### Abstract

Paired experimental design is widely used in clinical and health behavioral studies, where each study unit contributes a pair of observations. Investigators often encounter incomplete observations of paired outcomes in the data collected. Some study units contribute complete pairs of observations, while the others contribute either pre- or post-intervention observations. Statistical inference for paired experimental design with incomplete observations of continuous outcomes has been extensively studied in literature. However, sample size method for such study design is sparsely available. We derive a closed-form sample size formula based on the generalized estimating equation approach by treating the incomplete observations as missing data in a linear model. The proposed method properly accounts for the impact of mixed structure of observed data: a combination of paired and unpaired outcomes. The sample size formula is flexible to accommodate different missing patterns, magnitude of missingness, and correlation parameter values. We demonstrate that under complete observations, the proposed generalized estimating equation sample size estimate is the same as that based on the paired t-test. In the presence of missing data, the proposed method would lead to a more accurate sample size estimate comparing with the crude adjustment. Simulation studies are conducted to evaluate the finite-sample performance of the generalized estimating equation sample size formula. A real application example is presented for illustration.

Original language | English (US) |
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Journal | Statistical Methods in Medical Research |

DOIs | |

State | Accepted/In press - Jan 1 2017 |

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### Keywords

- continuous outcomes
- generalized estimating equation
- incomplete observations
- paired design
- Sample size

### ASJC Scopus subject areas

- Epidemiology
- Statistics and Probability
- Health Information Management

### Cite this

**Sample size considerations for paired experimental design with incomplete observations of continuous outcomes.** / Zhu, Hong; Xu, Xiaohan; Ahn, Chul.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Sample size considerations for paired experimental design with incomplete observations of continuous outcomes

AU - Zhu, Hong

AU - Xu, Xiaohan

AU - Ahn, Chul

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Paired experimental design is widely used in clinical and health behavioral studies, where each study unit contributes a pair of observations. Investigators often encounter incomplete observations of paired outcomes in the data collected. Some study units contribute complete pairs of observations, while the others contribute either pre- or post-intervention observations. Statistical inference for paired experimental design with incomplete observations of continuous outcomes has been extensively studied in literature. However, sample size method for such study design is sparsely available. We derive a closed-form sample size formula based on the generalized estimating equation approach by treating the incomplete observations as missing data in a linear model. The proposed method properly accounts for the impact of mixed structure of observed data: a combination of paired and unpaired outcomes. The sample size formula is flexible to accommodate different missing patterns, magnitude of missingness, and correlation parameter values. We demonstrate that under complete observations, the proposed generalized estimating equation sample size estimate is the same as that based on the paired t-test. In the presence of missing data, the proposed method would lead to a more accurate sample size estimate comparing with the crude adjustment. Simulation studies are conducted to evaluate the finite-sample performance of the generalized estimating equation sample size formula. A real application example is presented for illustration.

AB - Paired experimental design is widely used in clinical and health behavioral studies, where each study unit contributes a pair of observations. Investigators often encounter incomplete observations of paired outcomes in the data collected. Some study units contribute complete pairs of observations, while the others contribute either pre- or post-intervention observations. Statistical inference for paired experimental design with incomplete observations of continuous outcomes has been extensively studied in literature. However, sample size method for such study design is sparsely available. We derive a closed-form sample size formula based on the generalized estimating equation approach by treating the incomplete observations as missing data in a linear model. The proposed method properly accounts for the impact of mixed structure of observed data: a combination of paired and unpaired outcomes. The sample size formula is flexible to accommodate different missing patterns, magnitude of missingness, and correlation parameter values. We demonstrate that under complete observations, the proposed generalized estimating equation sample size estimate is the same as that based on the paired t-test. In the presence of missing data, the proposed method would lead to a more accurate sample size estimate comparing with the crude adjustment. Simulation studies are conducted to evaluate the finite-sample performance of the generalized estimating equation sample size formula. A real application example is presented for illustration.

KW - continuous outcomes

KW - generalized estimating equation

KW - incomplete observations

KW - paired design

KW - Sample size

UR - http://www.scopus.com/inward/record.url?scp=85043702267&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043702267&partnerID=8YFLogxK

U2 - 10.1177/0962280217731595

DO - 10.1177/0962280217731595

M3 - Article

JO - Statistical Methods in Medical Research

JF - Statistical Methods in Medical Research

SN - 0962-2802

ER -