We performed experiments with our proposed method, ClusTric, in the Lisbon ALS Clinic Dataset and verified the outcomes through external validation using the Pooled Resource Open-Access ALS Clinical Trials (PRO-ACT) cohort28. We conducted an extensive analysis of ClusTric results regarding patients’ follow-up and studied how the patients’ progression evolved in 6 months of follow-up by studying each progression group. Moreover, we performed experiments using a state-of-the-art framework named MoGP, which consists of an unsupervised approach to aggregate patient trajectories into clusters using Gaussian processes, and determine the number of clusters using a Dirichlet process mixture model9. Finally, we explored the survival of the progression groups identified by both methodologies, ClusTric and MoGP. In this section, we present the results obtained.ALS datasetsWe conducted our study using the Lisbon ALS Clinic dataset, which consists of Electronic Health Records from ALS Patients who have been regularly monitored at the local ALS clinic since 1995. The used dataset was last updated in May 2023 and includes 1677 patients. Each patient in the dataset has a set of static features (Table 1) such as demographics, disease severity, co-morbidities, medication, genetic information, exercise and smoking habits, past trauma/surgery, occupations, and familial history. Sex was considered in the study design as it is an important attribute to be considered in the disease study. In the context of the medical evaluation, the sex of human research participants was determined by self-report as well as physical and physiological characteristics, such as genetics, hormone function, and reproductive anatomy. Additionally, there are temporal features collected repeatedly during follow-up, including disease progression tests such as the ALSFRS-R scale and respiratory tests. Patients are assessed with an average frequency of 3 months. The study was conducted in accordance with the Declaration of Helsinki and was approved by the local (Faculty of Medicine, University of Lisbon) ethics committee. Informed consent to participate in the study was obtained from all patients. No individual-level data was shared. No compensation was given for participation.Table 1 Characterization of the population used in the case studyAdditionally, we performed an external validation of the proposed stratification method on a publicly available repository of merged ALS clinical trials data, the Pooled Resource Open-Access ALS Clinical Trials dataset (PRO-ACT)28. PRO-ACT includes information from a specific population of 11675 ALS patients who participated in clinical trials. It provides a comprehensive range of data features, including demographic details, laboratory results, past medical and familial history, and more (Table 1). However, since multiple trials were merged to create this dataset, different types of information are available for different patients. The PRO-ACT data went through a preprocessing phase to calculate the ALSFRS-R subscores (Table 2) used as input for our methodology. The records were sorted based on the difference between the first time a patient was observed and the time of each assessment over the trial. The records without the ALSFRS-R score or its respiratory items were removed.Table 2 ClusTric input featuresThe physical condition of ALS patients hampers them from completing all the prescribed tests in a single day. Therefore, the dates of the different performed tests are misaligned. To tackle this problem, the Lisbon ALS Clinic Dataset went through a preprocessing phase, following the methodology proposed by Carreiro et al.27.This methodology considers the temporal distribution of tests by creating snapshots of the patient’s condition. These snapshots group together tests that were performed within a clinically accepted time window, which in this case is set to 100 days (as in ref. 27), given the mean frequency of patient assessments.To generate these snapshots, the process employed a hierarchical (agglomerative) clustering method with constraints, which is a state-of-the-art procedure for aligning data along a follow-up period27. The constraints applied during the grouping of evaluation sets followed the originally established principles, with just one constraint: all the tests within a snapshot must be different, as clinicians do not prescribe the same test in the same appointment. Other constraints previously considered relevant for predictive models were irrelevant here since we are dealing with an unsupervised method.Finally, note that for the application of the proposed method, we have to understand our datasets as three-way data, with patients, features, and time as dimensions (as illustrated in Fig. 6). In