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PubMedDate not supplied

Trying to do better than average: a commentary on 'statistical inference for cost-effectiveness ratios'.

In a recent paper, Laska, Meisner and Siegel address issues concerning hypothesis testing in cost-effectiveness analysis. They relate the relative magnitude of two average cost-effectiveness ratios to the incremental cost-effectiveness ratio and go on to propose a statistical procedure for testing the equality of two average ratios. In this paper, we show why the use of average cost-effectiveness ratios is misleading and argue that the appropriate focus for cost-effectiveness analysis is the estimation of confidence intervals around incremental cost-effectiveness ratios.

Confidence Intervals↗
PubMed2005

Frequent mistakes in the statistical inference of biomedical data.

Although there is a plethora of books, reviews and articles defining the meaning of the p value, many investigators make errors when reaching conclusions from their work based on this p value. Most report their data using rigid sentences such as "the results are not statistically significant, p > 0.05", frequently misunderstood by the authors and the readers. Many professionals are not aware of their limitations in this field rendering the problem even more complicated. In this article we include advice from experts against mistakes frequently made by investigators, such as the plea made by Rothman that a correct interpretation of the data should not be replaced by sentences such as "statistically significant" or "statistically non-significant". Detailed comments on the more frequent mistakes as well as the reasons for their appearance and persistence during the decades are presented. Finally, a comprehensive explanation of the p value is included, to emphasize that to avoid these mistakes there is no need to learn the mathematical basis of tests but that logic alone would suffice.

Biomedical Research↗
PubMed1992

The reporting of statistical inferences in selected prosthodontic journals.

Dental periodicals are the fundamental source of prosthodontic research. The ability to understand and contribute to dental literature is basic to the prosthodontic profession. The purpose of this study is to tally relative frequency with which various descriptive (n = 18), graphical (n = 7), and inferential statistical procedures (n = 68) are used in the prosthodontic literature. Our method consists of four procedures: journal selection, choice of 1987 through 1988 articles with inferential statistical content, tally of the statistical procedures in those articles, and quality control procedures used in obtaining these data. At least 50% of 10 prosthodontists selected 17 of 100 journals most likely to be read by prosthodontists. In the 17 journals, 1,320 articles were screened of which 406 were selected and evaluated for their statistical procedures. The bar and line plots were the most common graphical procedures occurring in over one fourth of the 406 articles. Percentages, means, and standard deviations occurred in more than 40%. Although 58% used the .05 significance level, only 0.3% mentioned power. Analysis of variance was used more often than the t tests (42% v 29%), whereas correlation/regression (21%) and chi-square tests (14%) were used less often. The t tests, analysis of variance (Duncan, Tukey, and Student-Newman-Keuls multiple comparison procedures), chi-square tests, correlation and regression, and the Wilcoxon tests occurred in at least 5% of the 406 articles.

Analysis of Variance↗
PubMed1993

Tasks in statistical inference for studying variation in medicine.

When studying variation in medicine, traditional hypothesis-testing procedures are too limited to obtain useful inferences except in special situations. More generally, full probability modelling is necessary. Even a relatively simple example can illustrate this point rather dramatically. The development and application of full-probability methods for medical problems comprise exciting areas for statistical and medical researchers, especially if working together.

Health Services Research↗
PubMed2003

Statistical inference methods for detecting altered gene associations.

The higher incidence of liver disease in the Asian population raises a great concern to clinicians. To understand the gene functions involved in different stages of the disease, microarray expression data of histological progressive grades, starting from the dysplastic nodule in cirrhotic liver to hepatocellular carcinoma Edmonson grade III are analyzed. The statistical procedures are divided into two parts: First, microarray data are suitably normalized, including a method of analysis of variance (ANOVA). There are great differences of opinion regarding the currently used normalization methods. In order to proceed to the second part of statistical analyses of gene-pair associations, these normalization methods need first to be compared. Based on the assumption that a union set of significant genes from these normalization methods includes sufficiently general and well-defined, differentially expressed genes, one must carry out the second part of statistical analyses of searching for evidence of altered gene-gene relationships with progression of the disease. Significantly altered gene-pair associations are identified with the ratio of gene-pair correlations. The methods are illustrated with replicated microarray expression data.

Analysis of Variance↗
PubMed2001

A Bayesian framework for the analysis of microarray expression data: regularized t -test and statistical inferences of gene changes.

MOTIVATION: DNA microarrays are now capable of providing genome-wide patterns of gene expression across many different conditions. The first level of analysis of these patterns requires determining whether observed differences in expression are significant or not. Current methods are unsatisfactory due to the lack of a systematic framework that can accommodate noise, variability, and low replication often typical of microarray data. RESULTS: We develop a Bayesian probabilistic framework for microarray data analysis. At the simplest level, we model log-expression values by independent normal distributions, parameterized by corresponding means and variances with hierarchical prior distributions. We derive point estimates for both parameters and hyperparameters, and regularized expressions for the variance of each gene by combining the empirical variance with a local background variance associated with neighboring genes. An additional hyperparameter, inversely related to the number of empirical observations, determines the strength of the background variance. Simulations show that these point estimates, combined with a t -test, provide a systematic inference approach that compares favorably with simple t -test or fold methods, and partly compensate for the lack of replication.

