Synthesizing secondary data into survival analysis to improve estimation efficiency

The accelerated failure time (AFT) model and Cox proportional hazards (PH) model are broadly used for survival endpoints of primary interest. However, the estimation efficiency from those models can be further enhanced by incorporating the information from secondary outcomes that are increasingly available and highly correlated with primary outcomes. Those secondary outcomes could be longitudinal laboratory measures collected from doctor visits or cross-sectional disease-relevant variables, which are believed to contain extra information related to primary survival endpoints to a certain extent. In this paper, we develop a two-stage estimation framework to combine a survival model with a secondary model that contains secondary outcomes, named as the empirical-likelihood-based weighting (ELW), which comprises two weighting schemes accommodated to the AFT model (ELW-AFT) and the Cox PH model (ELW-Cox), respectively. This innovative framework is flexibly adaptive to secondary outcomes with complex data features, and it leads to more efficient parameter estimation in the survival model even if the secondary model is misspecified. Extensive simulation studies showcase more efficiency gain from ELW compared to conventional approaches, and an application in the Atherosclerosis Risk in Communities study also demonstrates the superiority of ELW by successfully detecting risk factors at the time of hospitalization for acute myocardial infarction.     

Symmetric tests and confidence intervals for survival probabilities and quantiles of censored survival data

We describe existing tests and introduce two new tests concerning the value of a survival function. These tests may be used to construct a confidence interval for the survival probability at a given time or for a quantile of the survival distribution. Simulation studies show that error rates can differ substantially from their nominal values, particularly at survival probabilities close to zero or one. We recommend our new constrained bootstrap test for its good overall performance.     

Simultaneous estimation ofV max,Km, and the rate of endogenous substrate production (R) from substrate depletion data

The nonlinear and 3 linearized forms of the integrated Michaelis-Menten equation were evaluated for their ability to provide reliable estimates of uptake kinetic parameters, when the initial substrate concentration (S₀) is not error-free. Of the 3 linearized forms, the one where t/(S₀–S) is regressed against ln(S₀/S)/(S₀–S) gave estimates ofV _max and K_m closest to the true population means of these parameters. Further, this linearization was the least sensitive of the 3 to errors (±1%) in S₀. Our results illustrate the danger of relying on r² values for choosing among the 3 linearized forms of the integrated Michaelis-Menten equation. Nonlinear regression analysis of progress curve data, when S₀ is not free of error, was superior to even the best of the 3 linearized forms. The integrated Michaelis-Menten equation should not be used to estimateV _max and K_m when substrate production occurs concomitant with consumption of added substrate. We propose the use of a new equation for estimation of these parameters along with a parameter describing endogenous substrate production (R) for kinetic studies done with samples from natural habitats, in which the substrate of interest is an intermediate. The application of this new equation was illustrated for both simulated data and previously obtained H₂ depletion data. The only means by whichV _max, K_m, and R may be evaluated from progress curve data using this new equation is via nonlinear regression, since a linearized form of this equation could not be derived. Mathematical components of computer programs written for fitting data to either of the above nonlinear models using nonlinear least squares analysis are presented.     

Individual-based perspectives on R(0)

Without doubt the basic reproductive ratio, R(0), is the most widely used quantity in epidemic theory. Standard compartmental models show how R(0)is related to the average age of infection, vaccination thresholds for eradication and equilibrium solutions. However, many of the basic formulae for R(0)break down when we consider transmission of infection to be a stochastic process involving discrete individuals. This paper clarifies why and when these differences arise and predicts when individual-based considerations are likely to be important in modelling infection dynamics.     

Generation interval contraction and epidemic data analysis

The generation interval is the time between the infection time of an infected person and the infection time of his or her infector. Probability density functions for generation intervals have been an important input for epidemic models and epidemic data analysis. In this paper, we specify a general stochastic SIR epidemic model and prove that the mean generation interval decreases when susceptible persons are at risk of infectious contact from multiple sources. The intuition behind this is that when a susceptible person has multiple potential infectors, there is a "race" to infect him or her in which only the first infectious contact leads to infection. In an epidemic, the mean generation interval contracts as the prevalence of infection increases. We call this global competition among potential infectors. When there is rapid transmission within clusters of contacts, generation interval contraction can be caused by a high local prevalence of infection even when the global prevalence is low. We call this local competition among potential infectors. Using simulations, we illustrate both types of competition. Finally, we show that hazards of infectious contact can be used instead of generation intervals to estimate the time course of the effective reproductive number in an epidemic. This approach leads naturally to partial likelihoods for epidemic data that are very similar to those that arise in survival analysis, opening a promising avenue of methodological research in infectious disease epidemiology.     

