Mixed-SuStaIn: Heterogeneous Disease Progression

• Mixed-SuStaIn is a unified disease progression framework that models heterogeneous biomarkers—continuous, ordinal, and binary—using the Mixed Events approach.
• It leverages a generalized progression model to infer both subtype structures and disease stages via type-specific likelihoods for each biomarker.
• Applied in neurodegeneration studies such as Alzheimer’s, it offers flexible integration of multimodal data and comparable predictive performance to traditional methods.

Mixed-SuStaIn is an extension of the Subtype and Stage Inference (SuStaIn) disease progression framework to mixed biomarker data, meaning datasets that contain some biomarkers best modeled as continuous trajectories and others best modeled as discrete state changes. In (Jonge et al., 25 Feb 2026), the framework is built on a generalized progression model termed the Mixed Events model, in which a disease trajectory is represented as a single ordered sequence of heterogeneous events: binary events, ordinal score transitions, and z-score threshold crossings. Mixed-SuStaIn uses that mixed-data progression model inside the SuStaIn mixture formulation so that it can infer both subtype structure and stage while allowing each biomarker to contribute according to its own measurement and likelihood model.

1. Problem setting and conceptual motivation

Classical disease progression models, including earlier forms of EBM and SuStaIn, typically assume a single trajectory type per analysis. The event-based model treats biomarkers as switching from normal to abnormal and is suited to binary abnormality events derived from bimodal data. Scored Events or Ordinal SuStaIn treats biomarkers as moving through ordered discrete severity levels. Piecewise linear z-score SuStaIn models biomarkers as accumulating continuously through prespecified z-score thresholds. Mixed-SuStaIn was introduced to address the limitation that such single-family formulations do not naturally accommodate heterogeneous real-world datasets containing continuous, binary, and ordinal variables in the same analysis (Jonge et al., 25 Feb 2026).

The motivating example in (Jonge et al., 25 Feb 2026) is Alzheimer’s disease, where MRI regional atrophy is naturally handled as continuous z-scored biomarkers, CSF markers may be represented well by normal/abnormal thresholds, and clinical scores or visual ratings may be ordinal. The core claim is that forcing all biomarkers into one trajectory family can be unnatural and may discard information. The work further argues that, before this model, no current alternative offered the same flexibility for combining z-score, ordinal, and binary biomarkers in one SuStaIn analysis (Jonge et al., 25 Feb 2026).

This design places Mixed-SuStaIn between two established modeling needs. First, it retains SuStaIn’s objective of discovering multiple progression patterns rather than a single average trajectory. Second, it relaxes the assumption that all biomarkers must share the same event semantics. A plausible implication is that the framework is most relevant when multimodal disease characterization is central and when reduction of continuous variables to binary events would suppress clinically meaningful progression structure.

2. Mixed Events and the definition of Mixed-SuStaIn

The central methodological contribution is the Mixed Events model. In this formulation, disease progression is represented as a sequence $S$ of $K$ events, where an event means that a biomarker reaches a new disease level. Binary biomarkers contribute one event corresponding to a normal-to-abnormal transition. Ordinal biomarkers contribute multiple score-reaching events, for example $0 \to 1 \to 2 \to 3$. Z-score biomarkers contribute events corresponding to crossing prespecified z-score thresholds such as $z=1,2,3$, after which the biomarker may continue accumulating to $z_{\max}$ (Jonge et al., 25 Feb 2026).

Each biomarker $i$ is assigned a model type

$M(i) \in \{B, O, Z\},$

where $B$ denotes binary or event-based, $O$ denotes ordinal or scored-events, and $Z$ denotes z-score or piecewise-linear. This assignment is fundamental: the latent disease stage is shared across biomarkers, but the observation model is type-specific.

Mixed-SuStaIn is then obtained by embedding Mixed Events inside the standard SuStaIn subtype mixture. Conceptually, Mixed Events is the single-sequence progression model for heterogeneous data, whereas Mixed-SuStaIn is the corresponding subtype-and-stage model over multiple subtype-specific sequences (Jonge et al., 25 Feb 2026). The framework therefore performs three tasks simultaneously: subtyping through the inference of multiple progression patterns $K$0, staging through inference of subject position along each subtype trajectory, and mixed-data integration through biomarker-specific event likelihoods.

