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Direct regression for the cumulative incidence function (CIF) has become increasingly popular since the Fine and Gray model was suggested (Fine and Gray) due to its more direct interpretation on the probability risk scale. We here consider estimation within the Fine and Gray model using the theory of semiparametric efficient estimation. We show that the Fine and Gray estimator is semiparametrically efficient in the case without censoring. In the case of right-censored data, however, we show that the Fine and Gray estimator is no longer semiparametrically efficient and derive the semiparametrically efficient estimator. This estimation approach involves complicated integral equations, and we therefore also derive a simpler estimator as an augmented version of the Fine and Gray estimator with respect to the censoring nuisance space. While the augmentation term involves the CIF of the competing risk, it also leads to a robustness property: the proposed estimators remain consistent even if one of the models for the censoring mechanism or the CIF of the competing risk are misspecified. We illustrate this robustness property using simulation studies, comparing the Fine–Gray estimator and its augmented version. When the competing cause has a high cumulative incidence we see a substantial gain in efficiency from adding the augmentation term with a very reasonable computation time. for this article are available online. [ABSTRACT FROM AUTHOR]

Traumatic brain injury (TBI) is among the most devastating of injuries leading to death and disability among young people today. The major cause of TBI is motor vehicle crashes. One way to reduce the rates of such crashes and thus TBI is through prevention programs. This article analyzes a study conducted for assessing a 1-day educational traffic injury prevention program for young traffic offenders with speeding violations. The obtained data include information about traffic convictions for speeding violations on a group of 16-to 23-year-old drivers. A common method for analyzing such studies is to use simple two-sample rank tests on summary statistics. But this approach ignores the detailed conviction process information and can assess only the long-term overall effect of the program. In this article, we treat the data as recurrent event data and apply a novel approach based on counting processes to evaluate the program. Our approach makes use of the information ignored by the rank tests and allows the assessment of both short- and long-term effects of the program. The analysis results indicate that the prevention program has an effect for a short period and suggest that a long-term effect could be gained if the program is repeated. [ABSTRACT FROM AUTHOR]

In this article we survey existing results concerning the joint distribution of the sequence of estimates of the parameter vector when a model is fitted to accumulating data and provide a unified theory that explains the "independent increments" structure commonly seen in group-sequential test statistics. Our theory covers normal linear models, including the case of correlated observations, and asymptotic results extend to generalized linear models and the proportional hazards regression model for survival data. The asymptotic results are derived using standard methods for the nonsequential case, and they hold as long as these nonsequential techniques are applicable at each individual analysis. In all cases, the joint distribution of the sequence of parameter estimates has the same form, exactly or asymptotically, as that of the sequence of means of an increasing number of independent, identically distributed normal variables. Thus our results provide the formal basis for extending the scope of standard group-sequential methods to a wide range of problems. [ABSTRACT FROM AUTHOR]

When survival data can be divided into natural groups, such as in a clinical trial with patients from a number of different institutions, the question arises whether effects are different for the different groups. For situations where one is concerned with a random pattern of variation over groups, this article proposes testing the null hypothesis of no variation using statistics based on the sums of martingale residuals over subjects within groups. These tests are closely related to the locally most powerful tests of Lung for testing for variation across a large number of strata. The tests are applied to data from a lung cancer trial conducted by the Eastern Cooperative Oncology Group. [ABSTRACT FROM AUTHOR]

The article comments on the professor D.R. Cox's regression model. At the same time, the present article gives just a hint of how Cox's regression model can be extended in many useful ways. Also, taking Cox's model as an example, the article contains an introduction on a very intuitive level to the statistical theory of counting processes that is currently being used. The article will encourage those analyzing censored survival data to make use of the model. Even if a clinical cancer trial is designed to answer a simple yes/no question on the relative benefits of two treatments, there is no reason why after the trial, the data should not also be analyzed in a more exploratory fashion to look for variables or combinations of variables of prognostic importance and to quantify their simultaneous effects, or to look more closely at how a particular treatment influences survival, perhaps it only improves the hazard rate during the course of treatment and has no lasting effect. Just to provide motivation for the estimators used, Cox had to introduce a new principle for inference, based on the concept of partial likelihood.