Modeling Missingness for Time-to-Event Data: A Case Study in Osteoporosis

Abstract

Clinical trials of long duration are often hampered by high dropout rates, making statistical inference and interpretation of results difficult. Statistical inference should be based on models selected according to whether missingness is independent of response [missing completely at random (MCAR)], or depends on response either through observed responses only [missing at random (MAR)] or through unobserved responses [nonignorable missing (NIM)]. If the dropout rate is high and little is known about the dropout mechanism, plausible nonignorable missing scenarios should be investigated as a sensitivity tool, offering the data analyst an understanding of the robustness of conclusions. Modeling missingness is illustrated by an analysis of an interval censored time-to-event outcome from a 5-year clinical trial on fracture response in osteoporosis in which the overall dropout rate was substantial. In this article, we provide an overview of a reanalysis accounting for possible nonignorable missingness, emphasize the importance of modeling the dropout and response mechanisms jointly, and highlight critical points arising in missing data problems.

Key Words:

• Bayesian
• Continuation ratio model
• Nonignorable missing
• Interval censored

Mathematics Subject Classification:

• 62N01

Acknowledgments

We thank Melvin Olson for providing the data, Willi Maurer and Jean-Louis Steimer for starting the Missing Data Initiative at Novartis, Paul Gallo, Jerry Nedelman, José Pinheiro, and Heinz Schmidli for their continued support of any activities regarding this initiative, and Amy Racine for her helpful comments.

Notes

^aThe bracket notation is used to denote probability distributions. For example, [A], [A, B], and [A|B] denote the marginal distribution of A, the joint distribution of A and B, and the conditional distribution of A given B, respectively. Moreover, for simplicity the subscript i is omitted.