Nonparametric and semiparametric estimation with sequentially truncated survival data

In observational cohort studies with complex sampling schemes, truncation arises when the time to event of interest is observed only when it falls below or exceeds another random time, that is, the truncation time. In more complex settings, observation may require a particular ordering of event times; we refer to this as sequential truncation. Estimators of the event time distribution have been developed for simple left-truncated or right-truncated data. However, these estimators may be inconsistent under sequential truncation. We propose nonparametric and semiparametric maximum likelihood estimators for the distribution of the event time of interest in the presence of sequential truncation, under two truncation models. We show the equivalence of an inverse probability weighted estimator and a product limit estimator under one of these models. We study the large sample properties of the proposed estimators and derive their asymptotic variance estimators. We evaluate the proposed methods through simulation studies and apply the methods to an Alzheimer's disease study. We have developed an R package, seqTrun , for implementation of our method.     

Bayesian estimation of movement and survival probabilities from capture-recapture data

The Arnason–Schwarz model is usually used for estimatingsurvival and movement probabilities of animal populations fromcapture-recapture data. The missing data structure of this capture-recapturemodel is exhibited and summarised via a directed graph representation.Taking advantage of this structure we implement a Gibbs samplingalgorithm from which Bayesian estimates and credible intervalsfor survival and movement probabilities are derived. Convergenceof the algorithm is proved using a duality principle. We illustrateour approach through a real example.     

Remarks on the conservatism of sigma(0 -- E)2/E in survival data.

This note presents theoretical and numerical calculations which investigate the adequacy of the sigma(0 -- E)2/E approximation (Peto and Pike [1973]) when applying the Mantel/Haenszel summary chisquare statistic to the comparison of r life tables in the manner suggested by Mantel [1966], Peto and Peto [1972], and Cox [1972]. These indicate that conservatism is mild unless there are marked differences in the withdrawal patterns in the r tables. Such differences may, however, be anticipated in the case of a generalization of the life table procedure suggested by Crowley [1973], Mantel and Byar [1974], and Turnbull, Brown, and Hu [1974], wherein individuals are moved from one life table to another according to changes in their treatment (or other) statuses.     

The estimation of parameters from population data on the general stochastic epidemic

This paper provides a method of using maximum likelihood to estimate the two unknown parameters, the contact rate and the removal rate, in the general stochastic epidemic, using only the observed interremoval times and the total number of cases occurring. A goodness-of-fit test is discussed, and the methods described are illustrated by means of data on an actual smallpox epidemic in a restricted community in southeastern Nigeria.     

Combining syndromic surveillance and ILI data using particle filter for epidemic state estimation

Designing effective mitigation strategies against influenza outbreak requires an accurate prediction of a disease’s future course of spreading. Real time information such as syndromic surveillance data and influenza-like-illness (ILI) reports by clinicians can be used to generate estimates of the current state of spreading of a disease. Syndromic surveillance data are immediately available, in contrast to ILI reports that require data collection and processing. On the other hand, they are less credible than ILI data because they are essentially behavioral responses from a community. In this paper, we present a method to combine immediately-available-but-less-reliable syndromic surveillance data with reliable-but-time-delayed ILI data. This problem is formulated as a non-linear stochastic filtering problem, and solved by a particle filtering method. Our experimental results from hypothetical pandemic scenarios show that state estimation is improved by utilizing both sets of data compared to when using only one set. However, the amount of improvement depends on the relative credibility and length of delay in ILI data. An analysis for a linear, Gaussian case is presented to support the results observed in the experiments.     

