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Regression modelling is an important statistical tool frequently utilized by cardiothoracic surgeons. However, these models-including linear, logistic and Cox proportional hazards regression-rely on certain assumptions. If these assumptions are violated, then a very cautious interpretation of the fitted model should be taken. Here, we discuss several assumptions and report diagnostics that can be used to detect departures from these assumptions. Most of the diagnostics discussed are based on residuals: a measure of the difference between the observed and model fitted values. Reliable and generalizable results depend on correctly developed statistical models, and proper diagnostics should play an integral part in the model development.
This article was published in the following journal.
Name: Interactive cardiovascular and thoracic surgery
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Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.
A principle of estimation in which the estimates of a set of parameters in a statistical model are those quantities minimizing the sum of squared differences between the observed values of a dependent variable and the values predicted by the model.
The constant checking on the state or condition of a patient during the course of a surgical operation (e.g., checking of vital signs).
Functions constructed from a statistical model and a set of observed data which give the probability of that data for various values of the unknown model parameters. Those parameter values that maximize the probability are the maximum likelihood estimates of the parameters.
A statistical analytic technique used with discrete dependent variables, concerned with separating sets of observed values and allocating new values. It is sometimes used instead of regression analysis.