On the use of partial area under the ROC curve for comparison of two diagnostic tests

Evaluation of diagnostic performance is typically based on the receiver operating characteristic (ROC) curve and the area under the curve (AUC) as its summary index. The partial area under the curve (pAUC) is an alternative index focusing on the range of practical/clinical relevance. One of the problems preventing more frequent use of the pAUC is the perceived loss of efficiency in cases of noncrossing ROC curves. In this paper, we investigated statistical properties of comparisons of two correlated pAUCs. We demonstrated that outside of the classic model there are practically reasonable ROC types for which comparisons of noncrossing concave curves would be more powerful when based on a part of the curve rather than the entire curve. We argue that this phenomenon stems in part from the exclusion of noninformative parts of the ROC curves that resemble straight‐lines. We conducted extensive simulation studies in families of binormal, straight‐line, and bigamma ROC curves. We demonstrated that comparison of pAUCs is statistically more powerful than comparison of full AUCs when ROC curves are close to a “straight line”. For less flat binormal ROC curves an increase in the integration range often leads to a disproportional increase in pAUCs’ difference, thereby contributing to an increase in statistical power. Thus, efficiency of differences in pAUCs of noncrossing ROC curves depends on the shape of the curves, and for families of ROC curves that are nearly straight‐line shaped, such as bigamma ROC curves, there are multiple practical scenarios in which comparisons of pAUCs are preferable.     

Geochemical baseline determination and pollution assessment of heavy metals in urban soils of Karachi,Pakistan

Karachi is one of the most populated urban agglomerations in the world. No categorical study has yet discussed the geochemical baseline concentrations of metals in the urban soil of Karachi. The main objectives of this study were to establish geochemical baseline values and to assess the pollution status of different heavy metals. Geochemical baseline concentrations of heavy metals were estimated using the cumulative frequency distribution (CDF) curves. The estimated baseline concentrations of Pb, Cr, Cu, Zn and Fe were 56.23, 12.9, 36.31, 123.03 and 11,776 mg kg⁻¹, respectively. The pollution status of heavy metals in urban soils was evaluated using different quantitative indices (enrichment factor–EF, Geo-accumulation Index–I_geo, and pollution index–PI). Enrichments factors of the selected heavy metals determined by using Fe as a normalizer showed that metal contamination was the product of anthropogenic activities. The urban soils of Karachi were found to have a moderate to moderately severe enrichment with Pb, whereas Cr and Cu has moderate and Zn has minor enrichment. I_geo results indicated moderate soil contamination by Pb at some of the sampling locations. PI for Pb, Cr, Cu and Zn was found in the range of 0.04–3.42, 0.19–1.55, 0.27–2.45 and 0.32–1.57, respectively. Large variations in PI values of Pb revealed that soil in those areas of the city which are influenced by intensive anthropogenic activities have exceptionally high concentrations of Pb. The findings of this study would contribute to the environmental database of the soil of the region and would also facilitate both at the local and the international scales, in a more accurate global environmental monitoring, which will eventually facilitate the development of management and remediation strategies for heavy metal contaminated urban soil.     

A Growth Curve Analysis for Bulls Tested at Station

Data on 2712 bulls tested at station were analysed to study the effect of certain external variables on growth traits of bulls. Most of the animals were Ayrshires (2136). Otherwise Finncattle bulls and Frisian bulls were involved. The testing covers the interval 60–365 days of age, although in part of the data the period is 30–365. Bulls were weighted every 30th day (between 1965 and 1970), or at the ages of 60 and 180 days, and thereafter every 30 days up to the age of 365 days (between 1971 and 1977). Also birth weight was available for 1250 calves. Feeding and general treatment of bulls at station was as uniform as possible for all animals. Conseqúently it can be assumed that effects of non-genetic factors on the growth traits of bulls are minimized. One of the objectives of this study was to compare the growth curves for the three breeds. In our data measurements at certain time-points have dropped out during the course of data collection. Therefore we study the influence of deleting measurements. We also consider the problem of influential measurements at both the design level and the inference level. Several types of growth curves are fitted to the data in order to find the most appropriate model.     

Mesocyclops longisetus effects on survivorship of Aedes aegypti immature stages in car tyres

Abstract .The effect of the introduction of the entomophagous copepod Mesocyclops longisetus (Acuacultura F.C.B. strain) on the survival of Aedes aegypti immature stages in car tyres was evaluated under semi-natural conditions in the municipality of Merida, Yucatan, Mexico. Life tables were constructed for the immature stages of the mosquito in the presence and absence of M. longisetus , and the survival data were compared using log–linear models. The data set was adjusted using the GLIM statistical package and the quality of adjustment was evaluated with a chi-squared test . Survivorship curves were constructed for each treatment.
In the absence of M. longisetus , the survivorship of Ae. aegypti immature stages averaged 9%. The highest mortality rate was observed during the fourth larval instar (54%) and the resulting survival pattern corresponded to a type II survivorship curve. The mortality rate of Ae. aegypti first-instar larvae (fifty per tyre) increased more than 200-fold in the presence of M. longisetus (twenty per tyre) and the highest mortality was during the first two larval instars, where it reached 98.9%, with a resulting survivorship of 0.2%. Overall mortality was sixfold greater in the presence of the copepod than in its absence. The survival pattern of immature stages of Ae. aegypti in the presence of the copepod corresponded to a type III survivorship curve. As M. longisetus was so effective against Ae. aegypti immature stages in tyres under semi-natural conditions, its long-term effectiveness should be evaluated under socially and ecologically realistic field conditions in Mexico.     

