Special issue dedicated to Odd O. Aalen

Lifetime Data Analysis -     

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.     

The Efficiency of Simple and Counter-matched Nested Case-control Sampling

This paper presents a study of the performance of simple and counter-matched nested case-control sampling relative to a full cohort study. First we review methods for estimating the regression parameters and the integrated baseline hazard for Cox's proportional hazards model from cohort and case-control data. Then the asymptotic distributional properties of these estimators are recapitulated, and relative efficiency results are presented both for regression and baseline hazard estimation.     

Estimating stage occupation probabilities in non-Markov models

We study non-Markov multistage models under dependent censoring regarding estimation of stage occupation probabilities. The individual transition and censoring mechanisms are linked together through covariate processes that affect both the transition intensities and the censoring hazard for the corresponding subjects. In order to adjust for the dependent censoring, an additive hazard regression model is applied to the censoring times, and all observed counting and “at risk” processes are subsequently given an inverse probability of censoring weighted form. We examine the bias of the Datta–Satten and Aalen–Johansen estimators of stage occupation probability, and also consider the variability of these estimators by studying their estimated standard errors and mean squared errors. Results from different simulation studies of frailty models indicate that the Datta–Satten estimator is approximately unbiased, whereas the Aalen–Johansen estimator either under- or overestimates the stage occupation probability due to the dependent nature of the censoring process. However, in our simulations, the mean squared error of the latter estimator tends to be slightly smaller than that of the former estimator. Studies on development of nephropathy among diabetics and on blood platelet recovery among bone marrow transplant patients are used as demonstrations on how the two estimation methods work in practice. Our analyses show that the Datta–Satten estimator performs well in estimating stage occupation probability, but that the censoring mechanism has to be quite selective before a deviation from the Aalen-Johansen estimator is of practical importance. N. Gunnes—Supported by a grant from the Norwegian Cancer Society.     

Dynamic path analysis—a new approach to analyzing time-dependent covariates

In this article we introduce a general approach to dynamic path analysis. This is an extension of classical path analysis to the situation where variables may be time-dependent and where the outcome of main interest is a stochastic process. In particular we will focus on the survival and event history analysis setting where the main outcome is a counting process. Our approach will be especially fruitful for analyzing event history data with internal time-dependent covariates, where an ordinary regression analysis may fail. The approach enables us to describe how the effect of a fixed covariate partly is working directly and partly indirectly through internal time-dependent covariates. For the sequence of times of event, we define a sequence of path analysis models. At each time of an event, ordinary linear regression is used to estimate the relation between the covariates, while the additive hazard model is used for the regression of the counting process on the covariates. The methodology is illustrated using data from a randomized trial on survival for patients with liver cirrhosis.     

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.     

Use of multiple imputation in supersampled nested case-control and case-cohort studies

Nested case-control and case-cohort studies are useful for studying associations between covariates and time-to-event when some covariates are expensive to measure. Full covariate information is collected in the nested case-control or case-cohort sample only, while cheaply measured covariates are often observed for the full cohort. Standard analysis of such case-control samples ignores any full cohort data. Previous work has shown how data for the full cohort can be used efficiently by multiple imputation of the expensive covariate(s), followed by a full-cohort analysis. For large cohorts this is computationally expensive or even infeasible. An alternative is to supplement the case-control samples with additional controls on which cheaply measured covariates are observed. We show how multiple imputation can be used for analysis of such supersampled data. Simulations show that this brings efficiency gains relative to a traditional analysis and that the efficiency loss relative to using the full cohort data is not substantial.     

A hierarchical frailty model applied to two-generation melanoma data

We present a hierarchical frailty model based on distributions derived from non-negative Lévy processes. The model may be applied to data with several levels of dependence, such as family data or other general clusters, and is an alternative to additive frailty models. We present several parametric examples of the model, and properties such as expected values, variance and covariance. The model is applied to a case-cohort sample of age at onset for melanoma from the Swedish Multi-Generation Register, organized in nuclear families of parents and one or two children. We compare the genetic component of the total frailty variance to the common environmental term, and estimate the effect of birth cohort and gender.