Sample sizes of studies on diagnostic accuracy: literature survey

OBJECTIVES: To determine sample sizes in studies on diagnostic accuracy and the proportion of studies that report calculations of sample size. DESIGN: Literature survey. DATA SOURCES: All issues of eight leading journals published in 2002. METHODS: Sample sizes, number of subgroup analyses, and how often studies reported calculations of sample size were extracted. RESULTS: 43 of 8999 articles were non-screening studies on diagnostic accuracy. The median sample size was 118 (interquartile range 71-350) and the median prevalence of the target condition was 43% (27-61%). The median number of patients with the target condition--needed to calculate a test's sensitivity--was 49 (28-91). The median number of patients without the target condition--needed to determine a test's specificity--was 76 (27-209). Two of the 43 studies (5%) reported a priori calculations of sample size. Twenty articles (47%) reported results for patient subgroups. The number of subgroups ranged from two to 19 (median four). No studies reported that sample size was calculated on the basis of preplanned analyses of subgroups. CONCLUSION: Few studies on diagnostic accuracy report considerations of sample size. The number of participants in most studies on diagnostic accuracy is probably too small to analyse variability of measures of accuracy across patient subgroups.

Long Versus Short Feeding Period for Steer Calves of Three Frame Sizes Fed High Energy Finishing Diets

An experiment was conducted using Angus cross steer calves of three frame sizes (small, medium, and large) to compare performance of two different grow/finish feeding programs. Half of the cattle in each frame size group were fed a high energy ration through the growing period, similar to calves going directly into the feedlot. The other half was fed a low energy ration, similar to a backgrounding diet, for a period prior to the finishing phase. All cattle were fed a high energy ration through the finishing period. The data showed the cattle fed the low energy growing diet experienced some compensatory gains as shown by ultrasound backfat and average daily gains coupled with intakes greater than the increases seen in the high energy treatment. Carcass data and overall performance data showed no ill effects due to the low energy growing ration.

Are sample sizes clear and justified in RCTs published in dental journals?

Sample size calculations are advocated by the CONSORT group to justify sample sizes in randomized controlled trials (RCTs). The aim of this study was primarily to evaluate the reporting of sample size calculations, to establish the accuracy of these calculations in dental RCTs and to explore potential predictors associated with adequate reporting. Electronic searching was undertaken in eight leading specific and general dental journals. Replication of sample size calculations was undertaken where possible. Assumed variances or odds for control and intervention groups were also compared against those observed. The relationship between parameters including journal type, number of authors, trial design, involvement of methodologist, single-/multi-center study and region and year of publication, and the accuracy of sample size reporting was assessed using univariable and multivariable logistic regression. Of 413 RCTs identified, sufficient information to allow replication of sample size calculations was provided in only 121 studies (29.3%). Recalculations demonstrated an overall median overestimation of sample size of 15.2% after provisions for losses to follow-up. There was evidence that journal, methodologist involvement (OR = 1.97, CI: 1.10, 3.53), multi-center settings (OR = 1.86, CI: 1.01, 3.43) and time since publication (OR = 1.24, CI: 1.12, 1.38) were significant predictors of adequate description of sample size assumptions. Among journals JCP had the highest odds of adequately reporting sufficient data to permit sample size recalculation, followed by AJODO and JDR, with 61% (OR = 0.39, CI: 0.19, 0.80) and 66% (OR = 0.34, CI: 0.15, 0.75) lower odds, respectively. Both assumed variances and odds were found to underestimate the observed values. Presentation of sample size calculations in the dental literature is suboptimal; incorrect assumptions may have a bearing on the power of RCTs.

Effect sizes and standardization in neighbourhood models of forest stands: potential biases and misinterpretations

Effects of conspecific neighbours on survival and growth of trees have been found to be related to species abundance. Both positive and negative relationships may explain observed abundance patterns. Surprisingly, it is rarely tested whether such relationships could be biased or even spurious due to transforming neighbourhood variables or influences of spatial aggregation, distance decay of neighbour effects and standardization of effect sizes. To investigate potential biases, communities of 20 identical species were simulated with log-series abundances but without species-specific interactions. No relationship of conspecific neighbour effects on survival or growth with species abundance was expected. Survival and growth of individuals was simulated in random and aggregated spatial patterns using no, linear, or squared distance decay of neighbour effects. Regression coefficients of statistical neighbourhood models were unbiased and unrelated to species abundance. However, variation in the number of conspecific neighbours was positively or negatively related to species abundance depending on transformations of neighbourhood variables, spatial pattern and distance decay. Consequently, effect sizes and standardized regression coefficients, often used in model fitting across large numbers of species, were also positively or negatively related to species abundance depending on transformation of neighbourhood variables, spatial pattern and distance decay. Tests using randomized tree positions and identities provide the best benchmarks by which to critically evaluate relationships of effect sizes or standardized regression coefficients with tree species abundance. This will better guard against potential misinterpretations.