Thermal melting and circular dichroism of DNA complexes with (Lys-Ala-Ala)10 and (Lys-Ala-Ala)n: effect of polypeptide chain length

DNA complexes with polypeptides (Lys-Ala-Ala)₁)] and (Lys-Ala-Ala)₃₄ have been studied using the methods of thermal melting and circular dichroism. Derivative melting curves of (Lys-Ala-Ala)₁₀ DNA differed substantially from those of (Lys-Ala-Ala)₃₄ prepared either by salt gradient dialysis or by direct mixing. Melting curves of the former complex were unimodal or bimodal with T_m increasing continuously withn input lysin-to-DNA phosphate ratio (r); those of the latter complex consisted of three separate transitions with T_m values almost independent of r. Complete reversibility of binding in the (Lys-Ala-Ala)₁₀-DNA system but a slow redistribution of (Lys-Ala-Ala)₃₄ on DNA at low temperature were found in the redistribution experiments Much faster redistribution from denatured to native DNA occurs at the temperature of melting, contributing to the unusual trimodal melting pattern. Circular dichroism curves are very similar for both complexes and indicate little change of DNA conformation upon polypeptide binding.     

The genetic structure of a tribal population,the Yanomama Indians. XII. Biodemographic studies

The Yanomama Indians of Southern Vanezuela and Northern Brazil are one of the largest, relatively unacculturated tribes of the tropical rain forest. Over a period of eight years data have been collected from a considerable portion of their territory on estimated age, sex ratio, fertility rates (as determined by physical examination and urine tests), and infant death rates. Although it has been impossible to collect direct data on infanticide, this subject can be approached indirectly through distortions of the sex ratio and anecdotal information. Some historical data are also available as a basis for estimating tribal expansion in the past 100 years. With this material it has been possible to construct Life Tables for the Yanomama, and to explore the results of various perturbations of the input parameters. Data are also presented on patterns of mating and reproduction: number of spouses, mean and variance in number of surviving children, frequency of “extra-marital conceptions” based on the results of extensive blood group typings, and consanguinity rates as determined by observation and computer simulation. Although we do not present the Yanomama as typical, these data are seen as providing a basis for more realistic population models than have existed in the past. In addition, the data provide a basis for relatively precise estimates of such demographic measures as Fisher's Reproductive Value, Crow's Index of Total Selection, and Weiss' Index of Growth Regulation.     

Estimation of Individual Growth Curves by Empirically Weighted Least Squares

The simultaneous estimation of individual growth curves and a mean growth curve is accomplished by weighted least squares. A polynomial curve is fitted for each individual and the polynomial parameters are linear functions of parameters corresponding to covariates. A simple, computationally efficient variance-covariance estimator is derived. The resultant estimate is used in the weighted least squares estimation. The results are compared to empirical Bayes estimation.     

A method to measure predictive ability of an injury risk curve using an observation-adjusted area under the receiver operating characteristic curve

Area under the receiver operating characteristic curve (AROC) is commonly used to choose a biomechanical metric from which to construct an injury risk curve (IRC). However, AROC may not handle censored datasets adequately. Survival analysis creates robust estimates of IRCs which accommodate censored data. We present an observation-adjusted ROC (oaROC) which uses the survival-based IRC to estimate the AROC. We verified and evaluated this method using simulated datasets of different censoring statuses and sample sizes. For a dataset with 1000 left and right censored observations, the median AROC closely approached the oaROC_True, or the oaROC calculated using an assumed “true” IRC, differing by a fraction of a percent, 0.1%. Using simulated datasets with various censoring, we found that oaROC converged onto oaROC_True in all cases. For datasets with right and non-censored observations, AROC did not converge onto oaROC_True. oaROC for datasets with only non-censored observations converged the fastest, and for a dataset with 10 observations, the median oaROC differed from oaROC_True by 2.74% while the corresponding median AROC with left and right censored data differed from oaROC_True by 9.74%. We also calculated the AROC and oaROC for a published side impact dataset, and differences between the two methods ranged between −24.08% and 24.55% depending on metric. Overall, when compared with AROC, we found oaROC performs equivalently for doubly censored data, better for non-censored data, and can accommodate more types of data than AROC. While more validation is needed, the results indicate that oaROC is a viable alternative which can be incorporated into the metric selection process for IRCs.     

Evaluating the performance of sampling plans for phycotoxins in shellfish: Improvement of an existing method

According to the EU Regulation 854/2004, sampling plans must be set up to monitor production areas for the level of okadaic acid (OA) equivalents in live mussel. The level of these toxins, which are produced by harmful algal blooms, must not exceed 160 μg/kg of raw meat (Regulation 853/2004/EC). A sampling plan assessment consists in obtaining an OC (Operating Characteristic) curve showing both consumer and producer risks. The first risk is the risk of opening a shellfish area for harvest while the contamination level is above the threshold; whereas the second risk is the risk of closing a shellfish area having a contamination level under the threshold.For sampling plan validation purposes, a classical mathematical method was improved for the prediction of variance as function of the mean contamination level thanks to prior knowledge of the theoretical distribution fitting the observed OA levels among individual mussels. Indeed, knowing that, thanks to a regression analysis of literature data, for the lognormal distribution the scale parameter was observed to be directly proportional to the location parameter, the regression bias could be lowered. Literature data from Norway and Sweden showed different levels of variability between contamination events and depuration. However, the highest variability level was chosen to propose a best fit sampling plan in order to have a better approach of reality. It consisted of taking two samples of 50 mussels (Mytilus sp.) for this geographic location (Norway and Sweden).