Bayes Theorem↗
PubMed1977

Parent Attitude Research Instrument (PARI): clinical vs. statistical inferences in understanding abusive mothers.

Attitudes toward child rearing and early experiences in childhood traditionally have been regarded as psychodynamic factors that influence adult behavior. The present study assessed the capacity of the Parent Attitude Research Instrument (PARI) to differentiate between court-identified abusive mothers and a control sample of nonabusive, well-baby clinic mothers of comparable socioeconomic status. While univariate t-tests showed statistical significance for 3 of the 23 PARI scales, more sophisticated and appropriate multivariate tests (Discriminant Function Analysis) demonstrated that the PARI correctly classified the experimental and control Ss only 65% of the time. It appears that the PARI alone should not be used to identify potentially abusive mothers. Even more important, the results caution and alert non-statistically informed clinicians and researchers to the pitfall of over-interpreting clinical data that are based on the more simple univariate tests of statistical significance.

Attitude↗
PubMed1999

Statistical inference for serial dilution assay data.

Serial dilution assays are widely employed for estimating substance concentrations and minimum inhibitory concentrations. The Poisson-Bernoulli model for such assays is appropriate for count data but not for continuous measurements that are encountered in applications involving substance concentrations. This paper presents practical inference methods based on a log-normal model and illustrates these methods using a case application involving bacterial toxins.

Algorithms↗
PubMed1999

Statistical inference for self-designing clinical trials with a one-sided hypothesis.

In the process of monitoring clinical trials, it seems appealing to use the interim findings to determine whether the sample size originally planned will provide adequate power when the alternative hypothesis is true, and to adjust the sample size if necessary. In the present paper, we propose a flexible sequential monitoring method following the work of Fisher (1998), in which the maximum sample size does not have to be specified in advance. The final test statistic is constructed based on a weighted average of the sequentially collected data, where the weight function at each stage is determined by the observed data prior to that stage. Such a weight function is used to maintain the integrity of the variance of the final test statistic so that the overall type I error rate is preserved. Moreover, the weight function plays an implicit role in termination of a trial when a treatment difference exists. Finally, the design allows the trial to be stopped early when the efficacy result is sufficiently negative. Simulation studies confirm the performance of the method.

Biometry↗
PubMed1995

Statistical inference in stationary populations.

A fixed ensemble of alternating renewal processes is proposed as a model for stationary populations. This model is applied to explore the relationship between survival times and forward recurrence times. In addition, it is shown that ergodic theory can be applied to the model. An example is presented.

Biometry↗
PubMed2004

Reform of statistical inference in psychology: the case of memory & cognition.

Geoffrey Loftus, Editor of Memory & Cognition from 1994 to 1997, strongly encouraged presentation of figures with error bars and avoidance of null hypothesis significance testing (NHST). The authors examined 696 Memory & Cognition articles published before, during, and after the Loftus editorship. Use of figures with bars increased to 47% under Loftus's editorship and then declined. Bars were rarely used for interpretation, and NHST remained almost universal. Analysis of 309 articles in other psychology journals confirmed that Loftus's influence was most evident in the articles he accepted for publication, but was otherwise limited. An e-mail survey of authors of papers accepted by Loftus revealed some support for his policy, but allegiance to traditional practices as well. Reform of psychologists' statistical practices would require more than editorial encouragement.

Bibliometrics↗
PubMed2000

Statistical inference on associated fertility life table parameters using jackknife technique: computational aspects.

Knowledge of population growth potential is crucial for studying population dynamics and for establishing management tactics for pest control. Estimation of population growth can be achieved with fertility life tables because they synthesize data on reproduction and mortality of a population. The five main parameters associated with a fertility life table are as follows: (1) the net reproductive rate (Ro), (2) the intrinsic rate of increase (rm), 3) the mean generation time (T), (4) the doubling time (Dt), and (5) the finite rate of increase (lambda). Jackknife and bootstrap techniques are used to calculate the variance of the rm estimate, which can be extended to the other parameters of life tables. Those methods are computer-intensive, their application requires the development of efficient algorithms, and their implementation is based on a programming language that encompasses quickness and reliability. The objectives of this article are to discuss statistical and computational aspects related to estimation of life table parameters and to present a SAS program that uses jackknife to estimate parameters for fertility life tables. The SAS program presented here allows the calculation of confidence intervals for all estimated parameters, as well as provides one-sided and two-sided t-tests to perform pairwise or multiple comparison between groups, with their respective P values.

Animals↗
PubMed2006

Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study.

