## Sequential Monitoring In Longitudinal Clinical Trials

Sequential monitoring in clinical trials in an important issue. Definitive clinical trials are usually set up to be monitored by an independent data safety and monitoring board (DSMB) which meets regularly to monitor the data for safety and efficacy. The board, which often meets at 3-6-month intervals over the length of the trial, must make a decision on whether the trial should be stopped at each meeting. The IPPB trial serves as an example. Longitudinal data (slopes) are being assessed at 3-month intervals, trends are examined, and the board is asked to make

Various approaches have been proposed for monitoring clinical trials with univariate response data. The primary focus was to develop sequential boundaries for detecting treatment effect which adjust for the inherent multiplicity in examining the data repeatedly over the duration of the trial. Pocock101 developed grouped sequential boundaries for the situation where the trial is monitored at equally spaced information times; the proposed boundaries were constant over the duration of the trial. O'Brien and Fleming102 proposed boundaries which are monotonically decreasing for monitoring at equally spaced information times. Slud and Wei103 proposed a technique for monitoring the trial at prespecified (before monitoring begins) unequally spaced information times. Lan and DeMetts104 proposed methodology that allows for monitoring at unequal information times and does not require prespecifying the monitoring times. They proposed a spending function approach where a certain percentage of the type I error is 'spent at

There have been extensions of the group-sequential methods of Slud-Wei and Lan-DeMets to a few longitudinal models. Geary105 developed sequential monitoring boundaries for repeated Gaussian data. This procedure assumes a basic four parameter model, that monitoring times are equally spaced, that patients enter the study all the same time and that there is no missing data. Lee and DeMets106 proposed a method that does not require the previous assumptions and uses the Lan-DeMets spending function approach to compute exit probabilities. The approach assumes a Laird-Ware model for change in a continuous response where the estimate for linear change is being monitored. The method allows for the specification of a mechanism for staggered entry (that is, how patients enter into the trial over time). This is an important feature since it allows for distinguishing between the sequential and longitudinal components of the problem. For example, following a group of simultaneously enrolled subjects for 3 years provides a different amount of information than following a group of staggeredly entered patients an average of

3 years. Wu and Lan107 further develop this approach by allowing for non-linear changes as well

These methods could be applied to the IPPB trial if it were being conducted today. One would need to propose a model for the longitudinal decline in FEVj (for example, a linear mixed model), a detectable difference in slope between the two treatment arms, the variation in slopes across subjects, and the within-subject variation. The variance estimates can be obtained from prior studies. In addition, a staggered entry mechanism (this was uniform over a 3-year accrual period in the IPPB trial) and an a spending function (choices corresponding to Pocock and O'Brien-Flemming boundaries are given in Lan and DeMets104) needs to be specified. With this information, sequential boundaries for multiple analyses can be computed using a spending

Sequential monitoring plans have been constructed for GEE models. Wei et al.108 have proposed sequential boundaries for GEE models that follow the prespecified 'looks' of Slud and Wei. Gange and DeMets109 proposed a spending function approach for monitoring correlated data using GEE. Cook and Lawless discussed sequential monitoring for recurrent events.110 They combined their non-parametric test for recurrent events83 with Lan-DeMets spending function approach to develop a robust approach for monitoring recurrent events.

Stochastic curtailment is an alternative approach to the previous discussed methodology developed by Lan et al.111 They proposed early stopping of a trial either for efficacy or futility based on conditional power. Specifically, at each monitoring time they proposed computing the power conditional on the available data and assuming a hypothesis for the future data. They proposed stopping the trial for efficacy when the conditional power is high and stopping the trial for futility when this power is low. Conditional power calculations for efficacy are often done assuming that future data is generated under the null hypothesis. The calculations for futility are performed assuming that future data are either generated similar to the data already observed or under another reasonable alternative hypothesis. McMahon et al.112 discussed a simulation-based technique for stochastic curtailment in recurrent event studies. Lan and Zucker113 discussed this idea applied to the basic single random-effects model for longitudinal Gaussian data. Halperin et a/.114 proposed stochastic curtailment methodology for the more general

Halperin et al.'s methodology was motivated by the IPPB trial. In the IPPB trial, patients were randomized uniformly over a 3-year follow-up and each patient was followed for 3 years. Halperin et al. provide estimates of the conditional power of accepting the null hypothesis (that is, the probability that we will fail to reject the null hypothesis at the end of the study given the available data and that the minimal detectable differences is true) of 0-71, 0-83 and 0-90 at 3 5, 4-5 and 5-5 years after the beginning of the study. Based on this, stopping the IBBP trial at between

Although sequential monitoring is useful in longitudinal studies, one has to be extremely cautious about stopping a trial just based on these statistical rules. Often, particularly in the early looks, linear effect estimates are based on short term data. It may be that long term effects are very different and this is most likely the reason for conducting a longitudinal study in the first place.

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