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PubMed1998

School size statistics of fish

A system of a fixed population size is considered in which fish schools break up and unite with other schools. The size distribution of schools is investigated on the basis of a balance equation, which corresponds to the mean-field theory of Smoluchowski-equation model of the coagulation-fragmentation process. The rates of fission and fusion are determined from a simple dynamic viewpoint of schooling. The size distribution, in effect, follows a power law up to a cutoff size, which can be fitted to data. The power index and the cutoff size depend on the population size. It is also elucidated how statistical properties of the system are regulated by the total population size. As the population size increases the number of schools increases, and asymptotically approaches a fixed value. If the population size is large, the mean school size depends linearly upon the population size. The standard deviation of the school-size distribution is proportional to the mean school size which is checked with data. Copyright 1998 Academic Press

Journal Article↗
PubMed1996

Evidence for the sensitivity of the SF-36 health status measure to inequalities in health: results from the Oxford healthy lifestyles survey.

OBJECTIVES: The short form 36 (SF-36) health questionnaire may not be appropriate for population surveys assessing health gain because of the low responsiveness (sensitivity to change) of domains on the measure. An hypothesised health gain of respondents in social class V to that of those in social class I indicated only marginal improvement in self reported health. Subgroup analysis, however, showed that the SF-36 would indicate dramatic changes if the health of social class V could be improved to that of social class I. DESIGN: Postal survey using a questionnaire booklet containing the SF-36 and a number of other items concerned with lifestyles and illness. A letter outlining the purpose of the study was included. SETTING: The sample was drawn from family health services authority (FHSA) computerised registers for Berkshire, Buckinghamshire, Northamptonshire, and Oxfordshire. SAMPLE: The questionnaire was sent to 13,042 randomly selected subjects between the ages of 17-65. Altogether 9332 (72%) responded. OUTCOME MEASURES: Scores for the eight dimensions of the SF-36. STATISTICS: The sensitivity of the SF-36 was tested by hypothesising that the scores of those in the bottom quartile of the SF-36 scores in class V could be improved to the level of the scores from the bottom quartile of SF-36 scores in class I using the effect size statistic. RESULTS: SF-36 scores for the population at the 25th, 50th, and 75th centiles were provided. Those who reported worse health on each dimension of the SF-36 (ie in the lowest 25% of scores) differ dramatically between social class I and V. Large effect sizes were gained on all but one dimension of the SF-36 when the health of those in the bottom quartile of the SF-36 scores in class V were hypothesised to have improved to the level of the scores from the bottom quartile of SF-36 scores in class I. CONCLUSIONS: Analysis of SF-36 data at a population level is inappropriate; subgroup analysis is more appropriate. The data suggest that if it were possible to improve the functioning and wellbeing of those in worst health in class V to those reporting the worst health in class I the improvement would be dramatic. Furthermore, differences between the classes detected by the SF-36 are substantial and more dramatic than might previously have been imagined.

Adolescent↗
PubMed2001

Consistency of atypical antipsychotic superiority to placebo in recent clinical trials.

BACKGROUND: The use of control placebos in clinical trials of new antipsychotic medications is increasingly under examination. The active controlled equivalence study could offer a potential alternative design. First, however, it must be clear that any proposed standard control agent has been consistently superior to placebo in previous studies. METHODS: Through a Freedom of Information Act request, we identified nine placebo-controlled trials of risperidone, olanzapine, or quetiapine. RESULTS: Meta-analysis indicated that the pooled estimate of the true population effect size +/- SE was 0.46 +/- 0.06 for categorical response rates and >0.53 +/- 0.07 for the continuous Brief Psychiatric Rating Scale change score outcome measure. If the desired detectable effect size is set very conservatively at a 95% confidence lower bound for the estimate of true effect size, statistical power for random samples of 80 per group drawn from a population of subjects similar to that of the nine meta-analyzed studies is.67 for categorical response rates and >.82 for the continuous measure, based on one-sided alpha =.05. CONCLUSIONS: These data suggest substantial confidence that a therapeutic dose of an atypical antipsychotic will be statistically superior to placebo in an adequately sized randomized trial, when reporting a continuous measure as the principal outcome.

Antipsychotic Agents↗
PubMed2001

Characterization of idiopathic scoliosis in a clinically well-defined population.

