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Semi-parametric survival analysis methods like the Cox Proportional Hazards (CPH) regression (Cox, 1972) are a popular approach for survival analysis. These methods involve fitting of the log-proportional hazard as a function of the covariates and are convenient as they do not require estimation of the baseline hazard rate. Recent approaches have involved learning non-linear representations of the input covariates and demonstrate improved performance. In this paper we argue against such deep parameterizations for survival analysis and experimentally demonstrate that more interpretable semi-parametric models inspired from mixtures of experts perform equally well or in some cases better than such overly parameterized deep models.
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In this paper, we make an experimental comparison of semi-parametric (Cox proportional hazards model, Aalens additive regression model), parametric (Weibull AFT model), and machine learning models (Random Survival Forest, Gradient Boosting with Cox Proportional Hazards Loss, DeepSurv) through the concordance index on two different datasets (PBC and GBCSG2). We present two comparisons: one with the default hyper-parameters of these models and one with the best hyper-parameters found by randomized search.
Survival analysis is a hotspot in statistical research for modeling time-to-event information with data censorship handling, which has been widely used in many applications such as clinical research, information system and other fields with survivorship bias. Many works have been proposed for survival analysis ranging from traditional statistic methods to machine learning models. However, the existing methodologies either utilize counting-based statistics on the segmented data, or have a pre-assumption on the event probability distribution w.r.t. time. Moreover, few works consider sequential patterns within the feature space. In this paper, we propose a Deep Recurrent Survival Analysis model which combines deep learning for conditional probability prediction at fine-grained level of the data, and survival analysis for tackling the censorship. By capturing the time dependency through modeling the conditional probability of the event for each sample, our method predicts the likelihood of the true event occurrence and estimates the survival rate over time, i.e., the probability of the non-occurrence of the event, for the censored data. Meanwhile, without assuming any specific form of the event probability distribution, our model shows great advantages over the previous works on fitting various sophisticated data distributions. In the experiments on the three real-world tasks from different fields, our model significantly outperforms the state-of-the-art solutions under various metrics.
Survival analysis in the presence of multiple possible adverse events, i.e., competing risks, is a pervasive problem in many industries (healthcare, finance, etc.). Since only one event is typically observed, the incidence of an event of interest is often obscured by other related competing events. This nonidentifiability, or inability to estimate true cause-specific survival curves from empirical data, further complicates competing risk survival analysis. We introduce Siamese Survival Prognosis Network (SSPN), a novel deep learning architecture for estimating personalized risk scores in the presence of competing risks. SSPN circumvents the nonidentifiability problem by avoiding the estimation of cause-specific survival curves and instead determines pairwise concordant time-dependent risks, where longer event times are assigned lower risks. Furthermore, SSPN is able to directly optimize an approximation to the C-discrimination index, rather than relying on well-known metrics which are unable to capture the unique requirements of survival analysis with competing risks.
Accelerated destructive degradation tests (ADDT) are widely used in industry to evaluate materials long term properties. Even though there has been tremendous statistical research in nonparametric methods, the current industrial practice is still to use application-specific parametric models to describe ADDT data. The challenge of using a nonparametric approach comes from the need to retain the physical meaning of degradation mechanisms and also perform extrapolation for predictions at the use condition. Motivated by this challenge, we propose a semi-parametric model to describe ADDT data. We use monotonic B-splines to model the degradation path, which not only provides flexible models with few assumptions, but also retains the physical meaning of degradation mechanisms (e.g., the degradation path is monotonically decreasing). Parametric models, such as the Arrhenius model, are used for modeling the relationship between the degradation and accelerating variable, allowing for extrapolation to the use conditions. We develop an efficient procedure to estimate model parameters. We also use simulation to validate the developed procedures and demonstrate the robustness of the semi-parametric model under model misspecification. Finally, the proposed method is illustrated by multiple industrial applications.
Semi-parametric regression models are used in several applications which require comprehensibility without sacrificing accuracy. Typical examples are spline interpolation in geophysics, or non-linear time series problems, where the system includes a linear and non-linear component. We discuss here the use of a finite Determinantal Point Process (DPP) for approximating semi-parametric models. Recently, Barthelme, Tremblay, Usevich, and Amblard introduced a novel representation of some finite DPPs. These authors formulated extended L-ensembles that can conveniently represent partial-projection DPPs and suggest their use for optimal interpolation. With the help of this formalism, we derive a key identity illustrating the implicit regularization effect of determinantal sampling for semi-parametric regression and interpolation. Also, a novel projected Nystrom approximation is defined and used to derive a bound on the expected risk for the corresponding approximation of semi-parametric regression. This work naturally extends similar results obtained for kernel ridge regression.
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