A comparison of reflected versus test-based confidence intervals for the median survival time, based on censored data

The small-sample performance of some recently proposed nonparametric methods of constructing confidence intervals for the median survival time, based on randomly right-censored data, is compared with that of two new methods. Most of these methods are equivalent for large samples. All proposed intervals are either 'test-based' or 'reflected' intervals, in the sense defined in the paper. Coverage probabilities for the interval estimates were obtained by exact calculation for uncensored data, and by stimulation for three life distributions and four censoring patterns. In the range of situations studied, 'test-based' methods often have less than nominal coverage, while the coverage of the new 'reflected' confidence intervals is closer to nominal (although somewhat conservative), and these intervals are easy to compute.     

Distribution-free regression analysis of grouped survival data

Methods based on regression models for logarithmic hazard functions, Cox models, are given for analysis of grouped and censored survival data. By making an approximation it is possible to obtain explicitly a maximum likelihood function involving only the regression parameters. This likelihood function is a convenient analog to Cox's partial likelihood for ungrouped data. The method is applied to data from a toxicological experiment.     

Germination,seedling occurrence and seedling survival of Spinifex sericeus R. Br. (Poaceae)

Abstract Spinifex sericeus is a clonal, perennial, dioecious, coastal foredune grass that is often used in beach rehabilitation programmes. The objectives of this study were to: (i) investigate the germination behaviour of S. sericeus; and (ii) examine the occurrence and survivorship of 5. sericeus seedlings in the dune systems on the mid-north coast of NSW. Diaspores and naked caryopses of S. sericeus require darkness for germination. Diaspore germination is adversely affected by leaching, probably due to the creation of anaerobic conditions around the caryopsis. Seedling emergence occurs mainly on the front of the foredune, as this is an area of active sand accretion and burial is necessary for germination. The presence of a hypocotyl allows germination and emergence from depths as great as 12.5 cm. In the two populations studied, seedling survival was low and probably made little contribution to population recruitment. The factors that appear to be responsible for the high mortality rate of seedlings are sand erosion, sand deposition and desiccation.     

Synthesis and antioxidant evaluation of (S,S)- and (R,R)-secoisolariciresinol diglucosides (SDGs)

Secoisolariciresinol diglucosides (SDGs) (S,S)-SDG-1 (major isomer in flaxseed) and (R,R)-SDG-2 (minor isomer in flaxseed) were synthesized from vanillin via secoisolariciresinol (6) and glucosyl donor 7 through a concise route that involved chromatographic separation of diastereomeric diglucoside derivatives (S,S)-8 and (R,R)-9. Synthetic (S,S)-SDG-1 and (R,R)-SDG-2 exhibited potent antioxidant properties (EC₅₀ = 292.17 ± 27.71 μM and 331.94 ± 21.21 μM, respectively), which compared well with that of natural (S,S)-SDG-1 (EC₅₀ = 275.24 ± 13.15 μM). These values are significantly lower than those of ascorbic acid (EC₅₀ = 1129.32 ± 88.79 μM) and α-tocopherol (EC₅₀ = 944.62 ± 148.00 μM). Compounds (S,S)-SDG-1 and (R,R)-SDG-2 also demonstrated powerful scavenging activities against hydroxyl [natural (S,S)-SDG-1: 3.68 ± 0.27; synthetic (S,S)-SDG-1: 2.09 ± 0.16; synthetic (R,R)-SDG-2: 1.96 ± 0.27], peroxyl [natural (S,S)-SDG-1: 2.55 ± 0.11; synthetic (S,S)-SDG-1: 2.20 ± 0.10; synthetic (R,R)-SDG-2: 3.03 ± 0.04] and DPPH [natural (S,S)-SDG-1: EC₅₀ = 83.94 ± 2.80 μM; synthetic (S,S)-SDG-1: EC₅₀ = 157.54 ± 21.30 μM; synthetic (R,R)-SDG-2: EC₅₀ = 123.63 ± 8.67 μM] radicals. These results confirm previous studies with naturally occurring (S,S)-SDG-1 and establish both (S,S)-SDG-1 and (R,R)-SDG-2 as potent antioxidants and free radical scavengers for potential in vivo use.