Group-Sequential Analysis Incorporating Covariate Information

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...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1997-12, Vol.92 (440), p.1330-1341
Main Authors: Jennison, Christopher, Turnbull, Bruce W.
Format: Article
Language:English
Subjects:
Analytical estimating
Applications
Biology, psychology, social sciences
Censored data
Censored survival data
Clinical trials
Counting processes
Estimation
Estimation theory
Exact sciences and technology
General linear model
Generalized linear model
Group-sequential testing
Insurance, economics, finance
Longitudinal data
Martingales
Mathematics
Maximum likelihood estimation
Medical sciences
Mixed-effects model
Multivariate analysis
Parametric models
Probability and statistics
Proportional hazards regression model
Regression analysis
Reliability, life testing, quality control
Repeated measurements
Sciences and techniques of general use
Score statistics
Statistical analysis
Statistical data
Statistical models
Statistical theories
Statistical variance
Statistics
Theory and Methods
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Description
Summary: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.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1997.10473654