Estimating the mean and standard deviation of concentration distributions using censored samples

Environmental data sets of pollutant concentrations in air, water, and soil frequently include unquantified sample values reported only as being below the analytical method detection limit. These values, referred to as censored values, should be considered in the estimation of distribution parameters as each represents some value of pollutant concentration between zero and the detection limit. Most of the currently accepted methods for estimating the population parameters of environmental data sets containing censored values rely upon the assumption of an underlying normal (or transformed normal) distribution. This assumption can result in unacceptable levels of error in parameter estimation due to the unbounded left tail of the normal distribution. With the beta distribution, which is bounded by the same range of a distribution of concentrations, $\rm\lbrack0\le x\le1\rbrack,$ parameter estimation errors resulting from improper distribution bounds are avoided. This work developed a method that uses the beta distribution to estimate population parameters from censored environmental data sets and evaluated its performance in comparison to currently accepted methods that rely upon an underlying normal (or transformed normal) distribution. Data sets were generated assuming typical values encountered in environmental pollutant evaluation for mean, standard deviation, and number of variates. For each set of model values, data sets were generated assuming that the data was distributed either normally, lognormally, or according to a beta distribution. For varying levels of censoring, two established methods of parameter estimation, regression on normal ordered statistics, and regression on lognormal ordered statistics, were used to estimate the known mean and standard deviation of each data set. The method developed for this study, employing a beta distribution assumption, was also used to estimate parameters and the relative accuracy of all three methods were compared. For data sets of all three distribution types, and for censoring levels up to 50%, the performance of the new method equaled, if not exceeded, the performance of the two established methods. Because of its robustness in parameter estimation regardless of distribution type or censoring level, the method employing the beta distribution should be considered for full development in estimating parameters for censored environmental data sets. ^

Statistical characterization and development of summary measures of non-normal distributions of nuclear morphometry data from prostate cancer cells for use as prognostic indicators

Nuclear morphometry (NM) uses image analysis to measure features of the cell nucleus which are classified as: bulk properties, shape or form, and DNA distribution. Studies have used these measurements as diagnostic and prognostic indicators of disease with inconclusive results. The distributional properties of these variables have not been systematically investigated although much of the medical data exhibit nonnormal distributions. Measurements are done on several hundred cells per patient so summary measurements reflecting the underlying distribution are needed.^ Distributional characteristics of 34 NM variables from prostate cancer cells were investigated using graphical and analytical techniques. Cells per sample ranged from 52 to 458. A small sample of patients with benign prostatic hyperplasia (BPH), representing non-cancer cells, was used for general comparison with the cancer cells.^ Data transformations such as log, square root and 1/x did not yield normality as measured by the Shapiro-Wilks test for normality. A modulus transformation, used for distributions having abnormal kurtosis values, also did not produce normality.^ Kernel density histograms of the 34 variables exhibited non-normality and 18 variables also exhibited bimodality. A bimodality coefficient was calculated and 3 variables: DNA concentration, shape and elongation, showed the strongest evidence of bimodality and were studied further.^ Two analytical approaches were used to obtain a summary measure for each variable for each patient: cluster analysis to determine significant clusters and a mixture model analysis using a two component model having a Gaussian distribution with equal variances. The mixture component parameters were used to bootstrap the log likelihood ratio to determine the significant number of components, 1 or 2. These summary measures were used as predictors of disease severity in several proportional odds logistic regression models. The disease severity scale had 5 levels and was constructed of 3 components: extracapsulary penetration (ECP), lymph node involvement (LN+) and seminal vesicle involvement (SV+) which represent surrogate measures of prognosis. The summary measures were not strong predictors of disease severity. There was some indication from the mixture model results that there were changes in mean levels and proportions of the components in the lower severity levels. ^

Total cholesterol and anthropometric measurements distributions in a cross-sectional study of school children

Cross-sectional age and sex specific distributions of serum total cholesterol were described for 1091 children age 6-18 years, in The Woodlands, Texas. Associations of serum total cholesterol with five anthropometric measurements (weight, height, body mass index, arm circumference, and triceps skinfold thickness) were examined by correlation and regression analyses. Examination of serum total cholesterol distributions showed lower levels in boys than in girls for most of the age groups studied. Mean levels of total cholesterol peaked at age 9 for boys and 8 for girls. Serum total cholesterol leveled off until age 14 for boys and 11 for girls, and then dropped through age 18 for both boys and girls. These results support the hypothesis that serum total cholesterol concentration drops at pre-adolescence.^ Age adjusted correlations were observed between serum total cholesterol and triceps skinfold thickness for both boys and girls. This association was stronger in boys. Triceps skinfold thickness and arm circumference were consistently the strongest correlates for serum total cholesterol in boys. Weight and arm circumference were consistently the strongest correlates for serum total cholesterol in girls. ^

