Ørnulf Borgan

Survival and Event History Analysis

An introduction to survival and event history analysis.- Stochastic processes in event history analysis.- Nonparametric analysis of survival and event history data.- Regression models.- Parametric counting process models.- Unobserved heterogeneity: The odd effects of frailty.- Multivariate frailty models.- Marginal and dynamic models for recurrent events and clustered survival data.- Causality.- First passage time models: Understanding the shape of the hazard rate.- Diffusion and L#x00E9 vy process models for dynamic frailty.

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 Coxs 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/.

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.

Linear Nonparametric Tests for Comparison of Counting Processes, with Applications to Censored Survival Data, Correspondent Paper

This paper surveys linear nonparametric oneand k-sample tests for counting processes. The necessary probabilistic background is outlined and a master theorem proved, which may be specialized to most known asymptotic results for linear rank tests for censored data as well as to asymptotic results for oneand k-sample tests in more general situations, an important feature being that very general censoring patterns are allowed. A survey is given of existing tests and their relation to the general theory, and we mention examples of applications to Markov processes. We also discuss the relation of the present approach to classical nonparametric hypothesis testing theory based on permutation distributions.

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.

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.

Survival prediction from clinico-genomic models - a comparative study

BackgroundSurvival prediction from high-dimensional genomic data is an active field in todays medical research. Most of the proposed prediction methods make use of genomic data alone without considering established clinical covariates that often are available and known to have predictive value. Recent studies suggest that combining clinical and genomic information may improve predictions, but there is a lack of systematic studies on the topic. Also, for the widely used Cox regression model, it is not obvious how to handle such combined models.ResultsWe propose a way to combine classical clinical covariates with genomic data in a clinico-genomic prediction model based on the Cox regression model. The prediction model is obtained by a simultaneous use of both types of covariates, but applying dimension reduction only to the high-dimensional genomic variables. We describe how this can be done for seven well-known prediction methods: variable selection, unsupervised and supervised principal components regression and partial least squares regression, ridge regression, and the lasso. We further perform a systematic comparison of the performance of prediction models using clinical covariates only, genomic data only, or a combination of the two. The comparison is done using three survival data sets containing both clinical information and microarray gene expression data. Matlab code for the clinico-genomic prediction methods is available at http://www.med.uio.no/imb/stat/bmms/software/clinico-genomic/.ConclusionsBased on our three data sets, the comparison shows that established clinical covariates will often lead to better predictions than what can be obtained from genomic data alone. In the cases where the genomic models are better than the clinical, ridge regression is used for dimension reduction. We also find that the clinico-genomic models tend to outperform the models based on only genomic data. Further, clinico-genomic models and the use of ridge regression gives for all three data sets better predictions than models based on the clinical covariates alone.

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.

On the theory of moving average graduation

Abstract In this paper a new criterion for judging the properties of moving averages is given, and moving averages which are optimal according to this criterion under general assumptions are derived. For the standard case where the observations are uncorrelated and have equal variance, our optimal moving averages generalize two well-known optimal moving averages: The minimum-variance and the minimum-Rz moving averages. This case is given some particular attention in the theoretical discussion, and some Monte Carlo experiments throw further light on it. These investigations indicate that our generalization is of practical as well as theoretical interest. The paper also contains the result that Spencers 21-term moving average is approximately equal to the corresponding minimum-R 5 moving average.

A nonasymptotic criterion for the evaluation of automobile bonus systems

Abstract A new criterion for the evaluation of automobile bonus systems is proposed. It states that a bonus system should be constructed such as to minimize a weighted average of the expected squared rating errors in various insurance periods. The criterion generalizes an asymptotic criterion given earlier by Norberg in 1976. In addition, the new nonasymptotic criterion makes it possible to discuss various short term aspects such as the optimal choice of starting class and the time heterogeneity of risks. Our treatment is illustrated by examples with numerical results.