Idiopathic scoliosis is a highly prevalent disorder, familial in nature, with marked clinical variability. The purpose of this study was to characterize idiopathic scoliosis in a large series of families to be used for a genome-wide search. One hundred thirty-one multigenerational families (892 individuals) with at least two affected individuals were studied. Data obtained included curve pattern, treatment, and back pain. Maximum curvature as a continuous variable was evaluated using t tests for dichotomous characteristics and linear correlation for continuous variables. An analysis of familial loading was done. Four hundred forty-four individuals were classified as affected (82% female; 18% male). The right thoracic and left lumbar curves had the highest mean curvature (49 degrees). Mean curve size was greater in individuals with back pain. Back pain was most prevalent in the right thoracic and left lumbar curve pattern. The Pearson correlation coefficient between the number of affected family members and the maximum degree of curvature was 0.16, suggesting that the greater the lateral curvature, the higher the proportion of family members affected with scoliosis. The sample population is consistent with those of previous studies in relation to gender and curve size. Statistically, the familial nature of this disorder is supported.

Biomechanical Phenomena↗
PubMed2001

Review of assumptions and problems in the appropriate conceptualization of effect size.

Estimation of the effect size parameter, D, the standardized difference between population means, is sensitive to heterogeneity of variance (heteroscedasticity), which seems to abound in psychological data. Pooling s2s assumes homoscedasticity, as do methods for constructing a confidence interval for D, estimating D from t or analysis of variance results, formulas that adjust estimates for inflation by main effects or covariates, and the Q statistic. The common language effect size statistic as an estimate of Pr(X1 > X2), the probability that a randomly sampled member of Population 1 will outscore a randomly sampled member of Population 2, also assumes normality and homoscedasticity. Various proposed solutions are reviewed, including measures that do not make these assumptions, such as the probability of superiority estimate of Pr(X1 > X2). Ways to reconceptualize effect size when treatments may affect moments such as the variance are also discussed.

Analysis of Variance↗
PubMed1999

Psychosocial outcome assessments for use in cardiac rehabilitation service evaluation: a 10-year systematic review.

A variety of measures are currently used to assess psychosocial outcome (quality of life) in cardiac rehabilitation programmes. However, there is no consensus on the most appropriate instruments to use. Instruments that are not sufficiently responsive to change in cardiac populations are unsuitable as audit tools as they underrepresent the benefits of programme attendance. To identify the most responsive instruments in cardiac rehabilitation populations a systematic overview of studies for the 10-year period 1986-1995 was conducted. The following databases were searched: Medline, Psychlit, Cinahl and Sociofile and 32 relevant studies were identified. The effect size statistic (a comparison of the magnitude of change to the variability in baseline scores) was used to determine those instruments most responsive to change. The following instruments were identified as being responsive in more than one study: Beck Depression Inventory, Global Mood Scale, Health Complaints Checklist, Heart Patients Psychological Questionnaire and Speilberger State Anxiety Inventory. There is little consensus on psychosocial evaluation instrument use in the cardiac rehabilitation literature. A number of measures show significant potential for routine outcome assessment. Formal assessment of these instruments is recommended to inform final recommendations about instrument selection for audit and evaluation purposes in cardiac rehabilitation.

Cardiac Rehabilitation↗
PubMed1999

Sample size calculations in studies using the EuroQol 5D.

Health-related quality of life (HRQoL) instruments are increasingly used as outcome variables in clinical trials, leading to a requirement for sample size calculations based on these variables. This paper aims to provide a guide to sample size calculations for use with the EuroQol-5D. The paper focuses on sample sizes required for comparative studies, and uses scores from two reference groups of general population and critically ill patients to determine sample sizes using the three parts of the EQ-5D (descriptive system, visual analogue scale (VAS), and EQ-5D index). The effect on sample sizes of different methods of categorising the three variables are compared, and comparisons are also made between sample sizes using parametric and non-parametric methods. Sample sizes required when the EQ-5D descriptive system is used as a binary variable (problems/no problems) are higher than or equal to those required when each dimension is categorised in three levels of severity (no problems, moderate problems, extreme problems). The use of three categories is appropriate in ill populations, though in more healthy populations two categories should be used. Due to the slight skewness of VAS data, and the equality of results using parametric and non-parametric methods, sample size calculations using the VAS should be based on a parametric approach. Sample sizes were considerably higher for the EQ-5D index when predefined intervals, as opposed to a score frequency based categorisation, were used with the general population reference group. Using the EQ-5D index in ill populations, it is recommended that sample size calculations are based on parametric methods, whilst in healthier populations non-parametric methods should be used.