particular, we considered the initial three appointments of the 7 features in Table 2 of the patients enrolled in the Lisbon ALS Clinic dataset and the PRO-ACT dataset. Patients with fewer than three appointments were excluded from the analysis, resulting in a total of 983 patients in the Lisbon ALS Clinic dataset and 3880 in the PRO-ACT dataset (see Tables 1 and S1 of the Supplementary material).ClusTric in Lisbon ALS clinic datasetClusTric was applied to the Lisbon ALS Clinic dataset. We performed experiments to determine the number of clusters, considering three, four and five clusters. The determination of the number of clusters was then guided by both the hierarchical clustering dendrogram (Fig. 1A), particularly by analyzing the inter-cluster difference, and by analyzing specific clustering metrics, namely the Silhouette score, and the Calinski-Harabsz and Davies-Bouldin indexes (Fig. 1B).Fig. 1: Cluster analysis and characterization on Lisbon ALS cohort.A Dendrogram resulting from ClusTric; (B) clustering evaluation scores obtained with 3, 4, and 5 clusters; (C) average temporal feature trajectories (lines) and 95% confidence intervals (shades around lines). The numbers next to each point in the trajectories represent the number of patients in the < cluster,appointment > set, whereas the numbers between consecutive appointments indicate the average slope between consecutive measurements in a cluster. Source data are provided as a Source Data file.The resulting four patient clusters were characterized by analyzing the temporal patterns of key features, as defined by clinicians, over five appointments, covering approximately one year of follow-up (Fig. 1C). To ensure consistency in the trajectories, an onset-anchor value was added, representing the maximum clinical score assigned to the date corresponding to symptom onset, designated as time point 0. Based on the trajectories, we designated the clusters as Slow Progressors (SP), Moderate Progressors mainly bulbar (MPb), Moderate Progressors mainly spinal (MPs), and Fast Progressors (FP).Furthermore, we examined the features at disease onset and at 1st visit of each cluster, and identified features that were more significant in distinguishing between the clusters compared to others (see Table 3). We applied the Chi-Square two-sided test to determine the difference between clusters in the proportion of sex. We also performed normality tests (Kolmogorov-Smirnov two-sided test) to determine which continuous features followed a normal distribution. For non-normal distribution features (age at onset, diagnostic delay, body mass index (BMI), the slope of ALSFRS-R at 6 months, ALSFRS-R at 1st visit, and phrenic nerve response latency at 1st visit) the non-parametric Kruskal–Wallis two-sided test was used to examine if the distribution of these features was the same for all the clusters. Pairwise comparisons between the clusters were performed with the Bonferroni correction. The vital capacity (VC) and the phrenic nerve response amplitude at 1st visit were the features following a normal distribution and the One-Way ANOVA was performed to compare the mean among the clusters in conjunction with a post-hoc Tukey’s Honestly Significant Difference (HSD) test to identify specific pairwise differences between the clusters. The significance of each feature was determined using a p-value threshold of 0.05. For example, the BMI and the latency of the phrenic nerve at 1st visit were deemed non-significant in characterizing the patient clusters. Additionally, the significance of the remaining features varied among pairs of clusters. Specifically:
The distribution of the diagnostic delay was only significantly different for the pair of clusters MPb and SP (p-value of 0.004).
The age at disease onset exhibited the same distribution for clusters SP and MPs, while the distributions were significantly different for the other pairs of clusters. In particular, a p-value < 0.001 was found for all the remaining pairwise comparisons, except for the pair {MPb,FP} where it was 0.037.
The difference in the vital capacity (VC) at 1st visit was not significant for the pair {MPb,MPs} (p-value of 0.692). In contrast, the VC for the cluster FP was notably lower than that of all the remaining clusters (p-value < 0.001 for the combinations involving cluster FP) and higher for the cluster SP (p-value < 0.001 for the combinations involving cluster SP).
The slope of the ALSFRS-R score in the first 6 months showed significant differences only among the pairwise combinations involving cluster SP (p-value < 0.001 for the combinations involving cluster SP), similar to the mean phrenic amplitude at 1st visit.
The ALSFRS-R at 1st visit distribution was significantly different in all the pairwise combinations.