Multivariate methods for correlated effects sizes

Current statistical methods for estimation of parametric effect sizes from a series of experiments are generally restricted to univariate comparisons of standardized mean differences between two treatments. Multivariate methods are presented for the case in which effect size is a vector of standardized multivariate mean differences and the number of treatment groups is two or more. The proposed methods employ a vector of independent sample means for each response variable that leads to a covariance structure which depends only on correlations among the $p$ responses on each subject. Using weighted least squares theory and the assumption that the observations are from normally distributed populations, multivariate hypotheses analogous to common hypotheses used for testing effect sizes were formulated and tested for treatment effects which are correlated through a common control group, through multiple response variables observed on each subject, or both conditions.^ The asymptotic multivariate distribution for correlated effect sizes is obtained by extending univariate methods for estimating effect sizes which are correlated through common control groups. The joint distribution of vectors of effect sizes (from $p$ responses on each subject) from one treatment and one control group and from several treatment groups sharing a common control group are derived. Methods are given for estimation of linear combinations of effect sizes when certain homogeneity conditions are met, and for estimation of vectors of effect sizes and confidence intervals from $p$ responses on each subject. Computational illustrations are provided using data from studies of effects of electric field exposure on small laboratory animals. ^

Robust effect sizes and their confidence intervals for group difference between trajectories in hierarchical linear growth model

Hierarchical linear growth model (HLGM), as a flexible and powerful analytic method, has played an increased important role in psychology, public health and medical sciences in recent decades. Mostly, researchers who conduct HLGM are interested in the treatment effect on individual trajectories, which can be indicated by the cross-level interaction effects. However, the statistical hypothesis test for the effect of cross-level interaction in HLGM only show us whether there is a significant group difference in the average rate of change, rate of acceleration or higher polynomial effect; it fails to convey information about the magnitude of the difference between the group trajectories at specific time point. Thus, reporting and interpreting effect sizes have been increased emphases in HLGM in recent years, due to the limitations and increased criticisms for statistical hypothesis testing. However, most researchers fail to report these model-implied effect sizes for group trajectories comparison and their corresponding confidence intervals in HLGM analysis, since lack of appropriate and standard functions to estimate effect sizes associated with the model-implied difference between grouping trajectories in HLGM, and also lack of computing packages in the popular statistical software to automatically calculate them. ^ The present project is the first to establish the appropriate computing functions to assess the standard difference between grouping trajectories in HLGM. We proposed the two functions to estimate effect sizes on model-based grouping trajectories difference at specific time, we also suggested the robust effect sizes to reduce the bias of estimated effect sizes. Then, we applied the proposed functions to estimate the population effect sizes (d ) and robust effect sizes (du) on the cross-level interaction in HLGM by using the three simulated datasets, and also we compared the three methods of constructing confidence intervals around d and du recommended the best one for application. At the end, we constructed 95% confidence intervals with the suitable method for the effect sizes what we obtained with the three simulated datasets. ^ The effect sizes between grouping trajectories for the three simulated longitudinal datasets indicated that even though the statistical hypothesis test shows no significant difference between grouping trajectories, effect sizes between these grouping trajectories can still be large at some time points. Therefore, effect sizes between grouping trajectories in HLGM analysis provide us additional and meaningful information to assess group effect on individual trajectories. In addition, we also compared the three methods to construct 95% confident intervals around corresponding effect sizes in this project, which handled with the uncertainty of effect sizes to population parameter. We suggested the noncentral t-distribution based method when the assumptions held, and the bootstrap bias-corrected and accelerated method when the assumptions are not met.^

Magnetic properties, grain sizes, XRF Scanner Data of sediment core GeoB9307-3

Geochemical and mineralogical proxies for paleoenvironmental conditions have the underlying assumption that climate variations have an impact on terrestrial weathering conditions. Varying properties of terrigenous sediments deposited at sea are therefore often interpreted in terms of paleoenvironmental change. Also in gravity core GeoB9307-3 (18° 33.99' S, 37° 22.89' E), located off the Zambezi River, environmental changes during Heinrich Stadial 1 (HS 1) and the Younger Dryas (YD) are accompanied by changing properties of the terrigenous sediment fraction. Our study focuses on the relationship of variability in the hydrological system and changes in the magnetic properties, major element geochemistry and granulometry of the sediments. We propose that changes in bulk sedimentary properties concur with environmental change, although not as a direct response of climate driven pedogenic processes. Spatial varying rainfall intensities on a sub-basin scale modify sediment export from different parts of the Zambezi River basin. During humid phases, such as HS 1 and the YD, sediment was mainly exported from the coastal areas, while during more arid phases sediments mirror the hinterland soil and lithological properties and are likely derived from the northern Shire sub-basin. We propose that a de-coupling of sedimentological and organic signals with variable discharge and erosional activity can occur.

