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Data analytic procedures are proposed to examine the adequacy of the hypothesized link used in fitting a generalized linear model. Through model expansion and linearization, tests and estimation techniques are provided. These procedures, along with the release of GLIM3, enable the user to examine routinely and objectively the fit of an hypothesized model. Examples are presented to illustrate the testing and fitting procedure.

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Left ventricular hypertrophy (LVH), a target organ response in essential hypertension, is only weakly related to clinical measurements of blood pressure. To determine whether blood pressure measured under basal or stress conditions more closely determines LVH, we compared echocardiographic left ventricular mass index and relative wall thickness with clinical blood pressure and with 24 hr recordings (home, work, and sleep) in 19 normal subjects and 81 patients with mild hypertension. Only a weak correlation was observed in the entire group between left ventricular mass index and clinical measurements of systolic and diastolic blood pressure (r = .24, p < .02; r = .20, p < .05, respectively), which was only slightly improved by use of systolic and diastolic blood pressure readings taken in the home (r = .31, p < .005; r = .21, p < .05, respectively). Sleep and total 24 hr blood pressure also related poorly to left ventricular mass index. In contrast, substantially higher correlations existed between left ventricular mass index and systolic and diastolic blood pressure measured by portable recorder in 60 subjects at work (r = .50, p < .001; r = .39, p < .01, respectively). Similarly, work diastolic blood pressure bore the closest relationship to relative wall thickness (r = .59, p < .001). Home blood pressure readings taken on a work day also showed a moderate relationship with indices of LVH, whereas weaker correlations were found in employed subjects whose blood pressure was recorded on a non-workday, and no relationship between blood pressure and LVH existed in subjects who were not employed. We conclude that hypertensive LVH is poorly related to clinical or home measurements of blood pressure but that a substantially closer relationship exists between LVH and blood pressure during recurring stress at work and between LVH and home blood pressure on a workday. Thus hypertensive cardiac hypertrophy appears to be more closely related to blood pressure during stressful Circulation 68, No. 3, 470-476, 1983. NUMEROUS STUDIES have demonstrated that the risk of disease and death increases as blood pressure rises.'4 However, despite the consistency of this finding and its high statistical significance in large populations, the actual correlations between blood pressure measurements and the incidence of morbid events have generally been relatively low.'4 One possible explana-

This paper considers the franlework of the so-called "market basket problem", in which a database of transactions is mined for the occurrence of unusually frequent item sets. h~ our case, "unusually frequent" involves estimates of the frequency of each item set divided by a baseline frequency computed as if items occurred independently. The focus is on obtaining reliable estimates of this measure of interestingness for all item sets, even item sets with relatively low frequencies. For example, in a medical database of patient histories, unusual item sets including the item "patient death" (or other serious adverse event) might hopefully be flagged with as few as 5 or 10 occurrences of" the item set, it being unacceptable to require that item sets occur in as many as 0.1% of millions of patient reports before the data mining algorithm detects a signal. Similar considerations apply in fraud detection applications.Thus we abandon the requirement that interesting item sets must contain a relatively large fixed minimal support, and adopt a criterion based on the results of fitting an empirical Bayes model to the item set counts. The model allows us to define a 95% Bayesian lower confidence limit for the "interestingness" measure of every item set, whereupon the item sets can be ranked according to their empirical Bayes confidence limits. For item sets of size J > 2, we also distinguish between muhi-item associations that can be explained by the observed J(J-l)12 pairwise associations, and item sets that are significantly more frequent than their pairwise associations would suggest. Such item sets can uncover complex or synergistic mechanisms generating multi-item associations. This methodology has been applied within the U.S. Food and Drug Administration (FDA) to databases of adverse drug reaction reports and within AT&T to customer international calling histories. We also present graphical techniques for exploring and understanding the modeling results.

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Logistic regression-type models are used in many applications. Some examples include the classical dose-response experiment, prospective and retrospective studies of disease incidence (with and without matching), and the analysis of ordinal data. In most instances, the model is fitted by the method of maximum likelihood, which, like least squares, is sensitive to atypical observations. An alternative to maximum likelihood is proposed and illustrated by examples.

A method is proposed for examining a linear model for the presenceof one or more important outliers-deviant observations which have a potentially large influence on the resulting parameter estimates. For this purpose, a new statistic is proposed and its distributional properties are discussed. The method itself is exploratory in nature, but exact significance tests are available. Several examples illustrate the method. Computational aspects are discussed.