  We present a nonparametric Bayesian method for disease subtype discovery in
multi-dimensional cancer data. Our method can simultaneously analyse a wide
range of data types, allowing for both agreement and disagreement between their
underlying clustering structure. It includes feature selection and infers the
most likely number of disease subtypes, given the data.
  We apply the method to 277 glioblastoma samples from The Cancer Genome Atlas,
for which there are gene expression, copy number variation, methylation and
microRNA data. We identify 8 distinct consensus subtypes and study their
prognostic value for death, new tumour events, progression and recurrence. The
consensus subtypes are prognostic of tumour recurrence (log-rank p-value of
$3.6 \times 10^{-4}$ after correction for multiple hypothesis tests). This is
driven principally by the methylation data (log-rank p-value of $2.0 \times
10^{-3}$) but the effect is strengthened by the other 3 data types,
demonstrating the value of integrating multiple data types.
  Of particular note is a subtype of 47 patients characterised by very low
levels of methylation. This subtype has very low rates of tumour recurrence and
no new events in 10 years of follow up. We also identify a small gene
expression subtype of 6 patients that shows particularly poor survival
outcomes. Additionally, we note a consensus subtype that showly a highly
distinctive data signature and suggest that it is therefore a biologically
distinct subtype of glioblastoma.
  The code is available from https://sites.google.com/site/multipledatafusion/
