Varying coefficient model with unknown within-subject covariance for analysis of tumor growth curves

SUMMARY: In this article we develop a nonparametric estimation procedure for the varying coefficient model when the within-subject covariance is unknown. Extending the idea of iterative reweighted least squares to the functional setting, we iterate between estimating the coefficients conditional on the covariance and estimating the functional covariance conditional on the coefficients. Smoothing splines for correlated errors are used to estimate the functional coefficients with smoothing parameters selected via the generalized maximum likelihood. The covariance is nonparametrically estimated using a penalized estimator with smoothing parameters chosen via a Kullback-Leibler criterion. Empirical properties of the proposed method are demonstrated in simulations and the method is applied to the data collected from an ovarian tumor study in mice to analyze the effects of different chemotherapy treatments on the volumes of two classes of tumors.     

水分胁迫对入侵植物薇甘菊幼苗生长的影响

水分是影响薇甘菊(Mikania micrantha)生长的重要环境因子,但通过调控生长环境包括土壤水分和空气湿度来探讨这一入侵植物的适应能力的报道较少.本文通过设置2个水分梯度:处理Ⅰ土壤含水量30%～60%和空气相对湿度80%～90%,处理Ⅱ土壤含水量10%～20%和空气相对湿度20%～30%进行试验.结果发现土壤含水量在10%～20%且空气相对湿度在20%～30%时,水分胁迫能显著影响薇甘菊的幼苗生长和光合特性.胁迫条件下植株生长速率明显降低,最大净光合速率和最大量子效率分别是1.94 μmol·m-2·s-1和64.91 mmol·mol-1,比对照8.63 μmol·m-2·s-1和211.34 mmol·mol-1明显偏低.本文将空气相对湿度作为水分胁迫条件之一,阐述了空气相对湿度的增加能扩大薇甘菊的适生范围,并分析得出气孔限制可能是水分胁迫下薇甘菊生长受抑制的主要原因.     

Assessing Homeostasis Through Circadian Patterns

An organism is thought to be in a dynamic state of homeostasis when each physiological and behavioral system reaches a delicate balance within the framework of other regulatory processes. Many biological systems target specific set-point variables and generate circadian patterns. In this article, we focus on specific measurements representative of two systems, namely deep-body temperature and activity counts. We examine data collected every 30 minutes in mice, assume there are underlying circadian patterns, and extend the approach presented in Brumback and Rice (1998, Journal of the American Statistical Association 93, 961-976) in order to obtain estimates in the presence of correlated data. We then assess homeostasis using these estimates and their statistical properties.     

Evaluation of methods for estimating macroinvertebrate species richness using individual stones in tropical streams

1. The most straightforward way to assess diversity in a site is the species count. However, a relatively large sample is needed for a reliable result because of the presence of many rare species in rich assemblages. The use of richness estimation methods is suggested by many authors as a solution for this problem in many cases.
2. We examined the performance of 13 methods for estimating richness of stream macroinvertebrates inhabiting riffles both at local (stream) and regional (catchment) scales. The evaluation was based on (1) the smallest sub-sample size needed to estimate total richness in the sample, (2) constancy of this size, (3) lack of erratic behaviour in curve shape and (4) similarity in curve shape through different data sets. Samples were from three single stream sites (local) and three from several streams within the same catchment basin (regional). All collections were made from protected forest areas in south-east Brazil.
3. All estimation methods were dependent on sub-sample size, producing higher estimates when using larger sub-sample sizes. The Stout and Vandermeer method estimated total richness in the samples with the smallest sub-sample size, but showed some erratic behaviour at small sub-sample sizes, and the estimated curves were not similar among the six samples. The Bootstrap method was the best estimator in relation to constancy of sub-sample sizes, but needed an unacceptably large sub-sample to estimate total richness in the samples. The second order Jackknife method was the second best estimator both for minimum sub-sample size and constancy of this size and we suggest its use in future studies of diversity in tropical streams. Despite the inferior performance of several other methods, some produced acceptable results. Comments are made on the utility of using these estimators for predicting species richness in an area and for comparative purposes in diversity studies.     