The relationship to prior SuStaIn variants is precise. Prior z-score SuStaIn assumes all biomarkers follow piecewise linear z-score trajectories. EBM-SuStaIn models one normal-to-abnormal event per biomarker and can only include continuous biomarkers after converting them into binary abnormality events. Ordinal SuStaIn models only ordered score transitions. Mixed-SuStaIn generalizes these settings by allowing the three event families to coexist within one common event ordering (Jonge et al., 25 Feb 2026).

3. Mathematical formulation and event-wise likelihoods

The unifying single-subject likelihood in the Mixed Events model is

$K$1

Here $K$2 is the biomarker vector for subject $K$3, $K$4 is the event ordering, $K$5 is latent disease stage, $K$6 is the stage prior, and $K$7 selects the model family for biomarker $K$8 (Jonge et al., 25 Feb 2026). The key structural point is that the latent-stage decomposition is shared, while the per-biomarker likelihood is chosen according to biomarker type.

The three likelihood families can be summarized as follows.

Biomarker type	Event interpretation	Likelihood form
Binary ($K$9)	One normal-to-abnormal event	Eq. (2)
Ordinal ($0 \to 1 \to 2 \to 3$0)	One event per score level	Eq. (3)
Z-score ($0 \to 1 \to 2 \to 3$1)	One event per z-threshold crossing	Eq. (4)

For binary biomarkers, each biomarker has a single event $0 \to 1 \to 2 \to 3$2 indicating abnormality. If $0 \to 1 \to 2 \to 3$3 denotes the position in the sequence where biomarker $0 \to 1 \to 2 \to 3$4 becomes abnormal, then

$0 \to 1 \to 2 \to 3$5

The normal and abnormal densities can be estimated with Gaussian mixture modeling or KDE; in the ADNI experiment, Gaussian mixture modeling was used for CSF markers (Jonge et al., 25 Feb 2026).

For ordinal biomarkers, the model generalizes the binary formulation to multiple ordered score-reaching events. If $0 \to 1 \to 2 \to 3$6 indexes ordinal score levels, the paper writes

$0 \to 1 \to 2 \to 3$7

The intended interpretation is that once stage $0 \to 1 \to 2 \to 3$8 implies that biomarker $0 \to 1 \to 2 \to 3$9 has reached score level $z=1,2,3$0, the observed value is evaluated under the likelihood for that score state. The score-state distribution may be chosen by the user, for example as a categorical distribution or a Gaussian distribution. The binary model is treated as a special case of the ordinal model with $z=1,2,3$1 (Jonge et al., 25 Feb 2026).

For z-score biomarkers, events are defined as reaching successive z-score thresholds, following piecewise linear z-score SuStaIn. The likelihood is

$z=1,2,3$2

In this expression, $z=1,2,3$3 is already transformed to a z-score, $z=1,2,3$4 is the stage-$z=1,2,3$5 point estimate of the piecewise linear trajectory for biomarker $z=1,2,3$6, and $z=1,2,3$7 is biomarker-specific noise (Jonge et al., 25 Feb 2026). An explicit implementation choice in the paper is that, rather than integrating over the piecewise linear trajectory, the likelihood compares the observation to a point estimate on the trajectory. This is described as more efficient while giving similar results.

Across subtypes, Mixed-SuStaIn uses the SuStaIn mixture

$z=1,2,3$8

Here $z=1,2,3$9 is the subtype proportion and $z_{\max}$0 is the Mixed Events likelihood from Eq. (1) (Jonge et al., 25 Feb 2026).

The formulation implies several structural assumptions. Progression is monotonic, biomarkers move only forward through events, and once an event occurs it remains occurred. Each subtype is represented by a single event ordering shared across subjects in that subtype, with subjects differing by stage. Because biomarker likelihoods are multiplied at fixed stage and subtype, the model also assumes conditional independence across biomarkers given stage and subtype (Jonge et al., 25 Feb 2026).

