Usage
• 183 views

# Residual Weighted Learning For Quantile Optimal Treatment Regimes

• Author / Creator
Xi Hu
• Optimal treatment regime, also called individualized treatment rule, is to seek a rule that assigns a treatment to the subject based on its covariates. It can be used in many areas such as: clinical studies, policy making and economics. In recent years, estimating optimal treatment regime has received considerable attention. However, most of the works focus on estimating the mean-optimal treatment regimes, while not many works have been done on estimating the quantile-optimal treatment regimes. In this thesis, we will focus on estimating quantile-optimal treatment regimes using the residuals. The quantile-optimal treatment regime is very important in many cases. For instance, if the interest is to find the optimal treatment regime to increase the benefit on the lower tails, or if the outcome distribution is heavily skewed, then estimating the quantile treatment regime is more desirable than the mean. In the former case, the optimal treatment regime should be the one which maximizes some quantile of the potential outcomes, and in the latter case, the treatment regime maximizing the median is more desirable than the one maximizing the mean. Wang et al. firstly worked on the single-index rule case in estimating then quantile-optimal treatment regime. However, the parameters indexing the quantile treatment regime estimated by their framework have large variances. This leads to the problem that their optimal treatment regime may be far away from the true optimal treatment regime, especially when the sample size is small.
To alleviate these problems, we proposed a new framework based on the residuals, which can be derive by removing the estimated common effect from the outcomes. Motivated by the residual learning framework proposed by Zhou et al. we remove the common effect from the observed outcomes, and define the rest as the residual. The quantile optimal treatment regime can be estimated from these residuals. However, it needs to note that quantile does not have the addition property as mean does. Therefore, this framework is limited to the case that removing the common effect does not change the order of the original outcomes.

From the four simulation examples, it can be seen that removing the common effect from the outcomes can significantly reduce the variances of the parameters indexing the treatment regime. This can stabilize the variance of value function. Further, even using smaller sample size data, the estimated quantile treatment regime is closer to the true treatment regime, comparing to the results from framework proposed by Wang et al.

We also analyzed Data ACTG175 using our proposed framework, and compare the results with Wang's framework on 9 quantile levels. It shows that in this data set, our new framework is comparable with the one from Wang et al. and on some of the quantile levels, our framework has better performance on providing higher value of the potential outcomes.

• Subjects / Keywords
Fall 2018
• Type of Item
Thesis
• Degree
Master of Science
• DOI
https://doi.org/10.7939/R3542JQ8F