Leaf Photosynthesis in Eight Almond Tree Cultivars

Response of gas exchange traits to irradiance were studied in eight almond tree (Prunus amygdalus) cultivars: Desmayo Largueta, Falsa Barese, Garrigues, Lauranne, Marcona, Masbovera, Nonpareil and Ramillete, grafted on a hybrid rootstock almond × peach GF-677. From these responses cultivars can be classified from the best to the worst photosynthetic performance as follows: Falsa Barese, Masbovera, Marcona, Nonpareil, Ramillete, Desmayo Largueta, Lauranne and Garrigues. The highest net photosynthetic rate was 20.3 μmol m⁻² s⁻¹ in Falsa Barese. In the absence of water stress, photosynthetic rate was not limited by stomatal conductance. Consequently, non-stomatal limitations prevailed under such conditions. This revised version was published online in July 2006 with corrections to the Cover Date.     

The use of low [CO2] to estimate diffusional and non-diffusional limitations of photosynthetic capacity of salt-stressed olive saplings

In this study it has been shown that increased diffusional resistances caused by salt stress may be fully overcome by exposing attached leaves to very low [CO₂] (～ 50 µmol mol^?1), and, thus a non‐destructive‐in vivo method to correctly estimate photosynthetic capacity in stressed plants is reported. Diffusional (i.e. stomatal conductance, g_s, and mesophyll conductance to CO₂, g_m) and biochemical limitations to photosynthesis (A) were measured in two 1‐year‐old Greek olive cultivars (Chalkidikis and Kerkiras) subjected to salt stress by adding 200 mm NaCl to the irrigation water. Two sets of A–C_i curves were measured. A first set of standard A–C_i curves (i.e. without pre‐conditioning plants at low [CO₂]), were generated for salt‐stressed plants. A second set of A–C_i curves were measured, on both control and salt‐stressed plants, after pre‐conditioning leaves at [CO₂] of ～ 50 µmol mol^?1 for about 1.5 h to force stomatal opening. This forced stomata to be wide open, and g_s increased to similar values in control and salt‐stressed plants of both cultivars. After g_s had approached the maximum value, the A–C_i response was again measured. The analysis of the photosynthetic capacity of the salt‐stressed plants based on the standard A–C_i curves, showed low values of the J_max (maximum rate of electron transport) to V_cmax (RuBP‐saturated rate of Rubisco) ratio (1.06), that would implicate a reduced rate of RuBP regeneration, and, thus, a metabolic impairment. However, the analysis of the A–C_i curves made on pre‐conditioned leaves, showed that the estimates of the photosynthetic capacity parameters were much higher than in the standard A–C_i responses. Moreover, these values were similar in magnitude to the average values reported by Wullschleger (Journal of Experimental Botany 44, 907–920, 1993) in a survey of 109 C₃ species. These findings clearly indicates that: (1) salt stress did affect g_s and g_m but not the biochemical capacity to assimilate CO₂ and therefore, in these conditions, the sum of the diffusional resistances set the limit to photosynthesis rates; (2) there was a linear relationship (r² = 0.68) between g_m and g_s, and, thus, changes of g_m can be as fast as those of g_s; (3) the estimates of photosynthetic capacity based on A–C_i curves made without removing diffusional limitations are artificially low and lead to incorrect interpretations of the actual limitations of photosynthesis; and (4) the analysis of the photosynthetic properties in terms of stomatal and non‐stomatal limitations should be replaced by the analysis of diffusional and non‐diffusional limitations of photosynthesis. Finally, the C₃ photosynthesis model parameterization using in vitro‐measured and in vivo‐measured kinetics parameters was compared. Applying the in vivo‐measured Rubisco kinetics parameters resulted in a better parameterization of the photosynthesis model.     

Photogravitropic equilibrium in <Emphasis Type="Italic">Avena</Emphasis> coleoptiles: fluence rate–response relationships and dependence on dark adaptation and clinostating

Phototropism of Avena coleoptiles was measured in response to blue-light irradiation lasting between 2 and 24 h. During this time the coleoptiles established a bending angle of photogravitropic equilibrium that was dependent on the time of irradiation and also on the pretreatment in light or darkness prior to stimulation. The absolute threshold for the photogravitropic equilibrium in response to blue light was 10⁻⁸ μmol m⁻² s⁻¹. Photon fluence rate–response curves, which were generated after several hours of dark adaptation, had a characteristic shape with a prominent optimum in the middle of the dynamic range. Curves which were generated without prior dark adaptation displayed no such optimum. Clinostating dark-adapted coleoptiles caused an increase of sensitivity and responsiveness during a 2-h period of unilateral irradiation. The advantages and the drawbacks of long-term irradiation experiments for the investigation of phototropism and the generation of action spectra are discussed. Received: May 14, 2001 / Accepted: December 7, 2001     

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.     

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.     

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.