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Today our professor was discussing Sutradhar, Gu and Paszat (2016). In this paper the authors decided to study the relationships between patient characteristics and following the "advice" of their doctors.

While reading this paper, I noticed (e.g., Page 4) that variables such as "Age" and "Neighborhood Income" are binned into quintiles. I have often read that arbitrary binning (e.g., why quintiles, why not deciles?) of a continuous variable should be avoided as it can both lead to biases as well as phenomena such as "p-hacking". As an example, is it possible that the authors tried different combinations of binning criteria until one of these criteria produced meaningful results?


My question: Ideally speaking, should this "binning" process not have been done and these variables (i.e., age, income) treated as continuous? Could it be said that this "binning" process might potentially take away from the results in this paper and add biases when compared to treating these variables as continuous?

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    $\begingroup$ Yes, this could be the case, although it is also probable that the authors got this data in this format already, and in that case there was probably no hacking involved. Some surveys still ask the participants to put their age in one of the pre-defined age groups. $\endgroup$ Commented Jan 12, 2023 at 7:15
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    $\begingroup$ Harrell’s Regression Modeling Strategies even discusses some reasons why surveys might do that. I recall an example about how people might be reluctant to give their exact salary but might be more willing to identify the range to which their salary belongs, so then it becomes a tradeoff between lower accuracy from having bins vs lower accuracy due to possible missing data. $\endgroup$
    – Dave
    Commented Jan 13, 2023 at 16:55
  • $\begingroup$ You can also use either interval arithmetic or Bayesian priors to represent the uncertainty in the unknown values within a bin. $\endgroup$
    – Galen
    Commented Jan 13, 2023 at 17:03
  • $\begingroup$ Thank you so much for your replies everyone! $\endgroup$
    – stats_noob
    Commented Jan 16, 2023 at 16:27

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should this "binning" process not have been done and these variables (i.e., age, income) treated as continuous?

Yes. Presumably this was done to allow for a non-linear effect of age (e.g. so that the difference between the first and third quintile need not be twice the difference of the first and second) but this approach leads to residual confounding and in some cases -- like using deciles -- spends degrees of freedom needlessly.

Instead, authors should use splines as recommended by Frank Harrell in his book Regression Modelling Strategies.

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  • $\begingroup$ @ Demetri Pananos: thank you for your answer! I have always heard that splines are complicated in the sense that its easy to overfit the data... I should try to learn more about this topic. Thank you so much! $\endgroup$
    – stats_noob
    Commented Feb 7, 2023 at 16:12
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    $\begingroup$ @stats_noob "I have always heard that splines are complicated in the sense that its easy to overfit the data." -- depends on the type of spline, depends on the degrees of freedom, depends on the knot locations, but splines are a great way to add non-linearity into the conditional mean $\endgroup$ Commented Feb 7, 2023 at 17:02
  • $\begingroup$ Thank you for your reply! I am interested in trying to learn more about GAM and survival splines $\endgroup$
    – stats_noob
    Commented Feb 7, 2023 at 19:41

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