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. 2024 Jan 29;80(1):ujad035.
doi: 10.1093/biomtc/ujad035.

A rank-based approach to evaluate a surrogate marker in a small sample setting

Layla Parast  1 , Tianxi Cai  2 , Lu Tian  3
Affiliations

A rank-based approach to evaluate a surrogate marker in a small sample setting

Layla Parast et al. Biometrics. .

Abstract

In clinical studies of chronic diseases, the effectiveness of an intervention is often assessed using "high cost" outcomes that require long-term patient follow-up and/or are invasive to obtain. While much progress has been made in the development of statistical methods to identify surrogate markers, that is, measurements that could replace such costly outcomes, they are generally not applicable to studies with a small sample size. These methods either rely on nonparametric smoothing which requires a relatively large sample size or rely on strict model assumptions that are unlikely to hold in practice and empirically difficult to verify with a small sample size. In this paper, we develop a novel rank-based nonparametric approach to evaluate a surrogate marker in a small sample size setting. The method developed in this paper is motivated by a small study of children with nonalcoholic fatty liver disease (NAFLD), a diagnosis for a range of liver conditions in individuals without significant history of alcohol intake. Specifically, we examine whether change in alanine aminotransferase (ALT; measured in blood) is a surrogate marker for change in NAFLD activity score (obtained by biopsy) in a trial, which compared Vitamin E ($n=50$) versus placebo ($n=46$) among children with NAFLD.

Keywords: randomized clinical trial; rank test; small sample size; surrogate marker evaluation.

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Conflict of interest statement

None declared.

Figures

FIGURE 1
FIGURE 1
General setting: Study A and Study B.
FIGURE 2
FIGURE 2
Illustration of formula image selection as a function of the total sample size: the black line shows the recommended formula image based on the proposed calculations at various sample sizes, assuming the desired power of formula image is 0.70 and assuming formula image; the gray line shows the recommended formula image based on the proposed calculations at various sample sizes, assuming the desired power for formula image is 0.70 and assuming formula image (formula image-level = 0.05).
FIGURE 3
FIGURE 3
Estimated power to identify a surrogate marker for various fixed alternatives formula image, as a function of formula image with formula image and formula image (formula image-level = 0.05).
See this image and copyright information in PMC

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