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Figure 2 | BMC Medical Research Methodology

Figure 2

From: Reducing bias through directed acyclic graphs

Figure 2

a-b. Diagrammatic equivalent of the 6-step process to determine if one obtains an unbiased estimate of the exposure of interest (X) on the Outcome by including a particular subset of covariates (see text for details of the specific steps). In this example, we are interested in minimizing the bias when estimating the causal effect of warming up on the risk of injury. In figure 2a, a possible causal diagram of variables that are associated with warming up (X) and injury (outcome) are shown. The main mediating variable is believed to be proprioception (balance and muscle-contraction coordination) during the game. Starting at the top of the figure, the coach affects the team motivation (including aggressiveness), which affects both the probability of previous injury and the player's compliance with warm-up exercises. A player's genetics affects their fitness level (along with the coach's fitness program) and whether there are any inherent connective tissue disorders (which leads to tissue weakness and injury). Both connective tissue disorders and fitness level affect neuromuscular fatigue, which independently affects proprioception during the game and the probability of injury. Finally, if the sport is a contact sport, the probability of previous injury is greater, as is the probability of minor bruises during the game that would affect proprioception. Although other causal models are also possible, we will use this one for illustrative purposes at this time. For this example, we have decided to include neuromuscular fatigue (Z1) and tissue weakness (Z2) in the statistical model. Step #1 is to ensure that these covariates are not descendants of (i.e. directly or indirectly caused by) warm-up exercises. Step 2 is illustrated in 2b. The open circle (previous injury, Z3) represents the only non-ancestor (an ancestor is direct or indirect cause of another variable) of warm up exercises (X), neuromuscular fatigue (Z1), tissue weakness (Z2) and injury (Outcome). It is therefore deleted from the causal diagram in figure 2b.

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