Partitioning of Functional Data for Understanding Heterogeneity in Psychiatric Conditions.

The issue of “specific” and “non-specific” effects in pharmacotherapy for mental disorders has been a long-standing problem in psychiatry [Quitkin et al., 1987b,a, 2000; Stewart et al., 1998; Ross et al., 2002], and we briefly state it below. Pharmacologic agents are tested in placebo controlled treatment trials and their efficacy is estimated by subtracting the proportion of responders in the placebo group from the proportion of responders in the active drug group. Behind this procedure is the idea that some of the responders in the drug group would have responded to non-specific aspects of the treatment and that the proportion of such subjects is equal to the proportion of responders in the placebo group. Responders in the placebo group are called “non-specific” responders and the reasons for their response have been postulated to include spontaneous remission, life events, the non-specific effect of contact with clinical staff and the non-specific effect of taking a pill. In addition, the responders in the drug group include “specific” responders, those who respond to the specific active chemical component in the drug that is not in the placebo pill. This suggests that the responders in the drug group are a mixture of (at least) two types of individuals: “non-specific” and “specific” responders to the medication. It would be important to be able to distinguish between such responders to drug treatment, since the type of response (“specific” or “non-specific”) might have meaningful implications for the treatment plan and maintenance of the clinical condition. For example, if a patient is not benefiting from the active chemical component in a drug, it is more likely that s/he would relapse while taking the medication than would a subjects who actually benefits from the active chemical in the medication. Conversely, a patient who discontinues the drug too soon after improving might be more likely to relapse if s/he was a specific responder than if s/he was a non-specific responder. Attempts to identify the non-specific responders to pharmacotherapy by examining the baseline characteristics of responders in the placebo arm and contrasting them to the characteristics of the responders in the drug arm of treatment trials have yielded limited results. Such an approach does not account for the fact that there might be non-specific responders among subjects treated with the drug and therefore it does not allow sufficiently precise differentiation between the specific and non-specific responders among subjects treated with the drug. In psychiatry, in addition to treatment trials for establishing drug efficacy, studies are performed to investigate the necessary duration of drug treatment after response to initial acute treatment for depression. These studies are called discontinuation trials and they offer an opportunity for the development of algorithms for identification of different type of responses to treatment. Discontinuation trials use the following two-phases design: Acute treatment phase: patients are openly treated with the antidepressant under investigation for a specific standard duration of time (say, 12 weeks); and Discontinuation phase: responders to the acute treatment are randomized to double blind continuation on the medication or a switch to placebo. In the discontinuation phase subjects are followed until relapse or end of the study. A variation of this design is to randomize the responders to the acute treatment to more than two groups allowing discontinuation of medication after different durations of the treatment. With respect to the outcome during the discontinuation phase one would hypothesize the following: (I) subjects with “specific” response should relapse when switched to placebo; and (II) subjects with “non-specific” response would relapse with equal frequency whether they remain on the drug or are switched to placebo. Data from such studies, including course of symptoms during acute treatment and baseline covariates, can be used for development and validation of algorithms for identifying specific and non-specific responders. In the manner this problem has been described so far, it appears that the goal is to identify two different classes of subjects: “specific” and “non-specific” responders. Cluster analysis and finite mixture models for cross sectional data [Titterington et al., 1985] and growth mixture models for longitudinal data are typically used for this purpose [Muthen and Shedden, 1999; James and Sugar, 2003; Elliot et al., 2005]. All of those methods presume the presence of distinct groups and attempt to find them using different approaches. If the distribution is homogeneous, however, they all fail in one way or another, e.g. lack of convergence, lack of unique solution, interpretability (for example, when three clusters are postulated by the theory, but only one is identified by clustering technique). Perhaps the biggest failing though is that the methods may converge to a solution with two or more latent groups that are artificial manifestations of the algorithm because the distribution is homogeneous [e.g. Tarpey et al., 2008]. Yet, even when the (multivariate) distribution of clinical and biological characteristics appears perfectly homogeneous, symmetric and even normal, individuals in the population can still exhibit widely different characteristics. For example, even though the distribution of blood pressure may be perfectly homogeneous symmetric and normal, the blood pressures of hypertensive subjects differ from those of normo-tensive individuals and, what is more important, these differences correspond to differences in a variety of other health outcomes. As another example, consider a bivariate normal distribution with mean (0, 0) and some variance S. Suppose this distribution represents the slope and concavity of curves with the same intercept. In this distribution there will be curves with an overall increasing or decreasing trend, with a concave up or concave down shape, depending on the values of the slope, and curvature. Thus, there are clearly distinct shapes in this distribution, which is perfectly homogeneous symmetric and normal. While it doesn't make sense to look for distinct clusters or mixtures in this case, a coherent question would be to identify shapes that are representative of the distribution. Symptomathology measures used for identification of types of treatment response (e.g. specific vs. non-specific) such as the longitudinal course of symptoms during acute treatment and baseline characteristics are typically homogeneous and lacking evidence for distinct categories or latent groups. Even though methods such as discriminant analysis, clustering, finite mixture models and latent class models and their variants for longitudinal data, such as growth mixture models, can still be applied to such data, here we take a different approach. We acknowledge explicitly that the distribution of symptom measures can be homogeneous and that distinct clusters may not exist. Never the less, we aim to find a partitioning of this (possibly) homogeneous distribution such that the characteristics of individuals are distinct between partitions. Recently, cluster analysis methods have been proposed for data consisting of curves [e.g. Heckman and Zamar, 2000; Abraham et al., 2003; Tarpey and Kinateder, 2003; Tarpey, 2007a]. Tarpey et al. [2003] used principal points [Flury, 1990, 1993] which are cluster means for theoretical distributions to identify representative curve profiles in a longitudinal depression study. These cluster and principal point methods can be applied to homogenous distribution. Tarpey et al. [2009] proposed a simple method for estimating principal points for longitudinal mixed effect models that directly models the random effects, can handle missing data and covariates, and can also be applied to growth mixture models. The partitioning based on this approach is a principled statistical method, optimizing criteria appropriate for the data at hand. We apply this method here for the purpose of identifying profiles of symptoms change during treatment that might be associated with type of treatment effect. Two studies are utilized in this investigation. Data from the Study A, serving as training data, is used to describe the distribution of drug-treated individuals with respect to the course of their symptoms severity during acute treatment (phase 1 data) and the partitioning method based on principal points for longitudinal mixed effects model is applied. Data from phase 2 is used for internally validating the clinical importance of the partitioning by examining outcomes during the randomized discontinuation phase of patients within a given section of the selected partition. As test data for external validation we use the data from Study B. The rest of this paper is organized as follows. Section 2 summarizes the partitioning method developed in Tarpey et al. [2009]; Section 3 describes two discontinuation studies. The selected partition and the validation results are reported in Section 4. In Section 5 we discuss why the approach taken here might be preferable to classical approaches for clustering in the context of mental health. We discuss limitations and extensions as well as implications for psychiatric research.