A stochastic discrete-time susceptible-exposed-infectious-recovered (SEIR) model for infectious diseases is developed with the aim of estimating parameters from daily incidence and mortality time series for an outbreak of Ebola in the Democratic Republic of Congo in 1995. The incidence time series exhibit many low integers as well as zero counts requiring an intrinsically stochastic modeling approach. In order to capture the stochastic nature of the transitions between the compartmental populations in such a model we specify appropriate conditional binomial distributions. In addition, a relatively simple temporally varying transmission rate function is introduced that allows for the effect of control interventions. We develop Markov chain Monte Carlo methods for inference that are used to explore the posterior distribution of the parameters. The algorithm is further extended to integrate numerically over state variables of the model, which are unobserved. This provides a realistic stochastic model that can be used by epidemiologists to study the dynamics of the disease and the effect of control interventions.

Algorithms↗
PubMed2001

Statistical inference of sequence-dependent mutation rates.

Several lines of research are now converging towards an integrated understanding of mutational mechanisms and their evolutionary implications. Experimentally, crystal structures reveal the effect of sequence context on polymerase fidelity; large-scale sequencing projects generate vast amounts of sequence polymorphism data; and locus-specific databases are being constructed. Computationally, software and analytical tools have been developed to analyze mutational data, to identify mutational hot spots, and to compare the signatures of mutagenic agents.

Computational Biology↗
PubMed2003

Statistical inference for well-ordered structures in nucleotide sequences.

Distinct, local structures are frequently correlated with functional RNA elements involved in post-transcriptional regulation of gene expression. Discovery of microRNAs (miRNAs) suggests that there are a large class of small non-coding RNAs in eukaryotic genomes. These miRNAs have the potential to form distinct fold-back stem-loop structures. The prediction of those well-ordered folding sequences (WFS) in genomic sequences is very helpful for our understanding of RNA-based gene regulation and the determination of local RNA elements with structure-dependent functions. In this study, we describe a novel method for discovering the local WFS in a nucleotide sequence by Monte Carlo simulation and RNA folding. In the approach the quality of a local WFS is assessed by the energy difference (E(diff)) between the optimal structure folded in the local segment and its corresponding optimal, restrained structure where all the previous base pairings formed in the optimal structure are prohibited. Distinct WFS can be discovered by scanning successive segments along a sequence for evaluating the difference between E(diff) of the natural sequence and those computed from randomly shuffled sequences. Our results indicate that the statistically significant WFS detected in the genomic sequences of Caenorhabditis elegans (C.elegans) F49E12, T07C5, T07D1, T10H9, Y56A3A and Y71G12B are coincident with known fold-back stem-loops found in miRNA precursors. The potential and implications of our method in searching for miRNAs in genomes is discussed.

Algorithms↗
PubMed1991

Statistical inference on mean dioptric power: asymmetric powers and singular covariance.

Methods have been developed recently for testing hypotheses on mean dioptric power and for constructing confidence regions in situations that are most likely to be encountered. In this paper the methods are extended to make the analysis complete. A new situation covered specifically is that of dioptric power not of the form sphere/cylinder x axis. Such powers, termed asymmetric powers because the dioptric power matrices are asymmetric, include the equivalent power of a thick obliquely crossed bitoric lens. A second situation is that in which the covariance matrix of the sample of powers is singular. Symmetric dioptric power (the more familiar form of power) can be represented by a point in three-dimensional space. In general, however, dioptric power is four dimensional in character. Singularity of covariance arises when variation in the sample is limited to a subspace of dimension less than the full three or four. The space spanned by the sample is called the range space of the sample. The dimension of the range space may be four, three, two, one or zero. Each case is considered in turn. Numerical examples of hypothesis testing are presented in range spaces of dimension four to one. The test statistic devised for each case also gives the equation of the confidence region about the mean of a sample of dioptric powers. Singularity can sometimes be avoided merely by taking larger samples and by taking more accurate readings. The problem of near singularity is briefly discussed. The paper allows basic hypothesis testing on mean dioptric power and the construction of confidence regions in all possible circumstances.

Multivariate Analysis↗
PubMed2005

Bootstrap methods for statistical inference from stereological estimates of volume fraction.

We suggest the use of bootstrap methods for inference from stereological estimates of volume fraction. An informal introduction to stereological estimation of volume fraction and to principles of bootstrap techniques is given. The bootstrap method is a robust computer-intensive resampling technique, based on independent random sampling from a data set with replacement. Bootstrap methods were used to estimate confidence intervals for volume fractions, and to test for a significant difference between estimated volume fractions from two samples. Two sampling designs are considered: independent replicated samples (visual fields) from a single object, and estimates of volume fraction from multiple independent objects. The methods are presented as worked examples on real data sets obtained from tumour pathology (mammary cancer, pancreatic cancer). The volume fraction of glandular lumina per total volume of the epithelial phase was chosen as target parameter. It indicates the degree of glandular differentiation in adenocarcinomas and is estimated as a ratio-of-means statistic with variable denominator within cases. The confidence intervals of the volume fraction estimated by the bootstrap method were slightly narrower than the parametrically calculated confidence intervals for all data sets. The outcomes of significance tests based on the bootstrap technique were unchanged as compared with classical tests based on the assumptions of normality and homoscedasticity of the data. Special attention was paid to the reproducibility of the bootstrap technique in replicated trials on the same data.

Breast Neoplasms↗