The relative efficiency of time-to-threshold and rate of change in longitudinal data

Abstract

Randomized, placebo-controlled trials often use time-to-event as the primary endpoint, even when a continuous measure of disease severity is available. We compare the power to detect a treatment effect using either rate of change, as estimated by linear models of longitudinal continuous data, or time-to-event estimated by Cox proportional hazards models. We propose an analytic inflation factor for comparing the two types of analyses assuming that the time-to-event can be expressed as a time-to-threshold of the continuous measure. We conduct simulations based on a publicly available Alzheimer's disease data set in which the time-to-event is algorithmically defined based on a battery of assessments. A Cox proportional hazards model of the time-to-event endpoint is compared to a linear model of a single assessment from the battery. The simulations also explore the impact of baseline covariates in either analysis.

The Alzheimer's Disease Neuroimaging Initiative: A review of papers published since its inception

“…Another issue with RCPTs is the selection of a primary end-point, which is often either time-to-event (for example, progression to dementia) or a continuous measure of disease severity such as ADAS-cog to assess the effect of the treatment. Donohue et al [266] compared the power to detect an effect of these two methods by using Cox proportional hazard models to estimate time-to endpoint, and linear mixed models to estimate continuous variables and found that linear models consistently demonstrated greater power than Cox proportional hazard models when tested on the ADNI data-set (Fig. 27).…”

IMPROVE trial: A randomized controlled trial of patient-controlled analgesia for sickle cell painful episodes: rationale, design challenges, initial experience, and recommendations for future studies

“…Recent statistical investigations [32] have provided some theoretical justification for the relative efficiency and practical advantage of longitudinal rate of change models versus time to threshold models in similar data settings. Our analysis was based upon 114 observations across 2 to 14 days for 22 adult participants.…”

“…Only 46 adult participants (23 per treatment arm) would be required to detect a difference between treatments in rate of change of 5 mm per day (25 mm across the five-day observation period) when using 120% of the variability observed in these data as a pilot estimate and allowing for a 20% fraction of missing data from incomplete follow-up (typically caused by early departure due to treatment efficacy). This sample size requirement was estimated based on the method described in Fitzmaurice [40] and Donohue [32, 41]. It also may be desirable to estimate between-site variance, which, in addition to the sample size requirement, typically requires that some minimum number of sites contribute several enrollees each in order to provide stable estimates; simulation studies are recommended for this purpose.…”

The Alzheimer's Disease Neuroimaging Initiative 3: Continued innovation for clinical trial improvement

“…This has now changed, in part due to the contributions of ADNI. ADNI investigators have advanced the design of pre-dementia trials in the statistical [21–24], methodological [25–34], cognitive [35] and clinical [31, 32, 36, 37] literature, and with regulators [25] in the US and abroad facilitating the design of major completed and ongoing trials (avagacestat, gantanerumab, aducanumab, solanezumab, Anti Amyloid Treatment in Asymptomatic Alzheimer’s Disease (A4) study, and A5 study). These advances have included the move from time-to-endpoint designs to continuous outcome measures as primaries [21, 25], the use of biomarker-based subject selection [22], single primary outcomes in prodromal trials [25], and cognitive endpoints in pre-dementia clinical trials [38–41].…”