On Asymptotically Distribution-Free Confidence Bounds for P (X1≥X2) Based on Samples not Necessarily Independent

If X₁, X₂, denote the random variables of measurement under two treatments then the probability P (X₁ ≥ X₂) is a quantity of great practical interest, especially if we consider both to be measured for the same unity. In this case the random variables cannot be assumed to be independent any longer. The following paper describes a procedure to compute approximate confidence bounds for P (X₁ ≥ X₂) where correlations between X₁, X₂ are admitted as well as between replications of the X_j. There is some relation to the FRIEDMAN-statistic with or without repeated measurements and as a special case to the sign-test. Application may be extended to ordinal data.     

On an Unbiased Variance Estimator for the WILCOXON-MANN-WHITNEY-Statistic Based on Ranks

For some applications of the WILCOXON-MANN-WHITNEY-statistic its variance has to be estimated. So e.g. for the test of POTTHOFF (1963) to detect differences in medians of two symmetric distributions as well as for the computation of approximate, confidence bounds for the probability P(X₁ ≥ X₂), cf. GOVINDARAJULU (1968). In the present paper an easy to compute variance estimator is proposed which as only information uses the ranks of the data with the additional property that it is unbiased for the finite variance. Because of its invariance under any monotone transformation of the data its applicability is not confined to quantitative data. The estimator may be applied to ordinal data just as well. Some properties are discussed and a numerical example is given.     

The Point Evaluation Method for Approximating Function Means,Variances and Covariances

A perennial problem in statistics is the determination of biases, variances and covariances for functions of random variables X₁, X₂, …, X_n which themselves have a known distribution. A common approach is through equations based upon Taylor series approximations but a “point evaluation” method may sometimes be a useful alternative. This involves approximating the multivariate distribution of the X variables by the 2ⁿ points given by X₁=μ₁±₁, X₂ = μ₂ ±₂, …, X_n = = μ_n μ_n, where μ_i is the mean and σ_i the standard deviation of Xi, with appropriate point weights. An advantage over the Taylor series approach is that function derivatives do not have to be explicitely calculated. The point evaluation method is particularly useful in cases where the X variables are uncorrelated. Then the evaluation of the 2ⁿ points can be replaced by the evaluation of 2n points. The point evaluation method is illustrated with powers of a normally distributed variable, and with estimation of gene frequencies from ABO blood group frequencies.     

Various X2-Tests of Homogeneity: Some Comments

Methodological issues in the analysis of incidence rates or prevalence proportions for count data, presented in a form of a sequence of 2×2 tables, corresponding to levels (strata) of a specified variable (risk factor) X, are discussed. Suppose λ_1i and λ_2i are the incidence rates of an event D in the ith stratum for populations 1 and 2, respectively. The homogeneity (null) hypothesis is formulated in the form: H_0:λ1i=λ_2i for all i (i = 1, 2, …, I). Three X²-tests for H₀ and their theoretical bases are discussed: X_Total² which is sensitive to alternatives HA :λ1i± λ2i for at least some i; X_Comb² which is sensitive to alternatives H A : λ1iλ2i² or < λ_2i but not both for all i; and X_Diff² which is sensitive to alternatives H_A:λ1i>λ2i³ for some i and λ_1i′ < λ_2i′ for some i′ (i≠i′). These statistics satisfy the relation X_Total² = X_Comb² + X_Diff². Also, X′²-statistic for pooled data is calculated, which in conjunction with X_Comb² can serve for detecting confounding. Although most of these techniques are known, they are rather scattered in the literature, and not always considered jointly, as it is emphasized in the present paper. It is hoped that these comments will be helpful to biostatisticians as well as to epidemiologists and medical researchers in the analysis of mortality and morbidity data. For illustration, two examples with large sets of epidemiological data are given.     

Artefactual responses of mesophyll conductance to CO2 and irradiance estimated with the variable J and online isotope discrimination methods

Studies with the variable J method have reported that mesophyll conductance (g_m) rapidly decreases with increasing intercellular CO₂ partial pressures (C_i) or decreasing irradiance. Similar responses have been suggested with the online isotope discrimination method, although with less consistency. Here we show that even when the true g_m is constant, the variable J method can produce an artefactual dependence of g_m on C_i or irradiance similar to those reported in previous studies for any of the following factors: day respiration and chloroplastic CO₂ photocompensation point are estimated with Laisk method; C_i or electron transport rate is positively biased; net photosynthetic rate is negatively biased; insufficient NADPH is assumed while insufficient ATP limits RuBP regeneration. The isotopic method produces similar artefacts if fractionation of carboxylation or C_i is positively biased or Δ¹³ negatively biased. A non‐zero chloroplastic resistance to CO₂ movement results in a qualitatively different dependence of g_m on C_i or irradiance and this dependence is only sensitive at low C_i. We thus cannot rule out the possibility that previously reported dependence of g_m on C_i or irradiance is a methodological artefact. Recommendations are made to take advantage of sensitivities of the variable J and isotopic methods for estimating g_m.     

