### Abstract

Propensity score methods, such as subclassification, are a common approach to control for confounding when estimating causal effects in non-randomized studies. Propensity score subclassification groups individuals into subclasses based on their propensity score values. Effect estimates are obtained within each subclass and then combined by weighting by the proportion of observations in each subclass. Combining subclass-specific estimates by weighting by the inverse variance is a promising alternative approach; a similar strategy is used in meta-analysis for its efficiency. We use simulation to compare performance of each of the two methods while varying (i) the number of subclasses, (ii) extent of propensity score overlap between the treatment and control groups (i.e., positivity), (iii) incorporation of survey weighting, and (iv) presence of heterogeneous treatment effects across subclasses. Both methods perform well in the absence of positivity violations and with a constant treatment effect with weighting by the inverse variance performing slightly better. Weighting by the proportion in subclass performs better in the presence of heterogeneous treatment effects across subclasses. We apply these methods to an illustrative example estimating the effect of living in a disadvantaged neighborhood on risk of past-year anxiety and depressive disorders among U.S. urban adolescents. This example entails practical positivity violations but no evidence of treatment effect heterogeneity. In this case, weighting by the inverse variance when combining across propensity score subclasses results in more efficient estimates that ultimately change inference.

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

Pages (from-to) | 4937-4947 |

Number of pages | 11 |

Journal | Statistics in Medicine |

Volume | 35 |

Issue number | 27 |

DOIs | |

State | Published - Nov 30 2016 |

### Fingerprint

### Keywords

- observational studies
- propensity score
- stratification
- subclassification

### ASJC Scopus subject areas

- Epidemiology
- Statistics and Probability

### Cite this

*Statistics in Medicine*,

*35*(27), 4937-4947. https://doi.org/10.1002/sim.7046

**Optimally combining propensity score subclasses.** / Rudolph, Kara E.; Colson, K. Ellicott; Stuart, Elizabeth; Ahern, Jennifer.

Research output: Contribution to journal › Article

*Statistics in Medicine*, vol. 35, no. 27, pp. 4937-4947. https://doi.org/10.1002/sim.7046

}

TY - JOUR

T1 - Optimally combining propensity score subclasses

AU - Rudolph, Kara E.

AU - Colson, K. Ellicott

AU - Stuart, Elizabeth

AU - Ahern, Jennifer

PY - 2016/11/30

Y1 - 2016/11/30

N2 - Propensity score methods, such as subclassification, are a common approach to control for confounding when estimating causal effects in non-randomized studies. Propensity score subclassification groups individuals into subclasses based on their propensity score values. Effect estimates are obtained within each subclass and then combined by weighting by the proportion of observations in each subclass. Combining subclass-specific estimates by weighting by the inverse variance is a promising alternative approach; a similar strategy is used in meta-analysis for its efficiency. We use simulation to compare performance of each of the two methods while varying (i) the number of subclasses, (ii) extent of propensity score overlap between the treatment and control groups (i.e., positivity), (iii) incorporation of survey weighting, and (iv) presence of heterogeneous treatment effects across subclasses. Both methods perform well in the absence of positivity violations and with a constant treatment effect with weighting by the inverse variance performing slightly better. Weighting by the proportion in subclass performs better in the presence of heterogeneous treatment effects across subclasses. We apply these methods to an illustrative example estimating the effect of living in a disadvantaged neighborhood on risk of past-year anxiety and depressive disorders among U.S. urban adolescents. This example entails practical positivity violations but no evidence of treatment effect heterogeneity. In this case, weighting by the inverse variance when combining across propensity score subclasses results in more efficient estimates that ultimately change inference.

AB - Propensity score methods, such as subclassification, are a common approach to control for confounding when estimating causal effects in non-randomized studies. Propensity score subclassification groups individuals into subclasses based on their propensity score values. Effect estimates are obtained within each subclass and then combined by weighting by the proportion of observations in each subclass. Combining subclass-specific estimates by weighting by the inverse variance is a promising alternative approach; a similar strategy is used in meta-analysis for its efficiency. We use simulation to compare performance of each of the two methods while varying (i) the number of subclasses, (ii) extent of propensity score overlap between the treatment and control groups (i.e., positivity), (iii) incorporation of survey weighting, and (iv) presence of heterogeneous treatment effects across subclasses. Both methods perform well in the absence of positivity violations and with a constant treatment effect with weighting by the inverse variance performing slightly better. Weighting by the proportion in subclass performs better in the presence of heterogeneous treatment effects across subclasses. We apply these methods to an illustrative example estimating the effect of living in a disadvantaged neighborhood on risk of past-year anxiety and depressive disorders among U.S. urban adolescents. This example entails practical positivity violations but no evidence of treatment effect heterogeneity. In this case, weighting by the inverse variance when combining across propensity score subclasses results in more efficient estimates that ultimately change inference.

KW - observational studies

KW - propensity score

KW - stratification

KW - subclassification

UR - http://www.scopus.com/inward/record.url?scp=84993982925&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84993982925&partnerID=8YFLogxK

U2 - 10.1002/sim.7046

DO - 10.1002/sim.7046

M3 - Article

C2 - 27426623

AN - SCOPUS:84993982925

VL - 35

SP - 4937

EP - 4947

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 27

ER -