The identified groups showed specific disease progressions that are representative of the patients’ evolution, which cannot be understood as subtypes of the disease since a given patient could start progressing slower or faster at some point according to specific functional domains.Table 3 Disease onset and 1st visit characterizationClusTric in PRO-ACT datasetTo validate the proposed methodology, ClusTric was also applied to the PRO-ACT dataset. As before, we learned the triclustering patterns, performed the triclustering-based data transformation and determined the number of clusters guided by the dendrogram resulting from the application of hierarchical clustering (Fig. 2A) and of the different clustering metrics for three, four, and five clusters (Fig. 2B).Fig. 2: Cluster analysis and characterization on PRO-ACT ALS cohort.A Dendrogram resulting from ClusTric; (B) clustering evaluation scores obtained with 3, 4 and 5 clusters; (C) average temporal feature trajectories (lines) and 95% confidence intervals (shades around lines). The numbers next to each point in the trajectories represent the number of patients in the <cluster,appointment> set, whereas the numbers between consecutive appointments indicate the average slope between consecutive measurements in a cluster. Source data are provided as a Source Data file.As performed for the Lisbon ALS Clinic dataset, the resulting four groups were characterized using the progression of the clinically relevant temporal features across five appointments (see Fig. 2C). The obtained trajectories show similarities with the ones observed in the Lisbon ALS Clinic dataset. However, the cluster MPs exhibits a slower progression in the Upper Limb subscore (ALSFRSsUL) and a faster progression regarding the remaining motor subscores (ALSFRSsT and ALSFRSsLL). This difference arises because the measurements of the ALSFRSsUL subscore in the PRO-ACT dataset exhibit slight change over the considered timeframe when compared to the previously used Lisbon cohort (see Table S1 of the Supplementary material). Specifically, in the PRO-ACT dataset, the overall average ALSFRSsUL subscore is 5.80 ± 1.92 at the first appointment and 5.30 ± 2.20 at the third appointment. This contrasts with the Lisbon ALS Clinic dataset at equivalent time points, corresponding to 6.36 ± 1.86 at the first appointment and 4.92 ± 2.59 at the third appointment.Another difference in the behavior of the cluster MPs when compared to the results from the Lisbon ALS Clinic dataset pertains to its MiToS stage’s trajectory. In particular, in the Lisbon ALS Clinic dataset, the MiToS stage of the patients in this progression group remains 2 at the first and second appointments and increases to 3 at the third appointment (Fig. 1C). In contrast, in the PRO-ACT cohort (Fig. 2C), the MiTos stage of the cluster MPs remains constant at 1, over five consecutive appointments, mirroring the MiTos stage’s trajectory of cluster SP until the third appointment.Comparing the onset features of the disease progression groups identified in the two datasets (Lisbon ALS Clinic dataset and PRO-ACT), there are also slight differences (see Tables 3 and S2 of the Supplementary material). Particularly, in PRO-ACT, the cluster FP is predominantly composed of young man (61.9%) with a mean onset age of 54.87 years. Additionally, the patients comprising the cluster MPs have a higher mean ALSFSR-R score at onset (39.08) compared to those in cluster MPb (35.60), which differs from the behavior verified in the Lisbon ALS Clinic dataset.Comparison with MoGPMoGP9 is a Gaussian process-based framework for aggregating patient trajectories into clusters with relevant results in ALS. This framework determines the number of clusters using a Dirichlet process mixture model and induces a monotonic bias to encourage the identification of declining trajectories. In this context, we compare ClusTric with MoGP. To ensure a fair analysis, we preprocessed the Lisbon ALS Clinic snapshots and the PRO-ACT following the same preprocessing steps imposed by MoGP9. This involved discarding patients who met any of the following criteria: (1) having fewer than three complete appointments, (2) exhibiting a difference of more than 7 years between the first visit and symptom onset, or (3) experiencing an increase of more than six points in ALSFRS-R between consecutive visits. Consequently, 954 patients from the Lisbon ALS Clinic dataset and 3801 patients from the PRO-ACT were included in this comparative experiment.MoGP identified 27 clusters in the Lisbon ALS Clinic dataset, with the largest cluster comprising 75 patients and the smallest containing only 1 patient (Fig. 3A). To compare with ClusTric, we provide a visual representation of the four most representative