1 Introduction
Heart failure affects twenty-six million people worldwide with increasing prevalence in an aging population (Savarese et al., 2017)
. Current tools for outcome prediction lack precision and are insensitive to the complex physiology of heart disease. Accurate risk stratification is important for ensuring individualised management and effective care to improve survival. Cardiac magnetic resonance imaging (CMR) is the gold standard for assessing biventricular function and recently computer vision techniques have been combined with supervised denoising autoencoders to learn motion features that are predictive of survival
(Bello et al., 2019). To handle right-censored survival outcomes, this network uses a Cox partial likelihood loss function. However, this architecture takes only high dimensional motion data as inputs and does not take advantage of low dimensional clinical risk factors. We proposed three different approaches to introduce conventional covariates such as age, haemodynamic measurements and exercise capacity to Bello’s model. We also adopted several statistical techniques, including canonical correlation analysis, to understand how new information interacts with prior knowledge.
2 Method
In this work, three extensions of Bello’s network (Model 0) are proposed to incorporate low dimensional clinical information. Model 1 (0(a)) adds clinical data to the input layer with corruption and reconstruction applied to both. Model 2 (0(b)) aims to intensify the effect of clinical data by adding it with the latent code, without corruption or reconstruction. Model 3 (0(c)) aims to model the nonlinear effect of clinical factors and interaction with the latent code using an additional hidden layer between the latent code and prediction layer.
3 Experiments and Results
A detailed description of the patient cohort and image analysis techniques can be found in Bello et al. (2019). We used eight new clinical factors in this work: age, sex, six-minute walk distance, functional class, mean pulmonary artery pressure and right ventricular (RV) end-diastolic volume, RV end-systolic volume, and RV ejection fraction. The models have several hyper-parameters. Indeed, in our experiments, Model 0, 1 and 2 have similar network structures (i.e they share the same set of hyper-parameters while Model 3 has a separate set of hyper-parameters). For model performance and validation we use Harrell’s concordance index (C-index, Harrell et al. (1982)) to measure the predictive accuracy based on bootstrap technique (due to small sample size).
model | c-index | 95% bootstrap CI | model | c-index | 95% bootstrap CI |
---|---|---|---|---|---|
Model 0 | 0.7979 | (0.7536, 0.8373) | |||
Model 1 | 0.7978 | (0.7522, 0.8402) | Model 1 with noise | 0.8068 | (0.7644, 0.8457) |
Model 2 | 0.7998 | (0.7564, 0.8371) | Model 2 with noise | 0.8012 | (0.7548, 0.8407) |
Model 3 | 0.8276 | (0.7837, 0.8681) | Model 3 with noise | 0.8087 | (0.7718, 0.8433) |
Model 0 represents the baseline model without clinical factors. Model 1, 2 and 3 (i.e described in methods section) are used for comparison. Models with noise replacing clinical factors with standard gaussian noise and use the same hyper-parameters with the corresponding models where 95% credible intervals are built by bootstrap.
The results can be found in table 1. Numerically, Model 1 and 2 have no significant over-performance compared with Model 0, while Model 3 has better prediction ability than Model 0. Pair-wise two sample test based on bootstrap was also conducted for model comparison. The p-value for testing Model 3 being better than Model 0 is , significant at level. And the p-value for Model 1 v.s. 0 and Model 2 v.s. 0 are and respectively, revealing no improvement.
Moreover, the preliminary correlation analysis shows that the Pearson correlation between all pairs of variables from latent code and clinical factors are below , which is the same level of correlation between noise and latent code in Model 2. Canonical Correlation Analysis (CCA, Hotelling (1992)) also shows that the latent code contains little information from clinical factors. Indeed, the overall linear correlation, mostly reflected by the first canonical component, between the latent code and clinical factors, are close to that of Gaussian noise (figure 2
). Furthermore, to evaluate if clinical factors can linearly contribute to survival prediction, we also conducted linear regressions between the predicted risk and clinical factors; as well as between the predicted risk and latent code (table
2). Then, through the Model 2, we found that the latent code explained almost all of the predicted risk; whereas the clinical factors have a similar effect to noise for survival prediction. These findings suggest non-linear effect of the clinical risk factors modelled by Model 3.model | the predicted risk v.s. clinical factors | predicted risk v.s. latent code |
---|---|---|
Model 2 | 0.02 | 0.84 |
Model 2 with noise | 0.03 | 0.95 |
4 Discussion
We found that combining routine clinical data with latent code from high dimensional cardiac motion can achieve improvements in survival prediction performance; as this allows for non-linear relationships and optimised the interaction between them. Such networks could be used in clinical practice for automated analysis of both cardiac imaging and routine clinical data for outcome prediction. Furthermore, this work suggests that other data, such as genetic variants and radiomic features, could be used in such survival networks to improve outcome prediction by jointly analysing cardiac motion traits with inheritable risk factors.
References
- Savarese et al. (2017) G. Savarese and L. H. Lund, Global public health burden of heart failure, Card Fail Rev, vol. 3, no. 1, p. 7, 2017.
- Bello et al. (2019) G. A. Bello, T. J. Dawes, J. Duan, C. Biffi, A. de Marvao, L. S. Howard, J. S. R. Gibbs, M. R. Wilkins, S. A. Cook, D. Rueckert, D. P. O’Regan. Deep-learning cardiac motion analysis for human survival prediction. Nat Mach Intell, 1(2):95, 2019.
- Harrell et al. (1982) F. E. Harrell, R. M. Califf, D. B. Pryor, K. L. Lee, and R. A. Rosati. Evaluating the yield of medical tests. JAMA, 247(18):2543–2546, 1982.
- Hotelling (1992) H. Hotelling. Relations between two sets of variates. In Breakthroughs in Statistics, pages 162–190. Springer, 1992.
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