Critical Illness↗
PubMed1999

Increasing physicians' awareness of the impact of statistics on research outcomes: comparative power of the t-test and and Wilcoxon Rank-Sum test in small samples applied research.

To effectively evaluate medical literature, practicing physicians and medical researchers must understand the impact of statistical tests on research outcomes. Applying inefficient statistics not only increases the need for resources, but more importantly increases the probability of committing a Type I or Type II error. The t-test is one of the most prevalent tests used in the medical field and is the uniformally most powerful unbiased test (UMPU) under normal curve theory. But does it maintain its UMPU properties when assumptions of normality are violated? A Monte Carlo investigation evaluates the comparative power of the independent samples t-test and its nonparametric counterpart, the Wilcoxon Rank-Sum (WRS) test, to violations from population normality, using three commonly occurring distributions and small sample sizes. The t-test was more powerful under relatively symmetric distributions, although the magnitude of the differences was moderate. Under distributions with extreme skews, the WRS held large power advantages. When distributions consist of heavier tails or extreme skews, the WRS should be the test of choice. In turn, when population characteristics are unknown, the WRS is recommended, based on the magnitude of these power differences in extreme skews, and the modest variation in symmetric distributions.

Epidemiologic Studies↗
PubMed2001

Treadmill training of infants with Down syndrome: evidence-based developmental outcomes.

OBJECTIVE: On average, infants with Down syndrome (DS) learn to walk about 1 year later than nondisabled (ND) infants. The purpose of this study was to determine if practice stepping on a motorized treadmill could help reduce the delay in walking onset normally experienced by these infants. METHODS: Thirty families of infants with DS were randomly assigned to the intervention or control group. All infants were karyotyped trisomy 21 and began participation in the study when they could sit alone for 30 seconds (Bayley Scales of Infant Development, Second Edition 1993, item 34). Infants received traditional physical therapy at least every other week. In addition, intervention infants received practice stepping on a small, motorized treadmill, 5 days per week, for 8 minutes a day, in their own homes. Parents were trained to support their infants on these specially engineered miniature treadmills. Every 2 weeks research staff went into the homes and tested infants' overall motor progress by administering the Bayley Scales of Infant Development, Second Edition, monitored growth status via a battery of 11 anthropometric measures, and checked parents' compliance with physical therapy and treadmill intervention. The primary measures of the intervention's effectiveness were comparisons between the groups on the length of time elapsed between sitting for 30 seconds (entry into the study) and 1) raising self to stand; 2) walking with help; and 3) walking independently. RESULTS: The experimental group learned to walk with help and to walk independently significantly faster (73.8 days and 101 days, respectively) than the control group, both of which also produced large effect size statistics for the group differences. The groups were not statistically different for rate of learning to raise self to stand but there was a moderate effect size statistic suggesting that the groups were meaningfully different in favor of the experimental group. CONCLUSIONS: These results provide evidence that, with training and support, parents can use these treadmills in their homes to help their infants with DS learn to walk earlier than they normally would. Current research is aimed at 1) improving the protocol to maximize outcome; 2) determining the impact of treadmill practice on walking gait patterns; 3) testing the application to other populations with a history of delays in walking; and 4) determining the long-term benefits that may accrue from this form of activity. motor development, Down syndrome, early intervention, walking.

Age Factors↗
PubMed1997

Pharmacokinetic modelling of intravenous tobramycin in adolescent and adult patients with cystic fibrosis using the nonparametric expectation maximization (NPEM) algorithm.

