would likely be deemed equivalent by very few people Second, the creation of a composite outcome might obscure differences between the individual outcomes Third, the risk for the component outcomes may be different with different associations In our example, we would not be able to detect if any variables were associated specifically with intensive care unit admission We would only be able to assess association with the composite outcome Thus specific outcomes should be favored over composite outcomes when feasible and relevant Data Description and Planning the Analysis A clear understanding of the basic characteristics of the study data is necessary to plan subsequent steps in analysis Description of the data is important in detailing the characteristics of the subjects to be studied, usually at baseline, and it allows the researcher to determine what next steps in analysis are feasible or valid Description is also used to determine issues that might have an impact on statistical testing, such as extreme values or outliers, missing values, categories with too few values, and skewed distributions These issues are very important in selecting appropriate statistical testing to help answer the research question Types of Relationships Between Variables An important defining feature of variables is the relationship between them The aim of many studies is to determine relationships that are cause leading to effect; this concept is termed causality The nature of associations and features of study designs that help to give confidence that a discovered association is cause and effect will be described later in this chapter Confounding occurs when the independent variable is associated with the dependent variable primarily through its relationship with a further independent variable that is more directly related to the dependent variable Confounding is most likely to occur when independent variables are highly related or correlated with one another, which is referred to as collinearity For example, a hypothetical study shows an association between increased use of systemic anticoagulation and increased risk of death after the Fontan procedure Consideration is given to recommending against the use of routine anticoagulation Further analysis, however, reveals that the use of systemic anticoagulation was predominately in those patients with poor ventricular function Poor ventricular function is then found to be causally and strongly related to mortality, and the association of anticoagulation with mortality is felt to be indirect and confounded because of its increased use in patients with poor ventricular function To combat confounding, stratified, or multivariable analyses are often used to explore, detect, and adjust for confounding and to determine relationships between variables that are most likely to be independent of other variables Interaction is a particular type of relationship between two or more independent variables and a dependent variable in which relationship between one independent variable and the dependent variable is influenced or modified by an additional independent variable For example, in our hypothetical study, further analysis shows that the relationship between systemic anticoagulation and mortality is more complex For patients with poor ventricular function who are treated with systemic anticoagulation, mortality is less than for those not treated For patients without poor ventricular function, there is no difference in mortality between those treated versus not treated with systemic anticoagulation Thus there is an important interaction present between systemic anticoagulation and poor ventricular function as demonstrated by the differential association of anticoagulation with mortality in the presence of poor ventricular function, but anticoagulation on its own does not influence mortality Principles of Probability and Probabilistic Distribution: the Science of Statistics Statistics is the science of how we make and test predictions about the true nature of the world based on measurements The distribution of our measured data has significant implications for how well we can predict an outcome, and these implications and how statistics accounts for them is the subject of this section While conducting a census of every citizen of a given country, you find that the proportion of women in the population is exactly 52%, and that their average systolic blood pressure is 100 mm Hg You select a random sample of 100 people from this same population and, to your surprise, 55% of your sample is composed of women, and their average blood pressure is 95 mm Hg Subsequently, you decide to select a second random sample of 100 people This time, 47% of your sample is women, and their average blood pressure is 106 mm Hg Why do these measures differ from one another and from the census (true) values in the population? The phenomenon at play here is called random error Each individual sample taken randomly from a larger population will have an uncertain distribution in terms of characteristics The distribution of characteristics in each sample is a description of the probability of each value for a given characteristic in the sample This distribution can be plotted into a probability curve The shape of each curve and the probability it implies have specific properties about the variation that allow us to be able to predict how frequently a given outcome will be observed in an infinite number of random samples This is the basis for statistical inference Inference Based on Samples From Random Distributions When we measure something in a research study, we may find that the values from our study subjects are different from what we might note in a normal or an alternative population We want to know if our findings represent a true deviation from normal or whether they were just due to chance or random effect Inferential statistics use probability distributions based on characteristics of the overall population to tell us what the likelihood might be for our observation in our subjects given that our subjects come from the overall population We can never know for certain if our subjects truly deviate from the norm, but we can infer the probability of our observation from the probability distribution In general, we assume that if we can be 95% certain and accept a 5% chance that our observation is really not different from normal, or the center of the probability distribution, then we state that our results are significant The probability that the observed result may be due to chance alone represents the P value of inferential statistics When a random sample is selected from a population, differences between the sample and population are due to the random effect, or random error Although the entire population in our census had an average systolic blood pressure of 100 mm Hg, this does not mean that everyone in this population had a blood pressure of 100 mm Hg Some had 90 mm Hg and others had 120 mm Hg Hence, if you select a random sample of 100 people, some will have higher or lower blood pressure By chance alone, it might be that a specific sample of the population will have more people with higher blood pressure As long as the sample was randomly chosen, the mean of your sample should be close to the mean of the