Worst-Rank Score Methods—A Nonparametric Approach to Informatively Missing Data

INTRODUCTION

This JAMA Guide to Statistics and Methods explains worst-rank score methods, a nonparametric statistical technique that assigns worst-case outcomes for patients with missing data to account for missingness that may reflect an adverse change in patient status (informative rather than random missingness).

A previous JAMA Guide to Statistics and Methods chapter¹ briefly reviewed nonparametric statistics. Such statistical approaches represent the data using ranks of values rather than the observed values. This provides valid tests of significance, regardless of the underlying distributions of the values and without the need to posit parametric assumptions—thus the term “nonparametric statistics.” In a clinical trial that was published in JAMA,² Baxter and colleagues from the N-TA³CT Research Group used a nonparametric analysis known as the worst-rank score method in a manner that also captured information from missing data that could result from worsening of the patient’s condition.

USE OF THE METHOD

Why Is the Worst-Rank Score Method Used?

Virtually all studies experience some missing data.³ Missing data are considered missing completely at random (MCAR) when the missing data are the result of random processes by which some values are observed and others are missing. If the missing data are indeed MCAR (an untestable hypothesis), then an analysis of the observed data using virtually any statistical method will provide an unbiased test. Such missing data are called noninformative because it is assumed that the missing data are the result of a random process, and a missing datum conveys no information about what the missing value might be.

However, it is possible that missing data are informatively missing, in which case the missing data result from other outcomes that reflect a change in the patient’s status, either improvement or deterioration. For example, in a study of congestive heart failure, missing data resulting from the death of a patient due to worsening heart failure would indicate that this patient had a worse outcome than any patient who survived. In such settings Wittes et al⁴ had suggested that a rank analysis could readily capture this information by assigning the worst ranks to study participants who died. Lachin⁵ then described the statistical properties of a worst-rank analysis and showed that a rank test using worst ranks provided an unbiased statistical test of the difference between groups.

Informatively missing data were an anticipated feature of the N-TA³CT study that was conducted to compare the effect of doxycycline vs placebo on aneurysm growth among patients with small infrarenal abdominal aortic aneurysms.² The primary outcome was the maximum transverse diameter (MTD) of the aneurysm relative to the initial baseline value after 2 years of treatment. However, it was possible that some patients might die or experience rupture of the aneurysm and would require endovascular repair. For such patients the MTD ...