The sequential analysis of repeated binary responses: a score test for the case of three time points

Abstract

In this paper a robust method is developed for the analysis of data consisting of repeated binary observations taken at up to three fixed time points on each subject. The primary objective is to compare outcomes at the last time point, using earlier observations to predict this for subjects with incomplete records. A score test is derived. The method is developed for application to sequential clinical trials, as at interim analyses there will be many incomplete records occurring in non-informative patterns. Motivation for the methodology comes from experience with clinical trials in stroke and head injury, and data from one such trial is used to illustrate the approach. Extensions to more than three time points and to allow for stratification are discussed.

A Comparison of Methods for Treatment Selection in Seamless Phase II/III Clinical Trials Incorporating Information on Short-Term Endpoints

“…The desire to do this arises when the primary endpoint of interest for each patient is only available after a number of months or even years and yet there are more immediately measured endpoints available, building on earlier work on incorporation of early endpoints in sequential clinical trials comparing a single experimental treatment with a control (Cook and Farewell, 1996;Marschner and Becker, 2001;Galbraith and Marschner, 2003;Sooriyarachchi et al, 2006;Whitehead et al, 2008). An example can be found in secondary progressive multiple sclerosis, where long-term changes in disability scales are the main goal, but early evidence of treatment effect may be observed as changes to lesions in the brain detected using magnetic resonance imaging scanning technology.…”

Incorporating intermediate binary responses into interim analyses of clinical trials: A comparison of four methods

“…The test statistics will now be derived using data available from the intermediate assessment for patients who have not yet had their final assessment. Using the notation introduced in [7], the following data structure is assumed. Patients are randomized between an experimental treatment T 1 and a control treatment T 2 serially over time, and at time t 1 after their recruitment their condition is assessed and classified as being in either category C 1 (satisfactory) or category C 2 (unsatisfactory).…”

“…The probability that a patient on treatment T g is in category C i at t 1 and category C j at t 2 will be denoted by p i j,g . The conditional probabilities q (1) i,g = P (category i at t 1 ; T g ) and q (2) i j,g = P(categories i at t 1 and j at t 2 | category i at t 1 ; T g ) can also be defined, and it follows that p i j,g = q (2) i j,g q (1) i,g (7) for i, j, g = 1, 2. Note that the probability that a patient changes category between the two assessments is allowed to differ between the two treatment groups.…”

“…They present the Wald test based on the probability difference parameterization.In this paper, the results of simulations comparing the properties of four methods for the case of binary observations taken at two time points are presented. The methods are the score and Wald approaches, each with the log-odds ratio and probability difference parameterizations, and so they include the method of [8] and a two-time point version of [7]. The test statistics for the four methods are presented in Section 2, and their use in a sequential design is described in Section 3.…”

Interim analysis for binary outcome trials with a long fixed follow-up time and repeated outcome assessments at pre-specified times

“…Several researchers have studied methods that combine data from subjects who have completed full follow-up with those who have been followed for duration R in situations where the outcome is reversible (Marschner and Becker 2001; Sooriyarachchi et al 2006; Whitehead et al 2008). In our research, however, the situation is different in that the outcome can be ascertained at any of the pre-specified visits during follow-up and is irreversible.…”