How to interpret multidimensional quality of life questionnaires for patients with schizophrenia?

Abstract

Purpose

The classification of patients into distinct categories of quality of life (QoL) levels may be useful for clinicians to interpret QoL scores from multidimensional questionnaires. The aim of this study had been to define clusters of QoL levels from a specific multidimensional questionnaire (SQoL18) for patients with schizophrenia by using a new method of interpretable clustering and to test its validity regarding socio-demographic, clinical, and QoL information.

Methods

In this multicentre cross-sectional study, patients with schizophrenia have been classified using a hierarchical top-down method called clustering using unsupervised binary trees (CUBT). A three-group structure has been employed to define QoL levels as “high”, “moderate”, or “low”. Socio-demographic, clinical, and QoL data have been compared between the three clusters to ensure their clinical relevance.

Results

A total of 514 patients have been analysed: 78 are classified as “low”, 265 as “moderate”, and 171 as “high”. The clustering shows satisfactory statistical properties, including reproducibility (using bootstrap analysis) and discriminancy (using factor analysis). The three clusters consistently differentiate patients. As expected, individuals in the “high” QoL level cluster report the lowest scores on the Positive and Negative Syndrome Scale (p = 0.01) and the Calgary Depression Scale (p < 0.01), and the highest scores on the Global Assessment of Functioning (p < 0.03), the SF36 (p < 0.01), the EuroQol (p < 0.01), and the Quality of Life Inventory (p < 0.01).

Conclusion

Given the ease with which this method can be applied, classification using CUBT may be useful for facilitating the interpretation of QoL scores in clinical practice.

Appendix: The CUBT procedure

The CUBT procedure consists of two stages: growing and tree reduction (i.e. pruning and joining). The clustering tree was built from the eight dimension scores of the SQoL18. The procedure was performed using the data from individuals without missing dimension scores.

The first stage of this method consists of growing a maximal tree from data using a recursive partitioning algorithm. The entire sample is assigned to a root node, which is denoted t. A heterogeneity measure R(t) of the node t, called the deviance, is defined and can be empirically computed as follows:

$$ \hat R\left( t \right) = \frac{{\mathop \sum \nolimits_{\left\{ {{X_i}\; \in \;\hat t} \right\}} {{\left\| {{X_i} - \left. {{{\bar X}_t}} \right\|} \right.}^2}}}{n_t}, $$

where n _t is the size of t and ${\bar X_t}$ is the empirical mean of the observations in t. Let p be the number of variables in the entire sample. For each node t, the best split in two subnodes t _l and t _r is obtained by defining the couple $\left( {j,a} \right) \in \left\{ {1, \ldots ,p} \right\} \times {\mathbb{R}}$ (a is a threshold value that could be taken by the variable X _j ) that maximises:

$$ \hat \Delta \left( {t,j,a} \right) = \hat R\left( t \right) - \hat R\left( {t_l} \right) - \hat R\left( {t_r} \right). $$

Each new terminal node is then split in this way until one of the two following stopping rules is satisfied. The two stopping rules are defined by fixing the two parameters minsize and mindev. The first rule is satisfied if $\widehat {\alpha_t} < minsize$ where $\widehat {\alpha_t} = \frac{n_t}{n},{\text{\;}}{n_t}$ is the size of the node t and n is the size of the entire sample. The second stopping rule is satisfied if the reduction in deviance is less than $mindev \times \hat \Delta \left( {\mathcal{S},{j_0},{a_0}} \right)$, where $\mathcal{S}$ is the entire sample and (j ₀, a ₀) is the best split for the root node. A partition of the data set is obtained, called the maximal tree, in which each leaf represents a cluster.

The second stage (tree reduction) uses two successive algorithms. The first algorithm consists of pruning the tree using a pruning criterion of minimum dissimilarity to reduce the number of clusters. The empirical dissimilarity measure between two adjacent nodes t _l and t _r is

$$ {d^\delta }\left( {{t_l},{t_r}} \right) = \hbox{max} \left( {\overline {d_l^\delta ,} \overline {d_r^\delta } } \right),$$

$$ \hbox{with }\overline {d_l^\delta ,} = \frac{1}{{\delta {n_l}}}\mathop \sum \limits_{i = 1}^{\delta {n_l}} {d_i} $$

$$ \hbox{and } \overline {d_r^\delta ,} = \frac{1}{{\delta {n_r}}}\mathop \sum \limits_{j = 1}^{\delta {n_r}} {d_j}, $$

where n _l and n _r are the sizes of t _l and t _r and δ ∊ [0, 1] is a proportion to address the potential presence of outliers. For each X _i  ∊ t _l and X _j  ∊ t _r , d _i and d _j are the ordered versions of

$$ {\tilde d_l} = {\text {min}}_{x \in {t_r}{\text{\;}}}d\left( {{X_i},x} \right) \hbox{ and } {\tilde d_j} = {\text{mi}}{{\text{n}}_{x \in {t_l}{\text{\;}}}}d\left( {{X_j},x} \right),$$

where d is the Euclidean distance. For the merging criterion, a parameter called mindist is fixed; two adjacent nodes are merged if d ^δ(t _l , t _r ) ≤ mindist.

The second algorithm, the joining step, consists of aggregating the leaves of the tree, even if they do not share the same direct ascendant, using the same criterion as that used in the pruning step. The following two stopping criteria can be considered: (1) the number of expected clusters k is obtained or (2) a fixed threshold value η (that must be specified) is reached by d ^δ(t _l , t _r ).

To define a stopping criterion for the algorithm, we considered a three-group structure of QoL clusters to simplify the interpretability of the partition. Pairs of terminal nodes (constrained to 50 observations) were successively aggregated, producing one less cluster at each step until three clusters remained. Other scenarios were performed by varying the number of final clusters (4, 5, and 6) and the minimum number of observations by the terminal node (25, 100, and 200).