Estimation of parameters in large offspring number models and ratios of coalescence times

The ratio of singletons to the total number of segregating sites is used to estimate a reproduction parameter in a population model of large offspring numbers without having to jointly estimate the mutation rate. For neutral genetic variation, the ratio of singletons to the total number of segregating sites is equivalent to the ratio of total length of external branches to the total length of the gene genealogy. A multinomial maximum likelihood method that takes into account more frequency classes than just the singletons is developed to estimate the parameter of another large offspring number model. The performance of these methods with regard to sample size, mutation rate, and bias, is investigated by simulation. The expected value of the ratio of the total length of external branches to the total length of the whole tree is, using simulation, shown to decrease for the Kingman coalescent as sample size increases, but can increase or decrease, depending on parameter values, for Λ coalescents. Considering ratios of tree statistics, as opposed to considering lengths of various subtrees separately, can yield better insight into the dynamics of gene genealogies.     

Quantile Inference with Multivariate Failure Time Data

Quantiles, especially the medians, of survival times are often used as summary statistics to compare the survival experiences between different groups. Quantiles are robust against outliers and preferred over the mean. Multivariate failure time data often arise in biomedical research. For example, in clinical trials, each patient in the study may experience multiple events which may be of the same type or distinct types, while in family studies of genetic diseases or litter matched mice studies, failure times for subjects in the same cluster may be correlated. In this article, we propose nonparametric procedures for the estimation of quantiles with multivariate failure time data. We show that the proposed estimators asymptotically follow a multivariate normal distribution. The asymptotic variance‐covariance matrix of the estimated quantiles is estimated based on the kernel smoothing and bootstrap techniques. Simulation results show that the proposed estimators perform well in finite samples. The methods are illustrated with the burn‐wound infection data and the Diabetic Retinopathy Study (DRS) data.     

Optimal approximate conversions of odds ratios and hazard ratios to risk ratios

Odds ratios approximate risk ratios when the outcome under consideration is rare but can diverge substantially from risk ratios when the outcome is common. In this paper, we derive optimal analytic conversions of odds ratios and hazard ratios to risk ratios that are minimax for the bias ratio when outcome probabilities are specified to fall in any fixed interval. The results for hazard ratios are derived under a proportional hazard assumption for the exposure. For outcome probabilities specified to lie in symmetric intervals centered around 0.5, it is shown that the square-root transformation of the odds ratio is the optimal minimax conversion for the risk ratio. General results for any nonsymmetric interval are given both for odds ratio and for hazard ratio conversions. The results are principally useful when odds ratios or hazard ratios are reported in papers, and the reader does not have access to the data or to information about the overall outcome prevalence.     

Sex ratios

Sex ratio theory attempts to explain variation at all levels (species, population, individual, brood) in the proportion of offspring that are male (the sex ratio). In many cases this work has been extremely successful, providing qualitative and even quantitative explanations of sex ratio variation. However, this is not always the situation, and one of the greatest remaining problems is explaining broad taxonomic patterns. Specifically, why do different organisms show so much variation in the amount and precision with which they adjust their offspring sex ratios?     

A bivariate cure-mixture approach for modeling familial association in diseases

For modeling correlation in familial diseases with variable ages at onset, we propose a bivariate model that incorporates two types of pairwise association, one between the lifetime risk or the overall susceptibility of two individuals and one between the ages at onset between two susceptible individuals. For estimation, we consider a two-stage estimation procedure similar to that of Shih (1998, Biometrics 54, 1115-1128). We evaluate the properties of the estimators through simulations and compare the performance with that from a bivariate survival model that allows correlation between ages at onset only. We apply the methodology to breast cancer using the kinship data from the Washington Ashkenazi Study. We also discuss potential applications of the proposed method in the area of cure modeling.     

Approximate Bayesian evaluation of multiple treatment effects

We propose an approximate Bayesian method for comparing an experimental treatment to a control based on a randomized clinical trial with multivariate patient outcomes. Overall treatment effect is characterized by a vector of parameters corresponding to effects on the individual patient outcomes. We partition the parameter space into four sets where, respectively, the experimental treatment is superior to the control, the control is superior to the experimental, the two treatments are equivalent, and the treatment effects are discordant. We compute posterior probabilities of the parameter sets by treating an estimator of the parameter vector like a random variable in the Bayesian paradigm. The approximation may be used in any setting where a consistent, asymptotically normal estimator of the parameter vector is available. The method is illustrated by application to a breast cancer data set consisting of multiple time-to-event outcomes with covariates and to count data arising from a cross-classification of response, infection, and treatment in an acute leukemia trial.     

