Optimal composite scores for longitudinal clinical trials under the linear mixed effects model

Abstract

Clinical trials of chronic, progressive conditions use rate of change on continuous measures as the primary outcome measure, with slowing of progression on the measure as evidence of clinical efficacy. For clinical trials with a single prespecified primary endpoint, it is important to choose an endpoint with the best signal-to-noise properties to optimize statistical power to detect a treatment effect. Composite endpoints composed of a linear weighted average of candidate outcome measures have also been proposed. Composites constructed as simple sums or averages of component tests, as well as composites constructed using weights derived from more sophisticated approaches, can be suboptimal, in some cases performing worse than individual outcome measures. We extend recent research on the construction of efficient linearly weighted composites by establishing the often overlooked connection between trial design and composite performance under linear mixed effects model assumptions and derive a formula for calculating composites that are optimal for longitudinal clinical trials of known, arbitrary design. Using data from a completed trial, we provide example calculations showing that the optimally weighted linear combination of scales can improve the efficiency of trials by almost 20% compared with the most efficient of the individual component scales. Additional simulations and analytical results demonstrate the potential losses in efficiency that can result from alternative published approaches to composite construction and explore the impact of weight estimation on composite performance.

Keywords: Alzheimer's disease; composite; linear mixed effects model; longitudinal clinical trial; mild cognitive impairment.

Figure 1

Subject‐specific longitudinal trajectories on the ADAS, CDR, MMSE, and LME‐weighted composite (optimized for 3‐year change from baseline), for n = 160 non‐converting completers from the vitamin E arm of the ADCS MCI/donepezil trial 9. Horizontal axes, time on trial (years); vertical axes, test scores.

Figure 2

Horizontal axis: w _Best−w _Worst, difference between weight assigned to the two tests, scaled to sum to 1; left vertical axis: N _Composite/N _Best, approximate ratio of required sample sizes to detect a nonzero slope in the composite relative to Best, with values <1 (dotted‐dashed horizontal line) indicating an efficient composite; right vertical axis: density, kernel density estimate for weight differences based on simulations; ρ _Slp, correlation of random slope coefficients between tests; U‐shaped curves in the upper portion of the figure plot N _Composite/N _Best as a function of w _Best−w _Worst for each value of ρ _Slp; points labeled ‘U’, ‘S’, and ‘L’ plot N _Composite/N _Best across simulations for UTD‐weighted, inverse baseline standard deviation‐weighted, and LME‐weighted composites; bell‐shaped curves at the bottom of the figure depict kernel density estimates for the w _Best−w _Worst values associated with LME weights estimated from simulated data for each value of ρ _Slp.