### Abstract

The augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems. An important component of this method is the propensity score. Popular parametric models for the propensity score include the logistic, probit, and complementary log-log models. A common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables. To avoid the need to choose a model, we model the propensity score via a semiparametric single-index model, in which the score is an unknown monotonic nondecreasing function of the given single index. Under this new model, the augmented inverse weighting estimator (AIWE) of the mean of the response is asymptotically linear, semiparametrically efficient, and more robust than existing estimators. Moreover, we have made a surprising observation. The inverse probability weighting and AIWEs based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model. A heuristic explanation of this phenomenon is provided. A real-data example is used to illustrate the proposed methods.

Original language | English (US) |
---|---|

Pages (from-to) | 1442-1458 |

Number of pages | 17 |

Journal | Statistics in Medicine |

Volume | 38 |

Issue number | 8 |

DOIs | |

State | Published - Apr 15 2019 |

### Fingerprint

### Keywords

- causal inference
- empirical process
- inverse weighting
- missing data
- pool adjacent violation algorithm
- single-index model

### ASJC Scopus subject areas

- Epidemiology
- Statistics and Probability

### Cite this

*Statistics in Medicine*,

*38*(8), 1442-1458. https://doi.org/10.1002/sim.8048

**Using a monotone single-index model to stabilize the propensity score in missing data problems and causal inference.** / Qin, Jing; Yu, Tao; Li, Pengfei; Liu, Hao; Chen, Baojiang.

Research output: Contribution to journal › Article

*Statistics in Medicine*, vol. 38, no. 8, pp. 1442-1458. https://doi.org/10.1002/sim.8048

}

TY - JOUR

T1 - Using a monotone single-index model to stabilize the propensity score in missing data problems and causal inference

AU - Qin, Jing

AU - Yu, Tao

AU - Li, Pengfei

AU - Liu, Hao

AU - Chen, Baojiang

PY - 2019/4/15

Y1 - 2019/4/15

N2 - The augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems. An important component of this method is the propensity score. Popular parametric models for the propensity score include the logistic, probit, and complementary log-log models. A common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables. To avoid the need to choose a model, we model the propensity score via a semiparametric single-index model, in which the score is an unknown monotonic nondecreasing function of the given single index. Under this new model, the augmented inverse weighting estimator (AIWE) of the mean of the response is asymptotically linear, semiparametrically efficient, and more robust than existing estimators. Moreover, we have made a surprising observation. The inverse probability weighting and AIWEs based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model. A heuristic explanation of this phenomenon is provided. A real-data example is used to illustrate the proposed methods.

AB - The augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems. An important component of this method is the propensity score. Popular parametric models for the propensity score include the logistic, probit, and complementary log-log models. A common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables. To avoid the need to choose a model, we model the propensity score via a semiparametric single-index model, in which the score is an unknown monotonic nondecreasing function of the given single index. Under this new model, the augmented inverse weighting estimator (AIWE) of the mean of the response is asymptotically linear, semiparametrically efficient, and more robust than existing estimators. Moreover, we have made a surprising observation. The inverse probability weighting and AIWEs based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model. A heuristic explanation of this phenomenon is provided. A real-data example is used to illustrate the proposed methods.

KW - causal inference

KW - empirical process

KW - inverse weighting

KW - missing data

KW - pool adjacent violation algorithm

KW - single-index model

UR - http://www.scopus.com/inward/record.url?scp=85058860772&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85058860772&partnerID=8YFLogxK

U2 - 10.1002/sim.8048

DO - 10.1002/sim.8048

M3 - Article

C2 - 30566258

AN - SCOPUS:85058860772

VL - 38

SP - 1442

EP - 1458

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 8

ER -