Nonparametric and semiparametric trend analysis for stratified recurrence times

Recurrent event data are frequently encountered in longitudinal follow-up studies when the occurrences of multiple events are considered as the major outcomes. Suppose that the recurrent events are of the same type and the variable of interest is the recurrence time between successive events. In many applications, the distributional pattern of recurrence times can be used as an index for the progression of a disease. Such a distributional pattern is important for understanding the natural history of a disease or for confirming long-term treatment effect. In this article, we discuss and define the comparability of recurrence times. Nonparametric and semiparametric methods are developed for testing trend of recurrence time distributions and estimating trend parameters in regression models. The construction of the methods is based on comparable recurrence times from stratified data. A real data example is presented to illustrate the use of methodology.     

Estimated quadratic inference function for correlated failure time data

An estimated quadratic inference function method is proposed for correlated failure time data with auxiliary covariates. The proposed method makes efficient use of the auxiliary information for the incomplete exposure covariates and preserves the property of the quadratic inference function method that requires the covariates to be completely observed. It can improve the estimation efficiency and easily deal with the situation when the cluster size is large. The proposed estimator which minimizes the estimated quadratic inference function is shown to be consistent and asymptotically normal. A chi-squared test based on the estimated quadratic inference function is proposed to test hypotheses about the regression parameters. The small-sample performance of the proposed method is investigated through extensive simulation studies. The proposed method is then applied to analyze the Study of Left Ventricular Dysfunction (SOLVD) data as an illustration.     

Activity ratios of ribulose-1,5-bisphosphate carboxylase accurately reflect carbamylation ratios

Activity ratios and carbamylation ratios of ribulose-1,5-bisphosphate carboxylase (RuBPCase) were determined for leaves of Phaseolus vulgaris and Spinacia oleracea exposed to a variety of partial pressures of CO₂ and O₂ and photon flux densities (PFD). It was found that activity ratios accurately predicted carbamylation ratios except in extracts from leaves held in low PFD. In particular, it was confirmed that the loss of RuBPCase activity in low partial pressure of O₂ and high PFD results from reduced carbamylation. Activity ratios of RuBPCase were lower than carbamylation ratios for Phaseolus leaves sampled in low PFD, presumably because of the presence of 2-carboxyarabinitol 1-phosphate. Spinacia leaves sampled in darkness also exhibited lower activity ratios than carbamylation ratios indicating that this species may also have an RuBPCase inhibitor even though carboxyarabinitol 1-phosphate has not been detected in this species in the past.     

Potassium-39 NMR of K+ interaction with the gramicidin channel and NMR-derived conductance ratios for Na+, K+ and Rb+

Summary A potassium-39 NMR study of potassium ion interaction with the gramicidin transmembrane channel in phospholipid bilayers at high ion activity is reported which allows determination of a weak binding constant, K _b ^w 8.3/m, and an off-rate constant for the weak site,k _off ^w 2.6×10⁷/sec. These values are interpreted with the aid of additional NMR data as the binding constant for formation of the doubly occupied channel state and the rate constant for an ion leaving the doubly occupied state. Considering the singly occupied channel state for the potassium ion to be electrically silent at 1 molar ion activity, as with the sodium ion, the single-channel conductance for 100 mV and 30°C calculated to be 29 pS, and using the same approximation with previous NMR results on the sodium and rubidium ions, reasonable conductance ratios were calculated. Further experimental estimates of the other three constants with the experimental location of binding sites and Eyring rate theory to introduce voltage dependence allowed a more complete calculation of the two-site channel. The single-channel conductance for potassium ion is calculated to be 24 pS at 1m activity and 26 pS at 0.6m activity, which compares for diphytanoyl phosphatidylcholine membranes to an experimental most probable single-channel conductance of 25 pS and a mean channel conductance of 20 pS. The calculated conductance ratios using NMR-derived constants were (K)/(Na)=2.0 and (Rb)/(Na)=4.3. These results are close to the experimental values and provide further basis for the use of NMR of quadrupolar ions to provide information on the ionic mechanism of channel transport.