Olcay Akman

A study of log-logistic model in survival analysis

In survival analysis when the mortality reaches a peak after some finite period and then slowly declines, it is appropriate to use a model which has a nonmonotonic failure rate. In this paper we study the log-logistic model whose failure rate exhibits the above behavior and its mean residual life behaves in the reverse fashion. The maximum likelihood estimation of the parameters is examined and it is proved analytically that unique maximum likelihood estimates exist for the parameters. A lung cancer data set is analyzed. Confidence intervals for the parameters as well as for the critical points of the failure rate and mean residual life functions are obtained for the high performance status (PS) and low PS subgroups, where the term performance status is a measure of general medical status.

Relationships among Water-Quality Parameters from the North Inlet–Winyah Bay National Estuarine Research Reserve, South Carolina

Abstract Estuaries integrate atmospheric, watershed, oceanic, and human influences over space and time. Therefore, spatial and temporal patterns in estuarine water-column properties are useful as metrics to evaluate external factors related to internal processes. The National Estuarine Research Reserve monitoring program, including the North Inlet–Winyah Bay complex in South Carolina, provides an ideal setting to track water quality relationships. Our goal was to assess hydrography, chlorophyll a, and particulate and dissolved materials from monitoring data collected at sites from both the salt and estuarine marsh components since 1993–94. Salinity, turbidity, dissolved organic carbon, suspended solids, and chlorophyll a were much greater at the estuarine site, whereas organic nitrogen dominated the total nitrogen pool at both locations. Nitrate was a significant fraction of the total nitrogen pool at the estuarine site but not within the salt marsh. Whereas dissolved organic nitrogen was positively correlated to water temperature, nitrate concentrations were the lowest in the summer. Principal components analysis identified seasonal patterns within the salt marsh for temperature, chlorophyll a, ammonium, suspended solids, and particulate nitrogen. These parameters, grouped together as a primary component, were positively correlated to Spartina alterniflora biomass. In contrast, the estuarine site was more characterized by salinity, pH, and dissolved organic carbon. Although the water-column properties of the salt marsh site reflected a high degree of internal production and remineralization in the summer, patterns at the estuarine site were more likely influenced by seasonal changes in circulation and biogeochemical processing common to coastal plain estuaries.

Analysis of body size and fecundity in a grasshopper

Abstract We used linear regression, nonlinear regression and principal component analysis to examine the relationships among morphology, fecundity, and mating variables for lab-reared adult female Romalea microptera (Beauvois) (fam. Romaleidae) grasshoppers. Morphological variables included head width, pronotum length, femur length, adult eclosion mass, maximum mass reached before the 1st oviposition, and maximum mass reached before the 2nd oviposition. Fecundity (= reproductive) variables included clutch size Pod 1, clutch size Pod 2, total eggs Pods 1 + 2, mass Pod 1, mass Pod 2, time between adult eclosion and Pod 1, time between Pod 1 and Pod 2, and time between eclosion and Pod 2. Mating variables included number of matings and age of 1st mating. Most morphological variables were strongly positively correlated, and morphological variables (especially femur length, eclosion mass, and maximum body mass reached prior to oviposition) predicted many fecundity variables. Maximum body mass reached prior to laying Pod 1 was highly correlated with maximum body mass reached prior to laying Pod 2 (r =0 .93), and clutch size Pod 1 predicted clutch size Pod 2 (r = 0.72). However, time to oviposit (= interval between adult eclosion and oviposition) was generally unrelated to body size, body mass, or clutch size or mass. Hence, clutch size and pod mass are strongly determined by body size and mass at adult eclosion, but timing of oviposition is independent of body size and mass at eclosion. The results also suggest that early mating speeds oviposition, but that excessive mating reduces female fecundity, as measured by clutch size.

