Collider-stratification bias

In public health research, adjusting for confounders using multivariable methods is a popular practice. That is necessary to deal with the menace of confounders. However, adjusting for confounders should be accomplished with the utmost care because a not-well-thought-about adjustment can take the data “from the frying pan into the fire”. To this end, multivariable analysis should not be a laissez faire practice where one plugs in as many variables as possible into the multivariable model and then see what comes out of the model. It should rather be carefully guided by a conceptual framework or causal diagrams. The mechanism by which each variable operates should be duly considered and analysis done accordingly. Otherwise, an unwise attempt to control so-called confounders would end up in biasing estimates.

      

Among such biases is a collider-stratification bias. Collider is “a variable directly affected by two or more variables in a causal diagram”^[1] (Figure 1). If variable C is directly affected by both variables X and Y, stratifying on (or controlling) C while assessing the association of X with Y, or the association of both X and Y with some other variable Z, tends to change the association between the variables X and Y^{[1, 2]}. That is, it may cause a spurious association to emerge between X and Y while there is none^{[2, 3]}; it may also cause a statistical association between the outcome of interest and an unmeasured factor U that is also causal of C while actually the variables are independent^[4] thus forcing the unmeasured variable U to be a confounder. Controlling the collider may also cause a risk factor to appear protective^[4]. Such biases resulting from controlling a collider variable during data analysis are called collider-stratification biases^[2] or biases due to conditioning on a collider^[3].

Fig. 1: A collider variable. Variable C is directly affected by both variables X and Y.

Ipso facto, as a way of avoiding collider-stratification bias, collider variables should not be controlled (or adjusted for) in multivariable models ^[2].

References and additional reading materials:

1.       Porta M, editor. A Dictionary of Epidemiology. 5th ed. New York: Oxford University Press; 2008.

2.       Greenland S. Quantifying Biases in Causal Models: Classical Confounding vs Collider-Stratification Bias. Epidemiology. 2003;14(3):300 –6.

3.       Cole SR, Platt RW, Schisterman EF, Chu H, Westreich D, Richardson D, et al. Illustrating bias due to conditioning on a collider. International Journal of Epidemiology. 2010;39:417-20.

4.       Whitcomb BW, Schisterman EF, Perkins NJ, Platt RW. Quantification of collider-stratification bias and the birthweight paradox. Paediatric and Perinatal Epidemiology. 2009;23:394-402.