Send to

Choose Destination
J Causal Inference. 2014 Mar;2(1):1-12.

Monotone Confounding, Monotone Treatment Selection and Monotone Treatment Response.

Author information

Departments of Epidemiology and biostatistics, Harvard School of Public Health, Boston, MA, USA,
Peking University, Beijing, China.
Division of Biostatistics, Clinical Research Center, Kinki University School of Medicine, Osaka, Japan,


Manski (1997) and Manski and Pepper (2000) gave sharp bounds on causal effects under the assumptions of monotone treatment response (MTR) and monotone treatment selection (MTS). VanderWeele (2008) provided bounds for binary treatment under an assumption of monotone confounding (MC). We discuss the relation between MC and MTS and provide bounds under various combinations of these assumptions. We show that MC and MTS coincide for a binary treatment, but MC does not imply MTS for a treatment variable with more than two levels.


bias; endogeneity; nonparametric bounds; partial identification

Supplemental Content

Full text links

Icon for PubMed Central
Loading ...
Support Center