Cumulative Damage Survival Models for the Randomized Complete Block Design

A continuous time discrete state cumulative damage process {X(t), t ≥ 0} is considered, based on a non‐homogeneous Poisson hit‐count process and discrete distribution of damage per hit, which can be negative binomial, Neyman type A, Polya‐Aeppli or Lagrangian Poisson. Intensity functions considered for the Poisson process comprise a flexible three‐parameter family. The survival function is S(t) = P(X(t) ≤ L) where L is fixed. Individual variation is accounted for within the construction for the initial damage distribution {P(X(0) = x) | x = 0, 1, …,}. This distribution has an essential cut‐off before x = L and the distribution of L – X(0) may be considered a tolerance distribution. A multivariate extension appropriate for the randomized complete block design is developed by constructing dependence in the initial damage distributions. Our multivariate model is applied (via maximum likelihood) to litter‐matched tumorigenesis data for rats. The litter effect accounts for 5.9 percent of the variance of the individual effect. Cumulative damage hazard functions are compared to nonparametric hazard functions and to hazard functions obtained from the PVF‐Weibull frailty model. The cumulative damage model has greater dimensionality for interpretation compared to other models, owing principally to the intensity function part of the model.     

Cytogenetic analysis shows extensive genomic rearrangements between red howler (Alouatta seniculus,Linnaeus) subspecies

A comparison of the G-banded karyotypes of two red howler subspecies, Alouatta seniculus arctoidea and A. s. sara, showed that they differed by at least 14 chromosomal rearrangements. Genomic reshuffling is so great that homologs between subspecies could not be found for some chromosome, while the assignment of homology for other chromosomes remains uncertain. The two red howlers, however, share an unusual X₁X₂Y₁Y₂/ X₁X₁X₂X₂ sex-chromosome system that resulted from a Y-autosome translocation, probably in a common ancestor. The great chromosomal variability resulting from rapid chromosomal evolution in howlers indicates that cytogenetic data could make an important contribution to resolving phylogenetic and conservation problems in this group of highly conspicuous New World Monkeys. © 1995 Wiley-Liss, Inc.     

Reduced Growth Yield of Activated Sludge in Organic Protonophore-Containing Batch Culture

Abstract The effects of organic protonophores 2,4-dinitrophenol (dNP) and para-nitrophenol (pNP) on the observed growth yield (Y _obs) was studied using batch cultures of activated sludge microorganisms. A growth yield model was proposed in relation to the ratio of initial protonophore concentration (C _u) to initial biomass concentration (X ₀) and was verified with experimental data. It was found that Y _obs decreased with the increase of the C _u/X ₀ ratio, while the specific rate of glucose consumption was increased. Results showed that the C _u/X ₀ ratio could more reasonably reflect the real strength of organic protonophore exerted to activated sludge than using C _u only. Based on the concept of growth yield, a model describing the uncoupling degree between energy generated via electron transport system and energy used for growth was further developed for protonophore-containing batch culture. It was shown that more than 60% of glucose was consumed through a futile cycle of energy rather than for growth at higher C _u/X ₀ ratios. This research usefully shows that the dissipation of energy via uncoupling biochemical processes can reduce excessive production of activated sludge markedly. Received: 28 April 1999; Accepted: 14 September 1999; Online Publication: 6 March 2000     

The estimation of the fitness function from two samples taken from a population

The fitness of animals subjected to natural selection can be defined as the probability of surviving selection for a given interval of time, or some convenient multiple of this probability. If the fitness of animals is related to some quantitative variable X (such as size) then this relationship is expressed mathematically in the fitness function w(x) and this function can be estimated by comparing the distribution of X in samples taken before and after selection. In this note five methods for estimating the fitness function on the basis of samples from a large population are discussed. They are compared on three previously published sets of data and as a result estimation according to weighted multiple regression is recommended.     

Recolonization of coastal heath by Pseudomys novaehollandiae (Muridae) following sand mining

The regeneration of coastal heath after disturbance by mineral sand mining was studied on mid-seral stages from 4 to 11 years old at Hawks Nest, N.S.W. The main purpose was to gain some understanding of factors influencing recolonization by pioneer species of small mammals such as Pseudomys novaehollandiae. Changes in floristics and vegetation structure with time were studied as possible contributing factors together with environmental variables. An apparently linear relationship was found between plant species diversity (X₁) and P. novaehollandiae biomass which was also correlated with an index representing the proportion of heath species present (X₂). Both plant species diversity and P. novaehollandiae biomass showed a linear increase with regeneration age. A multiple regression analysis revealed a predictive equation explaining 96% of the variation in P. novaehollandiae biomass (Y): Y=-7.92 + 1.21X₁+3.92X₂ - 3.09X₃ The third variable (X₃) is a measure of soil hardness. A path diagram using contribution coefficients based on a partial correlation analysis included the effects of vegetation structure below 50 cm and regeneration age. On mid-seral stages after sand mining P. novaehollandiae is associated with areas having a variety of heath plants, with vegetation cover below 50 cm and softer substrates; its abundance increases with increasing regeneration age and with the total amount of vegetation present. A minimum of 20 years is seen to be necessary for both total amount of vegetation and P. novaehollandiae biomass to reach values encountered on control plots of undisturbed heath.     