The availability of personal computer programs for individualizing drug dosage regimens has stimulated the interest in modelling population pharmacokinetics. Data from 82 adolescent and adult patients with cystic fibrosis (CF) who were treated with intravenous tobramycin because of an exacerbation of their pulmonary infection were analysed with a non-parametric expectation maximization (NPEM) algorithm. This algorithm estimates the entire discrete joint probability density of the pharmacokinetic parameters. It also provides traditional parametric statistics such as the means, standard deviation, median, covariances and correlations among the various parameters. It also provides graphic-2- and 3-dimensional representations of the marginal densities of the parameters investigated. Several models for intravenous tobramycin in adolescent and adult patients with CF were compared. Covariates were total body weight (for the volume of distribution) and creatinine clearance (for the total body clearance and elimination rate). Because of lack of data on patients with poor renal function, restricted models with non-renal clearance and the non-renal elimination rate constant fixed at literature values of 0.15 L/h and 0.01 h-1 were also included. In this population, intravenous tobramycin could be best described by median (+/-dispersion factor) volume of distribution per unit of total body weight of 0.28 +/- 0.05 L/kg, elimination rate constant of 0.25 +/- 0.10 h-1 and elimination rate constant per unit of creatinine clearance of 0.0008 +/- 0.0009 h-1/(ml/min/1.73 m2). Analysis of populations of increasing size showed that using a restricted model with a non-renal elimination rate constant fixed at 0.01 h-1, a model based on a population of only 10 to 20 patients, contained parameter values similar to those of the entire population and, using the full model, a larger population (at least 40 patients) was needed.

Adolescent↗
PubMedDate not supplied

Pleural malignant mesothelioma and environmental asbestos exposure in Casale Monferrato, Piedmont. Preliminary analysis of a case-control study.

A case-control study on pleural malignant mesothelioma (MM) was conducted in Casale Monferrato, where the largest Italian asbestos cement (AC) factory had been operating from 1907 to 1985. In a previous study we observed a five to seven-fold increase in the incidence of MM among people living in that city and never employed in the factory mentioned. The present study includes cases of MM with histological diagnosis over the period 1.1.1987-30.6.1993 among residents in the Local Health Unit (LHU) of Casale Monferrato. Population controls were randomly extracted from the list of the residents in the LHU, matched to cases on sex, date of birth, vital status and date of death. Cases and controls (or their closest relative) were interviewed with a standardised questionnaire focusing on asbestos exposure in the (life-long) residential and occupational histories and in leisure time activities as well as on occupational asbestos exposure of relatives and cohabitants, smoking and chest or occupational diseases. The interview was blind in respect to case or control status. For the analyses the addresses were coded on map grids with a 500 m. mesh size. Statistical analyses were conducted with conditional logistic regression in order to keep the matching between cases and controls. Eighty-eight cases and 244 controls were interviewed (95.6% of cases and 80.1% of controls): 26 and 11 respectively reported an activity in the AC industry. Seven cases and 7 controls were also exposed because of parental occupation. The main analyses are based on the conditional regression model including both occupational and residential exposure. The different modes of exposure are included on an ordinal scale: each subject is classified according to their highest level. Domestic exposure is included as an independent factor. Odds Ratios (OR) are estimated with reference to subjects without either occupational or residential exposure. The OR is 39.3 among subjects reporting occupational exposure, 11.9 among those never engaged in the AC industry but living within 1000 m. of the factory. A statistically significant risk is also observed for persons at some time living in the other areas of Casale Monferrato.

Aged↗
PubMed1977

Quick test for comparing two populations with bivariate data.

A simple nonparametric test is given for testing the equality of two populations when the observations (X, Y) are bivariate and the alternative of interest is that the conditional c.d.f. of Y given X for one population dominates that for the other for every value of X. The procedure consists of fitting a curve through the combined set of data points and considering and conditional distribution of the number of points above the curve from one population, given certain information (depending on the design of the experiment), on the combined set of data. When used to compare two bivariate distributions, the test reduces to Fisher's exact test for 2 X 2 tables.

Animals↗
PubMed2000

Sample size in guidelines trials.

In clinical trials, the statistical concepts of significance and power are used in the determination of sample size for trials. The trialist must provide an estimate of standard deviation and a hypothetical population difference to be detected. This must be modified to deal with the designs encountered in guideline research. These are cluster randomized trials, because the patients of a single doctor or practice form a cluster. The trialist must be able to provide information about the effects of clustering, in the form of an intraclass correlation coefficient.

Family Practice↗