Combining parametric and nonparametric models to estimate treatment effects in observational studies

Performing causal inference in observational studies requires we assume confounding variables are correctly adjusted for. In settings with few discrete-valued confounders, standard models can be employed. However, as the number of confounders increases these models become less feasible as there are fewer observations available for each unique combination of confounding variables. In this paper, we propose a new model for estimating treatment effects in observational studies that incorporates both parametric and nonparametric outcome models. By conceptually splitting the data, we can combine these models while maintaining a conjugate framework, allowing us to avoid the use of Markov chain Monte Carlo (MCMC) methods. Approximations using the central limit theorem and random sampling allow our method to be scaled to high-dimensional confounders. Through simulation studies we show our method can be competitive with benchmark models while maintaining efficient computation, and illustrate the method on a large epidemiological health survey.     

Insights into the local residual entropy of proteins provided by NMR relaxation.

A simple model is used to illustrate the relationship between the dynamics measured by NMR relaxation methods and the local residual entropy of proteins. The expected local dynamic behavior of well-packed extended amino acid side chains are described by employing a one-dimensional vibrator that encapsulates both the spatial and temporal character of the motion. This model is then related to entropy and to the generalized order parameter of the popular "model-free" treatment often used in the analysis of NMR relaxation data. Simulations indicate that order parameters observed for the methyl symmetry axes in, for example, human ubiquitin correspond to significant local entropies. These observations have obvious significance for the issue of the physical basis of protein structure, dynamics, and stability.     

Salt gland function in the common eider duck (Somateria mollissima)

The function of the supra-orbital salt gland was studied in the common eider duck (Somateria mollissima). The maximum salt-secreting capacity was determined in (1) wild ducks which had been living in a marine environment, (2) ducks reared in captivity on fresh water, and (3) ducks from group 2 adapted to salt water. The maximum secreting capacity was found by infusing a solution of NaCl (1000 mosmol·kg^-1) at increasing rates, from 0.691 to 1.671 mosmol·min^-1. Freshwater-adapted ducks secreted at a maximum rate of 0.785 mosmol·min^-1 (1500 mosmol·kg^-1). Adapted to salt water they increased their capacity, and the best duck secreted at a rate of 1215 mosmol·min^-1 (1600 mosmol·kg^-1). The best wild duck secreted at a rate of 1516 mosmol·min^-1. Ducks in group 3 were used to examine the response to a hyperosmotic or an isoosmotic infusion. The amount of salt (NaCl) given per unit time was the same. Given a hyperosmotic solution their salt glands secreted at a high rate: 30 min after the infusion had stopped the ducks had excreted 94% of the sodium infused, 92.9% via the salt gland. Given an isoosmotic solution they secreted at a rate about half the infusion rate: 30 min after cessation of infusion they had excreted 73% of the sodium, 42.9% via the salt gland and the rest by the kidneys.Abbreviations A II angiotensin II - AV I arginine vasotocin - ED freshwater-adapted ducks - FW fresh water - SD saltwater-adapted ducks - SW sea water - WD wild ducks     

Evaluation of several methods for estimating phylogenetic trees when substitution rates differ over nucleotide sites

Several maximum likelihood and distance matrix methods for estimating phylogenetic trees from homologous DNA sequences were compared when substitution rates at sites were assumed to follow a gamma distribution. Computer simulations were performed to estimate the probabilities that various tree estimation methods recover the true tree topology. The case of four species was considered, and a few combinations of parameters were examined. Attention was applied to discriminating among different sources of error in tree reconstruction, i.e., the inconsistency of the tree estimation method, the sampling error in the estimated tree due to limited sequence length, and the sampling error in the estimated probability due to the number of simulations being limited. Compared to the least squares method based on pairwise distance estimates, the joint likelihood analysis is found to be more robust when rate variation over sites is present but ignored and an assumption is thus violated. With limited data, the likelihood method has a much higher probability of recovering the true tree and is therefore more efficient than the least squares method. The concept of statistical consistency of a tree estimation method and its implications were explored, and it is suggested that, while the efficiency (or sampling error) of a tree estimation method is a very important property, statistical consistency of the method over a wide range of, if not all, parameter values is prerequisite.     

On-line state recognition in a yeast fed-batch culture using error vectors

The physiological states with respect to cell growth and ethanol production in a yeast fed-batch culture expressed in linguistic form could be recognized on-line by fuzzy inferencing based on error vectors. The error vector was newly defined here in a macroscopic elemental balance equation. The physiological states for cell growth and ethanol production were characterized by error vectors using many experimental data from fed-batch cultures. Fuzzy membership functions were constructed from the frequency distributions of the error vectors and state recognition was performed by fuzzy inferencing. In particular, an unusual physiological state for a yeast cultivation, in which aerobic ethanol production was accompanied by very low cell growth, could be recognized accurately. According to the results of the state recognition, an energy parameter, the P/O ratio in the metabolic reaction model was adaptively estimated, and the cell growth was successfully evaluated with the estimated P/O. (c) 1995 John Wiley & Sons, Inc.     

Evolution of Orthologous Intronless and Intron-Bearing Globin Genes in Two Insect Species

While globin genes ctt-2β and ctt-9.1 in Chironomus thummi thummi each have a single intron, all of the other insect globin genes reported so far are intronless. We analyzed four globin genes linked to the two intron-bearing genes in C. th. thummi. Three have a single intron at the same position as ctt-2β and ctt-9.1; the fourth is intronless and lies between intron bearing genes. Finally, in addition to its intron, one gene (ctt-13RT) was recently interrupted by retrotransposition. Phylogenetic analyses show that the six genes in C. th. thummi share common ancestry with five globin genes in the distantly related species C. tentans, and that a 5-gene ancestral cluster predates the divergence of the two species. One gene in the ancestral cluster gave rise to ctn-ORFB in C. tentans, and duplicated in C. th. thummi to create ctt-11 and ctt-12. From parsimonious calculations of evolutionary distances since speciation, ctt-11, ctt-12, and ctn-ORFB evolved rapidly, while ctn-ORFE in C. tentans evolved slowly compared to other globin genes in the clusters. While these four globins are under selective pressure, we suggest that most chironomid globin genes were not selected for their unique function. Instead, we propose that high gene copy number itself was selected because conditions favored organisms that could synthesize more hemoglobin. High gene copy number selection to produce more of a useful product may be the basis of forming multigene families, all of whose members initially accumulate neutral substitutions while retaining essential function. Maintenance of a large family of globin genes not only ensured high levels of hemoglobin production, but may have facilitated the extensive divergence of chironomids into as many as 5000 species. Received: 31 December 1996 / Accepted: 16 May 1997