The Estimation of a Multivariate Fitness Function from Several Samples Taken from a Population

The situation is considered where the multivariate distribution of certain variables X₁, X₂, …, X_p is changing with time in a population because natural selection related to the X's is taking place. It is assumed that random samples taken from the population at times t₁, t₂, …, t_s are available and it is desirable to estimate the fitness function w_t(x₁, x₂,…,x_p) which shows how the number of individuals with X_i = x_i, i = 1, 2, …, p at time t is related to the number of individuals with the same X values at time zero. Tests for population changes are discussed and indices of the selection on the population dispersion and the population mean are proposed. The situation with a multivariate normal distribution is considered as a special case. A maximum likelihood method that can be applied with any form of population distribution is proposed for estimating w_t. The methods discussed in the paper are illustrated with data on four dimensions of male Egyptian skulls covering a time span from about 4500 B.C. to about 300 A.D. In this case there seems to have been very little selection on the population dispersion but considerable selection on means.     

Kinetic resolution of ketoprofen ester catalyzed by lipase from a mutant of CBS 5791

A biotransformation process was developed for the production of (S)-ketoprofen by enantioseletive hydrolysis of racemic ketoprofen ester using the mutant Trichosporon laibacchii strain CBS 5791. A satisfactory result was obtained, in which the E was 82.5, with an ee of 0.94 and a conversion of 0.47 under the optimum hydrolysis conditions [E is enantiomeric ratio, E=ln[1–X(1+ee)]/ln[1–X(1–ee)]; ee is enantiomeric excess, ee=(C_S–C_R)/(C_S+C_R): temperature of hydrolysis was 23°C]. The medium used in biotransformation was a mixture of growth broth and biotransformation broth at a ratio of 1:9, the concentration of Tween 80 was 15 g/l, the time of hydrolysis, 72 h. These results are promising for further scale-up. Tween 80 significantly improved lipase enantioselectivity and activity at the optimum concentration.     

Use of Transformed Auxiliary Variable in Estimating the Finite Population Mean

For estimating the finite population mean Y- of the study character y, an estimator using a transformed auxiliary variable has been defined. The bias and mean-squared error (MSE) of the proposed estimator have been obtained. The regions of preference have been obtained under which it is better than usual unbiased estimator y-, the ratio estimator y-_R = y-X-/x-, Sisodia and Dwivedi (1981) estimator y-_s = y-(X- + C_x)/(x- + C_x) and Singh and Kakran (1993) estimator y-_k = y[X- + β₂(x)]/[x- + β₂(x)]. An empirical study has been carried out to demonstrate the superiority of the suggested estimator over the others.     

Experimental investigations on the backbone folding of proline-containing model tripeptides

Some proline-containing tripeptides with the general formulas R⁰CO-L -Pro-X-NHR³ (X = Gly,Sar,L -Ala,D -Ala) and R⁰CO-X-L -Pro-NHR³ (X = Gly,L -Ala,D -Ala) have been investigated in solution by ir and ¹H-nmr spectroscopies. Their favored conformational states depend mainly on both the primary structure and the chiral sequence of the molecules. In inert solvents the βII-folding mode is the most favored conformation for the L -Pro-D -Ala and L -Pro-Gly tripeptides, while the βII′-turn is largely preferred by D -Ala-L -Pro derivatives. Under the same conditions only about one-third of the whole conformers of L -Pro-L -Ala molecules adopts the βI-folding mode. Semiopened C₇C₅ and C₅C₇ conformations are appreciably populated in the L -Pro-L -Ala sequence, on the one hand, and in the Gly-L -Pro and L -Ala-L -Pro derivatives, on the other hand. In L -Pro-Sar and X-L -Pro models, the cis–trans isomerism around the middle tertiary amide function is observed. Thus cis L -Pro-Sar and L -Ala-L -Pro conformers are folded by an intramolecular i + 3 → i hydrogen bond, whereas cis D -Ala-L -Pro and Gly-L -Pro molecules accommodate an open conformation. In dimethylsulfoxide the βII- and βII′-folding modes are not essentially destabilized, as contrasted with the βI conformation, which is less populated. In water solution all the above-mentioned conformations, with the possible exception of the βII′-folding mode for D -Ala-L -Pro molecules, seem to vanish. Solute conformations are also compared with the crystal structures of four proline-containing tripeptides.     