Transformations of the Lognormal Distribution as a Selection Model

Abstract The length-biased lognormal distribution arises as a weighted lognormal distribution, via a process that distorts the probability of observations being selected. In this note we present some interesting transformations of the lognormal distribution to recover the information lost due to this lopsided selection process.

Estimation of critical points in the mixture inverse Gaussian model

The maximum likelihood estimation for the critical points of the failure rate and the mean residual life function are presented in the case of mixture inverse Gaussian model. Several important data sets are analyzed from this point of view. For each of the data sets, Bootstrapping is used to construct confidence intervals of the critical points.

Bayes computation for reliability estimation

Bayes estimation of complicated functions requires simpler estimation techniques due to the mathematical difficulties involved in the classical Bayes approach. Bayes estimation enjoys many approximation techniques and computational methods like Metropolis, and Gibbs sampler. Bayes estimation of the reliability of a mixture inverse Gaussian distribution requires a numerical approach since the calculations are immensely difficult from the exact Bayes point of view. Lack of full conditional prior distributions for all 3 parameters of this particular case makes the use of Gibbs sampler inefficient. Application of the rejection method, however, is reasonable since it is very simple to implement without any constraints on the prior distributions or on the hyper-parameters.

An evolutionary computing approach for parameter estimation investigation of a model for cholera

We consider the problem of using time-series data to inform a corresponding deterministic model and introduce the concept of genetic algorithms (GA) as a tool for parameter estimation, providing instructions for an implementation of the method that does not require access to special toolboxes or software. We give as an example a model for cholera, a disease for which there is much mechanistic uncertainty in the literature. We use GA to find parameter sets using available time-series data from the introduction of cholera in Haiti and we discuss the value of comparing multiple parameter sets with similar performances in describing the data.

Density-dependent polyphenism and geographic variation in size among two populations of lubber grasshoppers (Romalea microptera)

1. Density‐dependent phase polyphenism occurs when changes in density during the juvenile stages result in a developmental shift from one phenotype to another. Density‐dependent phase polyphenism is common among locusts (Orthoptera: Acrididae).

RELIABILITY ESTIMATION VIA LENGTH-BIASED TRANSFORMATION

The length-biased distribution arises as a weighted sampling distribution, via a process which distorts the probability of observations being selected. In this article we discuss estimation of reliability of the original distribution using information contained in length-biased sampling distribution. This could be achieved either by modeling the data with the length-biased version of the original random variable or by using a stochastic transformation which connects length-biased distribution to the original one. The first approach has been studied broadly in the literature, hence we present the latter.

Ontogenetic Mechanisms Underlying a Geographic Size Cline in a Grasshopper, Romalea microptera

ABSTRACT Geographic clines in body size have been described for many species, but relatively few investigations have tested hypotheses for the ontogenetic mechanisms maintaining geographic clines. We formalize and test the predictions for the role of ontogenetic mechanisms (e.g., hatching timing and size, juvenile developmental time, juvenile growth rate) in maintaining a longitudinal cline in adult body size of lubber grasshoppers [Romalea microptera (Beauvois)]. To obtain hatching timing and size, we collected eggs from wild females from several populations along the longitudinal gradient in 2 yr (2006 and 2007) and measured hatchling size and hatch date. To obtain juvenile developmental time and growth rates, we surveyed populations along the longitudinal gradient during 2 yr (2006 and 2007) and estimated developmental time and growth rates. We found the developmental time (hatching to fourth instar) and female growth rates increase from west to east along the cline. Patterns of hatching timing and hatching size were not consistent with the size cline. The size cline becomes evident in the third instar and is magnified in the fourth and fifth instars. Our data suggest that the size cline arises from some combination of clinal variation in developmental time and female growth rates; prolonged development and greater growth rates lead to larger mean size. Equally important, we found no evidence that differences in hatching time or size are ontogenetic causes of this cline. Our hypotheses for ontogenetic mechanisms producing an adult size cline should serve as a template for ecologists seeking to understand the ontogenetic basis of spatial variation in phenotypes.