4. Inference, preprocessing, and implementation

The likelihood formulation is described in substantially more detail than the optimization procedure. What is explicit in (Jonge et al., 25 Feb 2026) is that Mixed Events is implemented within the SuStaIn framework, the code is available in pySuStaIn, subtype count $z_{\max}$1 is selected by five-fold cross-validation, event ordering is estimated by maximizing the mixed-data likelihood, and subject staging and subtype assignment are inferred under the fitted mixture model. The paper does not provide explicit EM-style update equations, does not present MCMC formulas, and does not describe initialization in detail.

Accordingly, the inference description is intentionally limited. Sequence initialization is not explicitly described. The optimization routine for event ordering is not specified beyond the statement that Mixed Events provides a single objective function for estimating the event ordering. Practical inference appears to rely on the existing SuStaIn implementation machinery in pySuStaIn, but the exact optimization steps are not written out in the paper (Jonge et al., 25 Feb 2026). This suggests continuity with standard SuStaIn implementations, although the specific search strategy is not documented there.

The preprocessing requirements depend on biomarker type. Biomarkers must be assigned to one of the three model classes $z_{\max}$2, $z_{\max}$3, or $z_{\max}$4. Binary biomarkers require estimates of normal and abnormal distributions. Ordinal biomarkers require a probabilistic model over ordinal states. Z-score biomarkers require a reference distribution for z-scoring and user-specified event thresholds together with $z_{\max}$5 (Jonge et al., 25 Feb 2026).

For the ADNI application, MRI volumes were z-scored using cognitively normal participants as the reference group, corrected for age and intracranial volume, and ventricles were log-transformed. For z-score event design, the z-values were set as the integers up to the 95% quantile, and $z_{\max}$6 was set to the 99% quantile, rounded to the nearest integer. CSF markers amyloid-$z_{\max}$7, p-tau, and t-tau were log-transformed and modeled as binary biomarkers, with normal and abnormal likelihoods estimated using Gaussian mixture modeling (Jonge et al., 25 Feb 2026).

The paper does not discuss missing-data handling. It also does not document pySuStaIn API calls, class names, command-line usage, or exact optimization settings. Any implementation guidance beyond those points would therefore go beyond the documented description in (Jonge et al., 25 Feb 2026).

5. Simulation studies and the ADNI experiment

The simulation experiments were designed to test recovery of known mixed-type subtype trajectories. Synthetic data for each input type were generated using prior methods: z-scored data from prior z-score SuStaIn work, ordinal data from Ordinal SuStaIn, and binary data from EBM. The simulations varied the number of subjects $z_{\max}$8, number of subtypes $z_{\max}$9, number of biomarkers $i$0 corresponding to z-score plus ordinal plus binary biomarkers, and event or value settings $i$1 and $i$2. Each experiment was repeated 10 times with different randomly chosen subtype progression patterns and datasets (Jonge et al., 25 Feb 2026).

Performance was assessed using Kendall’s rank correlation between the inferred event ordering and the ground-truth subtype pattern. Across all settings, Kendall rank correlation ranged approximately from 0.6 to 1.0. Mixed-SuStaIn could recover ground-truth subtype patterns well. Performance decreased as the number of subtypes increased, which the paper attributes to fewer subjects per subtype, and decreased with fewer biomarkers, likely because subtype trajectories become less well defined and less separable (Jonge et al., 25 Feb 2026).

The real-data application used ADNIMERGE downloaded Feb 3, 2025, including all participants with baseline 3T MRI and CSF data. The cohort comprised 641 total subjects: 209 cognitively normal, 341 with MCI, and 91 with AD. Clinical diagnosis at 24 months served as an outcome measure (Jonge et al., 25 Feb 2026).

The biomarker set combined six MRI-derived continuous z-score biomarkers and three CSF binary biomarkers. The MRI biomarkers were total brain, ventricles, hippocampus, entorhinal cortex, middle temporal gyrus, and fusiform gyrus. The reported z-score event ranges were hippocampus $i$3 with $i$4, entorhinal cortex $i$5 with $i$6, total brain, middle temporal gyrus, and fusiform $i$7 with $i$8, and ventricles $i$9 with $M(i) \in \{B, O, Z\},$0. The CSF biomarkers were amyloid-$M(i) \in \{B, O, Z\},$1, phosphorylated tau, and total tau. No ordinal biomarkers were included in the ADNI experiment (Jonge et al., 25 Feb 2026).

