Multi-View Cluster Analysis with Incomplete Data to Understand Treatment Effects

Abstract

Multi-view cluster analysis, as a popular granular computing method, aims to partition sample subjects into consistent clusters across different views in which the subjects are characterized. Frequently, data entries can be missing from some of the views. The latest multi-view co-clustering methods cannot effectively deal with incomplete data, especially when there are mixed patterns of missing values. We propose an enhanced formulation for a family of multi-view co-clustering methods to cope with the missing data problem by introducing an indicator matrix whose elements indicate which data entries are observed and assessing cluster validity only on observed entries. In comparison with the simple strategy of removing subjects with missing values, our approach can use all available data in cluster analysis. In comparison with common methods that impute missing data in order to use regular multi-view analytics, our approach is less sensitive to imputation uncertainty. In comparison with other state-of-the-art multi-view incomplete clustering methods, our approach is sensible in the cases of missing any value in a view or missing the entire view, the most common scenario in practice. We first validated the proposed strategy in simulations, and then applied it to a treatment study of heroin dependence which would have been impossible with previous methods due to a number of missing-data patterns. Patients in a treatment study were naturally assessed in different feature spaces such as in the pre-, during-and post-treatment time windows. Our algorithm was able to identify subgroups where patients in each group showed similarities in all of the three time windows, thus leading to the recognition of pre-treatment (baseline) features predictive of post-treatment outcomes.

Keywords: co-clustering; granular computing; heroin pharmacotherapy; missing value; multi-view data analysis.

Figure 1

The distribution of the missing values in the heroin treatment dataset.

Figure 2

The simulated block data structure, the numbers in the vertical axis represent the associated variables, the number in the horizontal axis represent the subject index.

Figure 3

The adherence characteristics of the two clusters (high adherence (HA) versus low adherence (LA)) obtained by our algorithm when variables were grouped in the three views according to variable type.

Figure 4

The mean values of the selected variables by cluster when data were grouped in the three views according to variable type. Abbreviation: ∆Pre_Cra_Oth, change in craving for other drugs after cue exposure at baseline; Pre_THC, tetrahydrocannabinol level in urine drug screen at baseline; Pre_COC, cocaine level in urine drug screen at baseline; ∆Pre_MAP, change in mean arterial pressure after cue exposure at baseline.

Figure 5

The adherence characteristics of the two clusters (high adherence (HA) versus low adherence (LA)) obtained by our algorithm when variables were grouped in three time windows.

Figure 6

The mean values of the selected variables by cluster when data were grouped in three time windows. Abbreviation: ∆Pre_SOWS, change in the subjective opioid withdrawal scale after cue exposure at baseline; ∆Pre_Cra_Oth, change in craving for other drugs after cue exposure at baseline; ∆Pre_WD_Oth, change in withdrawal for other drugs after cue exposure at baseline; ∆Pre_Cra_Heroin, change in craving for heroin after cue exposure at baseline; ∆On_Cra_Oth, change in craving for other drugs after cue exposure during treatment; ∆On_WD_Oth, change in withdrawal for other drugs after cue exposure during treatment; Post_THC, tetrahydrocannabinol urine drug screen after treatment; ∆Post_high_Heroin, change in feeling “high” for heroin after cue exposure after treatment.