Modelling the spread of infectious salmon anaemia among salmon farms based on seaway distances between farms and genetic relationships between infectious salmon anaemia virus isolates.

Infectious salmon anaemia (ISA) is an important infectious disease in Atlantic salmon farming causing recurrent epidemic outbreaks worldwide. The focus of this paper is on tracing the spread of ISA among Norwegian salmon farms. To trace transmission pathways for the ISA virus (ISAV), we use phylogenetic relationships between virus isolates in combination with space-time data on disease occurrences. The rate of ISA infection of salmon farms is modelled stochastically, where seaway distances between farms and genetic distances between ISAV isolates from infected farms play prominent roles. The model was fitted to data covering all cohorts of farmed salmon and the history of all farms with ISA between 2003 and summer 2009. Both seaway and genetic distances were significantly associated with the rate of ISA infection. The fitted model predicts that the risk of infection from a neighbourhood infectious farm decreases with increasing seaway distance between the two farms. Furthermore, for a given infected farm with a given ISAV genotype, the source of infection is significantly more likely to be ISAV of a small genetic distance than of moderate or large genetic distances. Nearly half of the farms with ISA in the investigated period are predicted to have been infected by an infectious farm in their neighbourhood, whereas the remaining half of the infected farms had unknown sources. For many of the neighbourhood infected farms, it was possible to point out one or a few infectious farms as the most probable sources of infection. This makes it possible to map probable infection pathways.

Predicting survival from microarray data--a comparative study.

MOTIVATION: Survival prediction from gene expression data and other high-dimensional genomic data has been subject to much research during the last years. These kinds of data are associated with the methodological problem of having many more gene expression values than individuals. In addition, the responses are censored survival times. Most of the proposed methods handle this by using Cox's proportional hazards model and obtain parameter estimates by some dimension reduction or parameter shrinkage estimation technique. Using three well-known microarray gene expression data sets, we compare the prediction performance of seven such methods: univariate selection, forward stepwise selection, principal components regression (PCR), supervised principal components regression, partial least squares regression (PLS), ridge regression and the lasso. RESULTS: Statistical learning from subsets should be repeated several times in order to get a fair comparison between methods. Methods using coefficient shrinkage or linear combinations of the gene expression values have much better performance than the simple variable selection methods. For our data sets, ridge regression has the overall best performance. AVAILABILITY: Matlab and R code for the prediction methods are available at http://www.med.uio.no/imb/stat/bmms/software/microsurv/.

Covariate adjustment of event histories estimated from Markov chains: the additive approach.

Markov chain models are frequently used for studying event histories that include transitions between several states. An empirical transition matrix for nonhomogeneous Markov chains has previously been developed, including a detailed statistical theory based on counting processes and martingales. In this article, we show how to estimate transition probabilities dependent on covariates. This technique may, e.g., be used for making estimates of individual prognosis in epidemiological or clinical studies. The covariates are included through nonparametric additive models on the transition intensities of the Markov chain. The additive model allows for estimation of covariate-dependent transition intensities, and again a detailed theory exists based on counting processes. The martingale setting now allows for a very natural combination of the empirical transition matrix and the additive model, resulting in estimates that can be expressed as stochastic integrals, and hence their properties are easily evaluated. Two medical examples will be given. In the first example, we study how the lung cancer mortality of uranium miners depends on smoking and radon exposure. In the second example, we study how the probability of being in response depends on patient group and prophylactic treatment for leukemia patients who have had a bone marrow transplantation. A program in R and S-PLUS that can carry out the analyses described here has been developed and is freely available on the Internet.

Exposure stratified case-cohort designs.

A variant of the case-cohort design is proposed for the situation in which a correlate of the exposure (or prognostic factor) of interest is available for all cohort members, and exposure information is to be collected for a case-cohort sample. The cohort is stratified according to the correlate, and the subcohort is selected by stratified random sampling. A number of possible methods for the analysis of such exposure stratified case-cohort samples are presented, some of their statistical properties developed, and approximate relative efficiency and optimal allocation to the strata discussed. The methods are compared to each other, and to randomly sampled case-cohort studies, in a limited computer simulation study. We found that all of the proposed analysis methods performed well and were more efficient than a randomly sampled case-cohort study.

Aalen's linear model for sampled risk set data: a large sample study.

Borgan and Langholz (1997) describe a method for estimating the parameter functions in Aalen's linear hazard regression model from sampled risk set data. Using a counting process formulation and the martingale central limit theorem, we provide a study of the asymptotic distributional properties of the estimator. The results are applied to study the efficiencies of the nested case-control and counter-matched designs relative to a full cohort analysis.