Modulation of high voltage -activated calcium channels by phosphorylation

High voltage-activated (HVA) calcium channels from rat brain and rabbit heart are expressed in Xenopus laevis oocytes and their modulation by protein kinases studied. A subtype of the HVA calcium current expressed by rat brain RNA is potentiated by the phospholipid- and calcium-dependent protein kinase (PKC). The calcium channel clone $\alpha\sb{\rm1C}$ from rabbit heart is modulated by the cAMP-dependent protein kinase (PKA), and another factor present in the cytoplasm.^ The HVA calcium channels from rat brain do not belong to the L-type subclass since they are insensensitive to dihydropyridine (DHP) agonists and antagonists. The expressed currents do contain a N-type fraction which is identified by inactivation at depolarized potentials, and a P-type fraction as defined by blockade by the venom of the funnel web spider Agelenopsis Aperta. A non N-type fraction of this current is potentiated, by using phorbol esters to activate PKC. This residual fraction of current resembles the newly described Q-type channel from cerebellar granule cells in its biophysical properties, and potentiation by activation of PKC.^ The $\alpha\sb{\rm1C}$ clone from rabbit heart is expressed in oocytes and single-channel currents are measured using the cell-attached and cell-excised patch clamp technique. The single-channel current runs down within two minutes after patch excision into normal saline bath solution. The catalytic subunit of PKA + MgATP is capable of reversing this rundown for over 15 minutes. There also appears to be an additional factor present in the cytoplasm necessary for channel activity as revealed in experiments where PKA failed to prevent rundown.^ These data are important in that these types of channels are involved in synaptic transmission at many different types of synapses. The mammalian synapse is not accessible for these types of studies, however, the oocyte expression system allows access to HVA calcium channels for the study of their modulation by phosphorylation. ^

Calcium-dependent mechanisms and long-term potentiation: Role of NMDA receptors, voltage -dependent calcium channels and persistent protein kinase activity

Long-term potentiation (LTP) is a rapidly induced and long lasting increase in synaptic strength and is the leading cellular model for learning and memory in the mammalian brain. LTP was first identified in the hippocampus, a structure implicated in memory formation. LTP induction is dependent on postsynaptic Ca2+ increases mediated by N-methyl-D-aspartate (NMDA) receptors. Activation of other postsynaptic routes of Ca2+ entry, such as voltage-dependent Ca2+ channels (VDCCs) have subsequently been shown to induce a long-lasting increase in synaptic strength. However, it is unknown if VDCC-induced LTP utilized similar cellular mechanisms as the classical NMDA receptor-dependent LTP and if these two forms of LTP display similar properties. This dissertation determines the similarities and differences in VDCC and NMDA receptor-dependent LTP in area CA1 of hippocampal slices and demonstrates that VDCCs and NMDA receptors activate similar cellular mechanisms, such as protein kinases, to induce LTP. However, VDCC and NMDA receptor activated LTP induction mechanisms are compartmentalized in the postsynaptic neuron, such that they do not interact. Consistent with activation properties of NMDA receptors and VDCCs, NMDA receptor and VDCC-dependent LTP have different induction properties. In contrast to NMDA-dependent LTP, VDCC-induced potentiation does not require evoked presynaptic stimulation or display input specificity. These results indicate that there are two different routes of postsynaptic Ca2+ which can induce LTP and the compartmentation of VDCCs and NMDA receptors and/or their resulting Ca2+ increases may account for the distinction between these LTP induction mechanisms.^ One of the molecular targets for postsynaptic Ca2+ that is required for the induction of LTP is protein kinases. Evidence for the role of protein kinase activity in LTP expression is either correlational or controversial. We have utilized a broad range and potent inhibitors of protein kinases to systematically examine the temporal requirement for protein kinases in the induction and expression of LTP. Our results indicate that there is a critical period of persistent protein kinase activity required for LTP induction activated by tetanic stimulation and extending until 20 min after HFS. In addition, our results suggest that protein kinase activity during and immediately after HFS is not sufficient for LTP induction. These results provide evidence for persistent and/or Ca2+ independent protein kinase activity involvement in LTP induction. ^