Tab. 2: Grain-sizes of cobble on the surface of sanderwurzel

yResults of 13 field investigations between 1966 and 1990 of the southwestern to eastern margin of Kötlujökull and its proglacial area are summarized with respect to sandar and their formation. Generally, the results are based on sedimentological examinations in the field and laboratory, on analyses of aerial photographs, and investigations of the glacier slope. The methods permitted a more detailed reconstruction of sandar evolution in the proglacial area of Kötlujökull since 1945, of tendencies in development and of single data going back until the last decades of the 19th century. Accordingly, there existed special periods of "flachsander"-formations with raised coarsegrained "sanderwurzels" resultant from the outbreak of subglacial meltwater tunneloutlets and other periods with "hochsander-"formations by supraglacial drainage. At present the belts of hochsanders in front of the glacier come up to more than 4 m in thickness and 1000 m in width, therefore containing perhaps more sediment direct in front of Kötlujökull than the old belts of flachsanderwurzels. In one case the explosion-like subglacial meltwater outburst combined with the genesis of a sanderwurzel could be observed for a time and is thoroughly discussed. The event is referred to the outburst of a sub- to inglacial meltwater body being under extreme hydrostatic press ures which is combined with the genesis of a new subglacial tunneloutlet as a new flachsander. Often these outbursts led to the destruction of a morainic belt more than 1000 m in width. Presumably the whole event was finished in not more than a few days. In addition to a characteristic pear-shaped form and water-moved stones up to diameters of 1 m the wurzels possess a single "main-channel" with rectangular cross-sections as far as 4 m deep and 50 m wide just as small flat channels resembling fish bones in connection with the main channel. Presumably, they have been active only in the last stage of wurzel formation. With regard to the subglacial tunnel gates long-living L-meltwater outlets are distinguished from short-living K-meltwater outlets. These are always combined with a raised coarse-grained sanderwurzel, but its meltwater discharge is generally decreasing and ceases after some years, whereas the discharge of L-meltwater outlets continues unchanged for long times (except seasonal differences). The material of flachsanders is preponderantly composed of mugearitic and andesitic cobble extending at least for some kilometres from the glacier margin, whereas the hochsanders correspond to medium to coarse sands without clay and without alternations into the direction of flow. The hochsander fans are covered with small braidet channels. Their sedimentary structures are determined by the short time changing of supraglacial meltwater discharge and the upper flow regime combined with the development of antidunes, which rule the channel-flows during the main activity periods in summer. Unlike the subglacial drainage the supraglacial drainage led to only weak effects of erosion on the glacier foreland. So the hochsanders refilled depressions of morainic areas or grew up on older flachsanderwurzels. Whereas all large flachsanders developed in front of approximate stationary glacier margins, the evolution of coherent belts of hochsanders were combined with progressive glacier fronts. On the other hand, there was obviously no evolution at all of large sandar in front of back-melting margins of Kötlujökull. Based on examinations of the glacier surface and on analyses of aerial photographs the different types of sandar are referred to different structures of the glacier snout. Finally chances of surviving of sandar in the proglacial area of Kötlujökull are shortly discussed just as the possibility of an application of the Islandic research results on Pleistocene sandar in northern Germany.

Magnetic properties, grain sizes and minerals at DSDP Site 83-504B

Twenty-seven samples from the Leg 83 section of Hole 504B have been investigated using magnetic, optical, and electron optical methods. The primary magnetic mineral to crystallize was titanomagnetite of approximate composition Fe2.4Ti0.6O4 (TM60), but none survives, nor is there evidence of titanomaghemite produced by oxidation of TM60. The average measured magnetic properties can be interpreted in terms of magnetite, Fe3O4, having average grain size of <1 µm and present in average volume concentration of - 0.5%. The intensity of the natural remanent magnetization (NRM) of the rocks could also be accounted for as being a thermoremanence carried by this mineral. Although the heterogeneity of the titanomagnetite grains could be detected optically, the texture of the intergrown phases is poorly developed. In some samples from the massive units of the lower part of the section, trellis patterns were visible. The Fe3O4 present in the intergrowths is too intimately mixed with the other intergrown phases to be revealed by electron microprobe analysis that simply returns the bulk composition of the intergrowth (oxidized TM60). The path by which the mineral assemblage evolved from TM60 to an Fe304-containing intergrowth, under the temperature and pressure conditions obtaining in the Leg 83 section, makes interesting speculation. Deuteric oxidation, maghemitization/inversion, or some hypothetical low-temperature/high-pressure oxidation by a leaching-of-iron process may all play roles.