data driven design adaptations using all information gathered until an interim analysis. The basic principle is to use a test statistics which is invariant with respect to the design adaptations under the null hypothesis. This allows for a control of the type I error rate for the primary hypothesis even for adaptations not specified a priori in the study protocol. Estimation is usually another important part of a clinical trial, however, is more difficult in adaptive designs. In this research paper we give an overview of point and interval estimates for flexible designs and compare methods for typical sample size rules. We also make some proposals for confidence intervals which have nominal coverage probability also after an unforeseen design adaptation and which contain the maximum likelihood estimate and the usual unadjusted confidence interval.

Clinical Trials as Topic↗
PubMed2006

Analyzing oncology clinical trial data using the Q-TWiST method: clinical importance and sources for health state preference data.

PURPOSE: The Quality-adjusted Time Without Symptoms of disease and Toxicity (Q-TWiST) analysis method is frequently applied to evaluating outcomes in cancer clinical trials, but there is little information on what constitutes a clinically important difference (CID). We reviewed the Q-TWiST, health-related quality of life (HRQL) and utility measurement literature to develop recommendations for CID for the Q-TWiST. We also provide recommendations for measuring health utilities and for the design of Q-TWiST studies. METHODS: The English language literature was searched between 1986 and 2003 for Q-TWiST studies in oncology. We estimated the percent differences between treatments based on median follow-up duration for overall, progression-free and quality-adjusted survival. We also reviewed the relevant HRQL and utility literature on clinical importance. RESULTS: The overall differences between treatments for most (56%) of the observed, published values for Q-TWiST analyses ranged between 12% and 19%. Three-fourths of the Q-TWiST studies had gains in survival of 12%-17%, while differences in progression-free survival ranged from 12% to 26%. Studies that have evaluated the clinical importance of changes in HRQL scores suggest that changes of 5%-10% are clinically meaningful, and other research suggests that 0.5 standard deviation is a reasonable threshold for changes in HRQL for chronic diseases. Similarly, one guideline from the health state utility literature is that a 5%-10% difference in standard gamble utility scores is clinically important. Various sources are available for health utilities for Q-TWiST studies and the most valid are derived from patients or the general public, although most studies rely on sensitivity analyses with no collection of utilities. CONCLUSIONS: We recommend that the CID for Q-TWiST is 10% of overall survival in a study, and differences of 15% are clearly clinically important. If less is known about a specific treatment and/or disease area, the CID should be greater than 5% but not more than 10% in planning sample size and statistical power. These CID estimates should be interpreted with caution, pending confirmation in future studies by direct patient assessment of the clinically relevant health states for Q-TWiST.

Clinical Trials as Topic↗
PubMed2003

Likelihood inference for exchangeable binary data with varying cluster sizes.

This article investigates maximum likelihood estimation with saturated and unsaturated models for correlated exchangeable binary data, when a sample of independent clusters of varying sizes is available. We discuss various parameterizations of these models, and propose using the EM algorithm to obtain maximum likelihood estimates. The methodology is illustrated by applications to a study of familial disease aggregation and to the design of a proposed group randomized cancer prevention trial.

Algorithms↗