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.     

Nonparametric inference on median residual life function

Summary .  A simple approach to the estimation of the median residual lifetime is proposed for a single group by inverting a function of the Kaplan–Meier estimators. A test statistic is proposed to compare two median residual lifetimes at any fixed time point. The test statistic does not involve estimation of the underlying probability density function of failure times under censoring. Extensive simulation studies are performed to validate the proposed test statistic in terms of type I error probabilities and powers at various time points. One of the oldest data sets from the National Surgical Adjuvant Breast and Bowel Project (NSABP), which has more than a quarter century of follow-up, is used to illustrate the method. The analysis results indicate that, without systematic post-operative therapy, a significant difference in median residual lifetimes between node-negative and node-positive breast cancer patients persists for about 10 years after surgery. The new estimates of the median residual lifetime could serve as a baseline for physicians to explain any incremental effects of post-operative treatments in terms of delaying breast cancer recurrence or prolonging remaining lifetimes of breast cancer patients.     

An additive‐multiplicative mean residual life model for right‐censored data

Many studies have focused on determining the effect of the body mass index (BMI) on the mortality in different cohorts. In this article, we propose an additive‐multiplicative mean residual life (MRL) model to assess the effects of BMI and other risk factors on the MRL function of survival time in a cohort of Chinese type 2 diabetic patients. The proposed model can simultaneously manage additive and multiplicative risk factors and provide a comprehensible interpretation of their effects on the MRL function of interest. We develop an estimation procedure through pseudo partial score equations to obtain parameter estimates. We establish the asymptotic properties of the proposed estimators and conduct simulations to demonstrate the performance of the proposed method. The application of the procedure to a study on the life expectancy of type 2 diabetic patients reveals new insights into the extension of the life expectancy of such patients.     

Nonparametric inference on cause‐specific quantile residual life

In medical research, investigators are often interested in inferring time‐to‐event distributions under competing risks. It is well known, however, that the naive approach based on the Kaplan–Meier method to estimate the proportion of cause‐specific events overestimates the true quantity. In this paper, we show that the quantile residual life function, a natural and popular summary measure of survival data, could be also seriously affected by the competing events. An existing two‐sample test statistic for inference on median residual life is modified for competing risks data, which does not involve estimation of the improper probability density function of the subdistribution of cause‐specific events under censoring. Simulation results demonstrate that the test statistic controls the type 1 error probabilities reasonably well. The proposed method is applied to a real data example from a large‐scale phase III breast cancer study.     

Mean residual life cure models for right-censored data with and without length-biased sampling

We propose a semiparametric mean residual life mixture cure model for right-censored survival data with a cured fraction. The model employs the proportional mean residual life model to describe the effects of covariates on the mean residual time of uncured subjects and the logistic regression model to describe the effects of covariates on the cure rate. We develop estimating equations to estimate the proposed cure model for the right-censored data with and without length-biased sampling, the latter is often found in prevalent cohort studies. In particular, we propose two estimating equations to estimate the effects of covariates in the cure rate and a method to combine them to improve the estimation efficiency. The consistency and asymptotic normality of the proposed estimates are established. The finite sample performance of the estimates is confirmed with simulations. The proposed estimation methods are applied to a clinical trial study on melanoma and a prevalent cohort study on early-onset type 2 diabetes mellitus.     

Life table assay of field-caught Mediterranean fruit flies, Ceratitis capitata, reveals age bias

Though traps are used widely to sample phytophagous insects for research or management purposes, and recently in aging research, possible bias stemming from differential response of individuals of various ages to traps has never been examined. In this paper, we tested the response of Ceratitis capitata (Wiedemann) (Diptera: Tephritidae) males and females of four ages (spanning from 1 to 40 days) to McPhail-type traps baited with a synthetic food attractant in field cages and found that the probability of trapping was significantly influenced by age. The type of food on which flies were maintained before testing (sugar or protein) also had a strong effect and interacted with age. In another experiment, we collected wild C. capitata adults of unknown age using 1–3 methods and then reared them in the laboratory until death. The survival schedules of these flies were subsequently used in a life table assay to infer their age at the time of capture. Results showed that on a single sampling date, males captured in traps baited with a food attractant were younger compared with males aspirated from fruiting host trees, or males captured in traps baited with a sex attractant. Likewise, females captured in food-baited traps were younger compared with aspirated females. In addition to providing the first evidence of age-dependent sampling bias for a phytophagous insect species, this paper also provides a novel approach to estimate the differences in the age composition of samples collected with different techniques. These findings are of utmost importance for several categories of insects, medically important groups notwithstanding.     