Estimation of excess risk from case-control data using Aalen's linear regression model.

We introduce methods for statistical inference in Aalen's non-parametric linear regression model of disease incidence (Aalen, 1989, Statistics in Medicine 8, 907-925) from nested case-control data. These methods provide the basis for estimation of excess risk as a linear function of dose and absolute risk for a given exposure history. The methods are illustrated by estimating excess and absolute risks associated with radon exposure and smoking from nested case-control samples from the Colorado Plateau uranium miners cohort.

Estimation of absolute risk from nested case-control data.

Benichou and Gail (1995, Biometrics 51, 182-194) describe methods for estimating the absolute risk of developing disease given a set of covariate values over a specified time interval from a case-control study within a cohort. The methods are most suitable for unmatched case-control studies, and are restricted to categorical covariates. Expanding on methods for estimating relative mortality from nested case-control studies presented in Borgan and Langholz (1993, Biometrics 49, 593-602), we present methods for estimating absolute risk from individually matched nested case-control data. These methods accommodate continuous and time-dependent covariate histories, the sampling of cases, and various control sampling designs.

A method for checking regression models in survival analysis based on the risk score.

We propose to perform model check for the Cox and Aalen regression models using martingale residual processes grouped after the risk score. Asymptotic distributions of the grouped martingale residual processes are deduced, so both formal and graphical model check can be performed. The method is validated by stochastic simulation. A data example with patients with primary biliary cirrhosis of the liver is discussed.

Nonparametric estimation of relative mortality from nested case-control studies.

Andersen et al. (1985, Biometrics 41, 921-932) gave an estimator of the cumulative relative mortality comparing rates of death in an epidemiologic cohort to an external population as a function of time when covariate information is available on all cohort members. We present an analogous estimator when covariate information is known only on a nested case-control sample. Counting process techniques are used to show that this estimator is almost unbiased and an estimator of its variance is derived. Estimators of the relative mortality function, using kernel smoothing methods, and the average relative mortality over grouped time intervals are also presented. The methods are illustrated by comparing rates of lung cancer mortality in a cohort of Montana smelter workers to that in the United States population.

Efficiencies of experimental designs for an illness-death model.

Disease development is described by the progressive Markov illness-death model with one disease. The efficiencies of four experimental designs are discussed: the simple survival experiment, serial sacrifice, periodic diagnosis and complete observation. The discussion is based on the 'semiparametric' assumption of piecewise-constant intensities. Simple survival experiments are shown to have very low efficiency, serial sacrifice experiments to be moderately efficient, and periodic diagnosis to be almost as efficient as complete observation. An application to the analysis of the development of leukaemia in laboratory mice is given.

Decreasing leukemia risk in old AKR mice.

Leukemia incidence and survivorship were studied in 480 untreated adult female AKR mice using repeated blood testing on live animals and autopsy for diagnosis. The data were statistically analysed within the framework of a Markov illness-death model. The leukemia risk was close to zero below an age of four-five months, increased sharply to a maximum at eight-nine months, and then declined markedly. Old AKR mice therefore should be useful for studies of age dependent alterations that reduce the risk of leukemia development. The observed age-dependence of the leukemia risk is at variance with the simplest version of the multistep hypothesis. Allowing for individual tendencies for leukemia development, good correlation between expected and observed values can be obtained.

Nickel allergy and hand dermatitis in a stratified sample of the Danish female population: an epidemiological study including a statistic appendix.

The occurrence of nickel allergy and hand eczema has been investigated in a stratified sample (2 500) of the Danish female population by an interview technique. The incidence density (allergy intensity) has been estimated by standard maximum likelihood methods. The age-specific prevalence rates have been calculated by life table techniques. The incidence density has doubled in all age groups from 1948 to 1973. The highest prevalence rate of nickel allergy was found in the 45-year-olds (0.189 +/- 0.023). The possible interaction between nickel allergy and hand eczema was analysed by a Markov chain model. Compared with non-nickel-sensitive women, a woman who has become nickel sensitized ran an increased risk of developing hand eczema. And those who had first developed hand eczema ran an increased risk of subsequently developing nickel allergy. In future efforts to reduce direct skin contact with nickel, the close relation between nickel allergy and hand eczema should be the main argument. Statistical methods based on the incidence density will be useful in the evaluation of these efforts.