Focus on: Contemporary Methods in Biostatistics (I)Regression Modeling StrategiesEstrategias para la elaboración de modelos estadísticos de regresión
Introduction
Multivariable regression models are widely used in health science research. Data are frequently collected to investigate interrelationships among variables or to determine factors affecting an outcome of interest. It is here where multivariable regression models become a tool to find a simplified mathematical explanation between the candidate predictors and the outcome. The ultimate goal is to derive a parsimonious model that makes sense from the subject matter point of view, closely matches the observed data, and has valid predictions on independent data.
Due to advances in statistical software, which have made them friendlier to the user, more researchers with limited background in biostatistics are now engaged in data analysis. Thus, the goal of this review is to provide practical advice on how to build a parsimonious and more effective multivariable model. The overall steps in any regression model exercise are listed in Table 1. Due to limited space, only the most practical points are presented.
Section snippets
Data structure and type of regression analysis
Regression models share a general form that should be familiar to most, usually: response = weight1 × predictor1 + weight2 × predictor2 + … weightk × predictork | normal error term. The variable to be explained is called the dependent (or response) variable. When the dependent variable is binary, the medical literature refers to it as an outcome (or endpoint). The factors that explain the dependent variable are called independent variables, which encompass the variable of interest (or explanatory variable)
Data manipulation
Not infrequently, the data require clean-up before fitting the model. Three important areas need to be considered here:
- 1.
Missing data. This is a ubiquitous problem in health science research. Three types of missingness mechanisms have been distinguished19: missing completely at random (MCAR), missing at random (MAR) and not missing at random (NMAR) (Table 3). Multiple imputation was developed for dealing with missing data under MAR and MCAR assumptions by replacing missing values with a set of
Model building strategies
Variable selection is a crucial step in the process of model creation (Table 1). Including in the model the right variables is a process heavily influenced by the prespecified balance between complexity and parsimony (Table 3). Predictive models should include those variables that reflect the pattern in the population from which our sample was drawn. Here, what matters is the information that the model as a whole represents. For effect estimation, however, a fitted model that reflects the
Final model evaluation
Central to the idea of building a regression model is the question of model performance assessment. A number of model performance metrics have been proposed, although they can be grouped in two main categories: calibration and discrimination measures (Table 1, Table 3). Independent of the aim for which the model was created, these two performance measures need to be derived from the data which gave origin to the model, or even better, through bootstrap resampling (known as internal validity).
Results presentation
The final consideration in the process of model creation is how the estimated parameters will be presented. Commonly, the statistical packages, when comparing two groups on a binary outcome, express the effect size of the explanatory variable in relative metrics. For logistic and Cox regressions, the OR and HR are the traditional metrics to indicate the degree of association found between a factor and the outcome. Because these are a ratio of proportions, the information conveyed about their
Conflicts of interest
None declared.
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