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Impairment of left ventricular function is the major predictor of mortality after acute myocardial infarction, but it is not known whether this is best described by ejection fraction or by endsystolic or end-diastolic volume. We measured volumes, ejection fractions, and severity of coronary arterial occlusions and stenoses in 605 male patients under 60 years of age at 1 to 2 months after a first (n = 443) or recurrent (n = 162) myocardial infarction and followed these patients for a mean of 78 months for survivors (range 15 to 165 months). There were 101 cardiac deaths, 71 (70%) of which were sudden (instantaneous or found dead). Multivariate analysis with log rank testing and the Cox proportional hazards model showed that end-systolic volume (X2 = 82.9) had greater predictive value for survival than end-diastolic volume (X2 = 59.0) or ejection fraction (X2 = 46.6), whereas stepwise analysis showed that once the relationship between survival and end-systolic volume had been fitted, there was no additional significant predictive information in either end-diastolic volume or ejection fraction. Severity of coronary occlusions and stenoses showed additional prediction of only borderline significance (p = .04 in one analysis), but continued cigarette smoking did remain an independent risk factor after stepwise analysis. For a subset of patients (n = 200) who had taken part in a randomized trial of coronary artery surgery after recovery from infarction, surgical "intention to treat" showed no predictive value. We conclude that for prediction, end-systolic volume is the primary predictor of survival after myocardial infarction, being superior to ejection fraction when ejection fraction is low (<50%) or when end-systolic volume is high (< 100 ml). Treatment of infarction should be aimed at limitation of infarct size and prevention of ventricular dilation.Circulation 76, No. 1, 44-51, 1987. IT IS NOW RECOGNIZED that the major predictor of long-term survival after recovery from acute myocardial infarction is the functional status of the left ventricle. Left ventricular function has usually been described in terms of the ejection fraction (EF),1-4 but it is not clear whether EF is the most meaningful index of left ventricular function in the postinfarction situation. Low EF may, on the one hand, be caused by poor contractile function due to extensive myocardial damage or continuing ischemia or, on the other hand, to left ventricular dilation caused by infarct expansion and stretching of the myocardial scar. Thus end-systolic volume (ESV) or end-diastolic volume (EDV) might be more meaningful predictors of prognosis than

This paper discusses the thought processes involved in statistical problem solving in the broad sense from problem formulation to conclusions. It draws on the literature and in-depth interviews with statistics students and practising statisticians aimed at uncovering their statistical reasoning processes. From these interviews, a four-dimensional framework has been identified for statistical thinking in empirical enquiry. It includes an investigative cycle, an interrogative cycle, types of thinking and dispositions. We have begun to characterise these processes through models that can be used as a basis for thinking tools or frameworks for the enhancement of problem-solving. Tools of this form would complement the mathematical models used in analysis and address areas of the process of statistical investigation that the mathematical models do not, particularly areas requiring the synthesis of problem-contextual and statistical understanding. The central element of published definitions of statistical thinking is "variation". We further discuss the role of variation in the statistical conception of real-world problems, including the search for causes.

This paper discusses the thought processes involved in statistical problem solving in the broad sense from problem formulation to conclusions. It draws on the literature and in-depth interviews with statistics students and practising statisticians aimed at uncovering their statistical reasoning processes. From these interviews, a four-dimensional framework has been identified for statistical thinking in empirical enquiry. It includes an investigative cycle, an interrogative cycle, types of thinking and dispositions. We have begun to characterise these processes through models that can be used as a basis for thinking tools or frameworks for the enhancement of problem-solving. Tools of this form would complement the mathematical models used in analysis and address areas of the process of statistical investigation that the mathematical models do not, particularly areas requiring the synthesis of problem-contextual and statistical understanding. The central element of published definitions of statistical thinking is "variation". We further discuss the role of variation in the statistical conception of real-world problems, including the search for causes.

SUMMARY Vector smoothing is used to extend the class of generalized additive models in a very natural way to include a class of multivariate regression models. The resulting models are called ‘vector generalized additive models‘. The class of models for which the methodology gives generalized additive extensions includes the multiple logistic regression model for nominal responses, the continuation ratio model and the proportional and non‐proportional odds models for ordinal responses, and the bivariate probit and bivariate logistic models for correlated binary responses. They may also be applied to generalized estimating equations.