Five-fold cross-validation selected two subtypes. The first subtype was interpreted as typical AD progression, with earliest abnormalities in amyloid-$M(i) \in \{B, O, Z\},$2, p-tau, and t-tau, followed later by structural atrophy. The second subtype was characterized by early atrophy in hippocampus, total brain, and entorhinal cortex, followed by amyloid-$M(i) \in \{B, O, Z\},$3 and late tau pathology. The authors note similarity between the second subtype and a previously reported cortical subtype. The reported subtype counts contain an internal discrepancy: the textual description gives $M(i) \in \{B, O, Z\},$4 and $M(i) \in \{B, O, Z\},$5, whereas the figure caption reports different values (Jonge et al., 25 Feb 2026).

The staging results were clinically aligned in the limited sense reported in the paper. Cognitively normal and MCI subjects were generally assigned to lower stages than AD patients, and subjects who converted within 24 months tended to be assigned to higher stages (Jonge et al., 25 Feb 2026). This supports the clinical relevance of the inferred stage variable, although no stronger causal or prognostic claim is made.

6. Comparison with EBM-SuStaIn, scope of use, and limitations

For comparison with EBM-SuStaIn, the ADNI analysis was restricted to biomarkers compatible with both methods, excluding ordinal biomarkers and treating the benchmark as binary-event-based. EBM-SuStaIn also found two subtypes: a typical AD sequence with CSF abnormalities first followed by atrophy, and a second subtype with early hippocampal and entorhinal involvement and later tau changes. Thus the broad subtype structure was qualitatively similar across the two methods (Jonge et al., 25 Feb 2026).

Predictive performance using baseline stage to predict 24-month conversion was nearly identical. For CN $M(i) \in \{B, O, Z\},$6 MCI conversion, Mixed-SuStaIn achieved AUC $M(i) \in \{B, O, Z\},$7 and EBM-SuStaIn achieved AUC $M(i) \in \{B, O, Z\},$8. For MCI $M(i) \in \{B, O, Z\},$9 AD conversion, Mixed-SuStaIn achieved AUC $B$0 and EBM-SuStaIn achieved AUC $B$1. Correlation between SuStaIn stage and MMSE was also similar: for subtype 1, Mixed-SuStaIn had $B$2 versus $B$3 for EBM-SuStaIn, and for subtype 2, Mixed-SuStaIn had $B$4 versus $B$5 (Jonge et al., 25 Feb 2026).

The principal significance of Mixed-SuStaIn is therefore not superior performance in that restricted benchmark, but the broader modeling flexibility to combine multiple biomarker types in one coherent subtype-and-stage framework. The method is most appropriate when datasets contain multiple biomarker types, some variables are naturally continuous progression measures, others are better modeled as binary abnormality transitions or ordinal scores, and both subtyping and staging are of interest (Jonge et al., 25 Feb 2026). This is especially relevant in multimodal neurodegeneration studies combining imaging, fluid biomarkers, clinical scales, and visual ratings.

The limitations described in (Jonge et al., 25 Feb 2026) are equally central. Inference details are not fully described, so implementation specifics must be obtained from pySuStaIn rather than the article text itself. Recovery of subtype structure worsens with more subtypes, fewer biomarkers, and effectively fewer subjects per subtype, indicating a dependence of identifiability on data richness. The model assumes monotonic irreversible trajectories, which may be restrictive for noisy or non-monotone biomarkers. The z-score component depends on the specification of event thresholds and $B$6. The ADNI comparison may understate the distinctive value of Mixed-SuStaIn because ordinal biomarkers were excluded. The paper also does not discuss missing-data handling (Jonge et al., 25 Feb 2026).

Taken together, Mixed-SuStaIn can be understood as a heterogeneous event-sequence generalization of SuStaIn: it preserves the latent-stage and subtype-mixture structure of the original framework while replacing a single biomarker family with per-biomarker likelihoods for binary, ordinal, and z-score events. Its main contribution lies in enabling a unified progression model for mixed continuous and discrete biomarker data without requiring all variables to be coerced into one trajectory type (Jonge et al., 25 Feb 2026).