Rapid method for determination of riboflavin in urine by high-performance liquid chromatography

A simple, specific, and sensitive high-performance liquid chromatographic (HPLC) method for the determination of riboflavin directly in urine samples using a fixed-wave-length spectrofluorometer is described. Centrifuged raw urine samples (50 μl) are injected onto a reversed-phase microparticulate C₁₈ column. The eluent is 0.01 M KH₂PO₄ (pH 5.0)—methanol (65:35). This method is capable of differentiating riboflavin from riboflavin-5-phosphate, non-riboflavin fluorescing components in urine, and photo-degraded riboflavin. The method shows good reproducibility and is linear to at least 12 μg/ml. The sensitivity of this procedure, at the 95% confidence limit, determined by linear regression analysis, is estimated to be 0.05 μg/ml using peak height and 0.07 μg/ml using peak area. This HPLC method is compared to an automated fluorometric method for riboflavin. The coefficient of linear regression of this comparison is Y = 0.858 + 0.893X, where X is the HPLC method and Y is the fluorometric method.     

A Truncated Proportional Hazards Test

We present two truncated proportional hazards tests. The first, which is applicable to those cases in which the time of action of an agent or treatment is known, was studied in two forms: One uses expected Fisher information and the other observed Fisher information. In this case the expected information statistic, C₁(a₀), had properties superior to the observed information statistic and is recommended. The use of the X² distribution with one degree of freedom for percentiles appears to be satisfactory. When the time of action is unknown, a statistic based on the maximum of the C₁(a) statistics is used. A simulation study gives empirical percentiles for the Max C₁(a) statistic which agree with those given in a study by Muenz, Green and Byar (1977).     

Artificial neural network as an alternative to multiple regression analysis in optimizing formulation parmaeters of cytarabine liposomes

The objective of the study was to optimize the formulation parameters of cytarabine liposomes by using artificial neural networks (ANN) and multiple regression analysis using 3³ factorial design (FD). As model formulations, 27 formulations were prepared. The formulation variables, drug (cytarabine)/lipid (phosphatidyl choline [PC] and cholesterol [Chol]) molar ratio (X ₁, PC/Chol in percentage ratio of total lipids (X ₂), and the volume of hydration medium, (X ₃) were selected as the independent variables; and the percentage drug entrapment (PDE) was selected as the dependent variable. A set of causal factors was used as tutorial data for ANN and fed into a computer. The optimization was performed by minimizing the generalized distance between the predicted values of each response and the optimized one that was obtained individually. In case of 3³ factorial design, a second-order full-model polynomial equation and a reduced model were established by subjecting the transformed values of independent variables to multiple regression analysis, and contour plots were drawn using the equation. The optimization methods developed by both ANN and FD were validated by preparing another 5 liposomal formulations. The predetermined PDE and the experimental data were compared with predicted data by pairedt test, no statistically significant difference was observed. ANN showed less error compared with multiple regression analysis. These findings demonstrate that ANN provides more accurate prediction and is quite useful in the optimization of pharmaceutical formulations when compared with the multiple regression analysis method.     

Correlation between percentage guanine-cytosine content and melting temperature of deoxyribonucleic acid

An explicit relation between the percentage (G + C)-content X_GC, and the melting temperature (T_m) of a natural DNA, is derived froma a statistical mechanics calculation with due consideration given to the base pair bonding and stacking interactions. The well-known Marmur-Doty empirical formula, linearly relating these two quantities, can now be understood in terms of the fundamental processes. We also propose a simpler experimental procedure for the determination of X_GC. It is similar to the melting temperature method, but we take only one reading at a prescribed temperature of any natural DNA in addition to the two normalization readings. It should be more sensitive for DNAs having X_GC ranging from 35 to 65%.     

Strong coupling effects during <Emphasis Type="Italic">X</Emphasis>-pulse CPMG experiments recorded on heteronuclear <Emphasis Type="Italic">ABX</Emphasis> spin systems: artifacts and a simple solution

Simulation and experiment have been used to establish that significant artifacts can be generated in X-pulse CPMG relaxation dispersion experiments recorded on heteronuclear ABX spin-systems, such as ¹³C _i –¹³C _j –¹H, where ¹³C _i and ¹³C _j are strongly coupled. A qualitative explanation of the origin of these artifacts is presented along with a simple method to significantly reduce them. An application to the measurement of ¹H CPMG relaxation dispersion profiles in an HIV-2 TAR RNA molecule where all ribose sugars are protonated at the 2′ position, deuterated at all other sugar positions and ¹³C labeled at all sugar carbons is presented to illustrate the problems that strong ¹³C–¹³C coupling introduces and a simple solution is proposed.