Inbreeding alters context‐dependent reproductive effort and immunity in male crickets

Infection can cause hosts to drastically alter their investment in key life‐history traits of reproduction and defence. Infected individuals are expected to increase investment in defence (e.g., by increasing immune function) and, due to trade‐offs, investment in other traits (e.g., current reproduction) should decrease. However, the terminal investment hypothesis postulates that decreased lifespan due to infection and the associated reduction in the expectation for future offspring will favour increased investment towards current reproduction. Variation in intrinsic condition will likely influence shifts in reproductive investment post‐infection, but this is often not considered in such assessments. For example, the extent of inbreeding can significantly impact an individual's lifetime fitness and may influence its reproductive behaviour following a threat of infection. Here, we investigated the effects of inbreeding status on an individual's reproductive investment upon infection, including the propensity to terminally invest. Male crickets (Gryllodes sigillatus) from four genetically distinct inbred lines and one outbred line were subjected to a treatment from an increasing spectrum of simulated infection cue intensities, using heat‐killed bacteria. We then measured reproductive effort (calling effort), survival and immune function (antibacterial activity, circulating haemocytes and haemocyte microaggregations). Inbred and outbred males diverged in how they responded to a low‐dose infection cue: relative to unmanipulated males, outbred males decreased calling effort, whereas inbred males increased calling effort. Moreover, we found that inbred males exhibited higher antibacterial activity and numbers of circulating haemocytes compared with outbred males. These results suggest that an individual's inbreeding status may have consequences for context‐dependent shifts in reproductive strategies, such as those triggered by infection.     

How should we interpret and distinguish subsidiary cells?

The concept of subsidiary cells is discussed in the light of the existing literature correlating ontogeny arid mature structure. The protodermal origin of each epidermal component is illustrated and explained and the status of the ontogenetic classifications of these components has been analysed and discussed. Terminology is also defined and discussed.     

Effect of Danshen on the Zero-Stress State of Rat's Abdominal Aorta

The objective of our study was to study the effect of danshen, a Chinese herbal medicine known to prevent hypertension, on the zero-stress state of rat's abdominal aorta. The zero-stress state of a blood vessel represents the release of residual stress on the vessel wall, and is the basic configuration of blood vessel affected solely by intrinsic parameters. At the in vivo state, the rat's abdominal aorta was subjected to blood pressure and flow and longitudinal stress. After dissecting from the abdominal aorta, the aortic specimens were cut into small rings at no-load state, in which the internal pressure, external pressure, and longitudinal stress in a short ring-shaped segment were all zero; by cutting radially to release the residual stress in the wall, the vessel ring opened up into a sector quickly, and the sector's configuration would not change at 20 min after cutting and was defined as the zero-stress state of a blood vessel, which was characterized by its residual strain and opening angle. Then aqueous extract of danshen prepared with methanol was added in the Krebs solution, and the changes of the aorta's zero-stress state were monitored by taking photos routinely for analysis to determine the opening angle and residual strain. Additionally, other sets of samples were tested in a Norepinephrine-Krebs solution as positive control or a Krebs solution as negative control, respectively. It was demonstrated that the zero-stress state of rat's abdominal aorta was affected by danshen extract and norepinephrine in two different patterns, while the Krebs solution did not have similar effects. The present work provides a new approach to study the anti-hypertension effect and mechanism of danshen.     

Demographic window to aging in the wild: constructing life tables and estimating survival functions from marked individuals of unknown age

Summary We address the problem of establishing a survival schedule for wild populations. A demographic key identity is established, leading to a method whereby age-specific survival and mortality can be deduced from a marked cohort life table established for individuals that are randomly sampled at unknown age and marked, with subsequent recording of time-to-death. This identity permits the construction of life tables from data where the birth date of subjects is unknown. An analogous key identity is established for the continuous case in which the survival schedule of the wild population is related to the density of the survival distribution in the marked cohort. These identities are explored for both life tables and continuous lifetime data. For the continuous case, they are implemented with statistical methods using non-parametric density estimation methods to obtain flexible estimates for the unknown survival distribution of the wild population. The analytical model provided here serves as a starting point to develop more complex models for residual demography, i.e. models for estimating survival of wild populations in which age-at-entry is unknown and using remaining information in randomly encountered individuals. This is a first step towards a broad new concept of 'expressed demographic information content of marked or captured individuals'.     

Diagnostic Measures of Influence for s2

We present three intuitive diagnostic measures for judging the influence that single or multiple observations exert on the estimate s², the mean square error. The three measures are shown to be equivalent statistics. We discuss distributional properties of these measures and conclude with an example.     

Observation of residual dipolar couplings in short peptides

Residual dipolar couplings provide information on the orientation of individual bond vectors with respect to a unique set of molecular axes. We report that short peptides from 2 to 15 amino acids in length of arbitrary sequence exhibit a modest range of residual dipolar couplings when aligned in either strained polyacrylamide gels or alkyl-PEG bicelles. The absence of significant line broadening in gels suggests peptides align predominantly through steric interactions with the polyacrylamide matrix. However, broadening of NMR lines for a subset of residues aligned in bicelles indicates some peptides bind weakly to these lipid disks, yet a weak negative correlation between the couplings measured in gels and bicelles is consistent with steric hindrance playing a role in both media. The observation of dipolar couplings for peptides of length 10-15 suggests the statistical segment lengths of polypeptide chains must often be >10-15 residues, with data from denatured proteins indicating even larger values. Presumably, local side-chain backbone interactions severely restrict chain flexibility, with the cumulative effect of many such restrictions giving rise to biases in chain direction that may persist for the entire length of a protein chain. Comparison of experimental dipolar couplings for peptides with couplings calculated for ensembles of conformations generated by molecular dynamics should permit evaluation of the accuracy of molecular mechanics potentials in reproducing sequence-specific preferences for phi and psi angles.