Model-Based Analysis of a Longitudinal Binary Response as the Primary Analysis for a Phase II Study in Migraine Prophylaxis.
Bart Laurijssens1, Andreas Krause2, Lutz Harnisch3
1GlaxoSmithKline, 2Pharsight Corporation, 3Pfizer (Formerly GlaxoSmithKline).
Objectives: The objective was to design and evaluate a phase II proof of concept/dose-response study in Migraine Prophylaxis, exploiting the characteristics of the primary endpoint optimally and taking into account cost, time efficiency, as well as limiting unnecessary patient exposure to the drug.
Methods: The primary endpoint, Migraine Headache Day (MHD), was longitudinal in nature: 1 month of run-in to establish a baseline was followed by 3 months of treatment, and binary: For each patient, every day was either an event or a non-event day. A model describing the placebo time course and drug effect was constructed using literature and in-house historical data. The model had 3 components: 1) a constant and common baseline (base) for the probability of an event at a given day prior to treatment, 2) a fractional change in the probability of an event at a given day, expressed as 1-exp(-k*time), which described the expected probability of an event over the 12-week treatment period, and 3) 2 parameters which described the modification of the change in probability over time due to placebo treatment effect (plac) or active treatment effect (plac+drug).
Model : R = base + (1 - exp(-k*time)) *(plac + drug) and P(event) = InvLogit (R)
The study was set up in two parts. Part 1 investigated two active doses and placebo. Following an interim analysis the trial could be stopped for futility or continue in Part 2 a) to study the full dose response or b) to investigate one or two doses further (extending the samples size) in case initial assumptions had been violated. The model was used in clinical trial simulations to explore the behaviour of the proposed two-stage design, addressing both type I and II error rates. The Part 1 doses were selected based on human pharmacology, safety and tolerability. The null hypothesis assumed no treatment difference between either active treatment and placebo. A sequence of log-likelihood ratio tests was applied to assess the probability for the alternative hypotheses of a relevant treatment effect.
Results: The model-based analysis allowed for a reduction of the sample size for each treatment arm by almost 50 percent, compared to a more conventional end-of-treatment pairwise comparison. The trial design, given the assumptions, was robust: The power to detect the desired effect was 95% and the risk of not stopping trial if the true drug effect was zero was 1.3%. No statistically significant drug effect was observed for either dose in Part 1 of the study. Although the variance on treatment and the size of the placebo response were larger than assumed, the power was still sufficient to exclude the effect size of interest as a likely outcome. Further exploratory analysis suggested a potential drug effect in a subgroup of patients, and therefore in Part 2 one active dose and placebo were studied in this subgroup. Part 2 was powered for a smaller effect size using adjusted assumptions. No statistically significant drug effect was observed in Part 2 of the study. The model could adequately describe the data in both Parts. No Part 1 data was used in the analysis of Part 2.
Conclusions: The model-based analysis allowed for a much smaller sample size, and an intuitive outcome: the probability of a MHD. The two-stage design allowed for a proof of concept before committing to a full dose-response within one study, and the possibility to re-adjust our assumptions after Part 1 if necessary. With hindsight, this trial could have been stopped for futility after Part 1 if the historical data was investigated more extensively and if Part 1 was powered for the ultimate (smaller) effect size of interest.
