Abstract
Uplift modeling, a predictive modeling technique, empowers marketers or other researchers to identify the ‘true’ treatment responders who would be most positively influenced by the treatment or intervention through uncovering their characteristics separately from the characteristics of baseline or control responders (that is, those who would have responded anyway). This article briefly reviews the concept of uplift modeling and extends the current work to multiple treatment situations (where at least two treatments are available as options). It discusses the mathematical problem of optimizing treatment at the individual level, and proposes a practical heuristic solution. Finally, it presents a framework accounting for the variability in estimates when handling multiple assignments. An example from an online retailer is used to illustrate the methodologies.
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Notes
We will later introduce the concept of uplift modeling, where
would represent the incremental response (or lift) from the baseline control group. The objective function would then be to maximize the number of incremental responders due to treatment (over natural responders).There may be a different cost associated with contacting each individual – for example, the highest value customers may be reached with outbound telemarketing but the rest with a lower cost touch such as direct mail or email. Alternatively, higher value customers may have a different service level so the direct mail creative material for them may be different, or customers in different geographic regions may be contacted differently.
Prescriptive analytics is a recently popular industry term for applying analytics to support decision making, similar to operations research and management science; see Lustig et al (2010) and Banerjee et al (2013).
In marketing, this means contacting them would produce a negative effect. This can happen in certain retention efforts where customer contacts could lead to a higher attrition rate (sometimes known as ‘waking up the sleeping dog’ phenomenon). In medicine, this refers to the situation where the medical treatment has an adverse effect on certain individuals.
Separating model training and model assessment in randomly split training sample and holdout sample, respectively, is a standard practice recommended in the machine learning or data mining literature to minimize the bias of model assessment; see, for example, Hastie et al (2011) and James et al (2013).
Alternative clustering algorithms can be attempted and the number of clusters, K, can be pre-specified or determined through data analysis such as a scree plot; see Hastie et al (2011) for example.
In case more than one cluster solution is available (because of different clustering algorithms or different uplift models), one may choose the cluster solution with the cluster level lift scores as far from the overall sample lift scores as possible, that is, the solution such that the following Euclidean distance is the greatest, in order to support optimization: Euclidean distance to the overall sample mean=
where 
are the overall sample lift scores for treatments 1, …, M, respectively (averaging over all individuals in the entire holdout sample), and N
k
is the sample size of cluster k.Details of the data can be found at Kevin Hillstrom’s site at: http://blog.minethatdata.com/2008/03/minethatdata-e-mail-analytics-and-data.html. The data set has been analyzed in other papers such as Kane et al (2014).
In this example, two original clusters are merged into cluster 1 due to low quantities.
The efficient frontier can be calculated in multiple ways. It can be obtained by solving the MVO problem (5) in the section ‘A risk/return tradeoff approach’, or by solving one of two equivalent formulations: minimize the variance subject to a constraint on the expected lift, or maximize the expected lift subject to a constraint on the variance. See Chapter 7 in Fabozzi et al (2007) for a discussion of the three equivalent approaches.
would represent the incremental response (or lift) from the baseline control group. The objective function would then be to maximize the number of incremental responders due to treatment (over natural responders).
where 
are the overall sample lift scores for treatments 1, …, M, respectively (averaging over all individuals in the entire holdout sample), and N
k
is the sample size of cluster k.References
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The authors would like to thank Florence H. Yong and Kathleen Kane for reviewing an earlier version of this paper.
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Lo, V., Pachamanova, D. From predictive uplift modeling to prescriptive uplift analytics: A practical approach to treatment optimization while accounting for estimation risk. J Market Anal 3, 79–95 (2015). https://doi.org/10.1057/jma.2015.5
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DOI: https://doi.org/10.1057/jma.2015.5