cluster trajectories unveiled by MoGP (Fig. 3B). The cluster with the largest duration amongst these four clusters (G3, n = 73) exhibits an almost linear trajectory over time. On the other hand, cluster G1 with 71 patients presents a more irregular trajectory, with periods of increase and decrease of the ALSFRS-R score at different speeds. Finally, the trajectories of the clusters G4 and G2, with 75 and 72 patients, respectively, are very similar, starting with a rapid decline, and stabilizing around appointment 2. These four trajectories strongly overlap over time, therefore, MoGP does not allow the coherent characterization of the patients within each cluster.Fig. 3: Comparison of ALSFRS-R trajectories per cluster between ClusTric and MoGP.Top subfigures (A–C) show the results on the Lisbon ALS dataset, while bottom ones (D–F) present the results for the PRO-ACT dataset. A and D show all MOGP trajectories, with B and E highlighting the four most dominant MOGP trajectories; C and F show the ClusTric trajectories. Lines represent average values and shaded areas the corresponding 95% confidence interval. For this analysis we preprocessed both cohorts following the steps needed by MoGP9 on both methods (which is more restrictive than ClusTric), resulting in a total of 954 and 3801 included patients in the Lisbon and PRO-ACT cohorts, respectively. MoGP identified 27 clusters in the Lisbon cohort (A), while ClusTric identified 4 (C). Regarding the PRO-ACT dataset, MoGP identified 92 clusters (D), while ClusTric identified 4 clusters (F). MoGP does extensive smoothing on trajectories resulting in yy axis values out of scale.In contrast, our approach identified four clusters using the same set of patients, matching those previously found (SP, MPb, MPs and FP). The larger cluster (MPb) comprised 338 patients, while the smaller cluster (FP) comprised 66 patients. Figure 3C illustrates the trajectories of the ClusTric groups. Notably, the trajectories of the four groups demonstrate significant differences. The cluster with 318 patients (SP) displays an almost quadratic trajectory characterized by a gradual decline. This cluster exhibits the longest duration among the groups and matches the SP cluster of the previous analysis. The clusters with 338 (MPb) and 232 (MPs) patients share similarities; however, the latter exhibits a slower decline and a shorter follow-up duration compared to the former. Conversely, the cluster with fewer patients (FP) shows a more irregular trajectory over time. It demonstrates periods of steep decrease followed by periods of moderate decline, resulting in varying progressions in the ALSFRS-R score. This irregularity may potentially be attributed to the limited number of patients available for analysis over time.The comparison of the two approaches applied to the PRO-ACT dataset yielded similar conclusions (Fig. 3D–F). However, MoGP identified 92 overlapping clusters (more than in the Lisbon Clinic dataset), contrasting with the 4 different progression groups found by ClusTric.On the other hand, when comparing the trajectories found by ClusTric in the Lisbon and PRO-ACT datasets, two differences strike-out: in the PRO-ACT dataset, the FP cluster decreases less sharply, while the MPb and MPs clusters have more similar ALSFRS-R trajectories. As expected, patients with isolated bulbar dysfunction would not be recruited in clinical trials, some of these patients can progress without disease spreading for some time, giving this group a slower ALSFRS-R score decay, an observation not disclosed in bulbar-onset patients included in trials.Furthermore, we evaluated the clustering metrics of both models, MoGP and ClusTric (see Table 4). MoGP yielded negative Silhouette scores, indicating suboptimal partitioning of the data into meaningful clusters. In contrast, ClusTric demonstrated a more effective grouping of the patients.Table 4 Clustering evaluationIn conclusion, MoGP identifies trajectories solely based on a single feature, in this case, the ALSFRS-R total score. In contrast, our approach can uncover relationships between multiple features and patients over time. Additionally, it uncovers comprehensive patterns while relying less on exhaustive preprocessing and being approximately 367 times faster than MoGP in this experiment.Survival analysis in the Lisbon ALS clinic datasetTo validate the predictive utility of the proposed stratification we performed a survival analysis on the Lisbon ALS Clinic dataset and compared the results with the 4 most dominant clusters obtained by MoGP.Survival analysis was done using the Kaplan-Meier method and the log-rank test was used to test the difference between survival curves. The study was conducted by considering an 8-year follow-up and reflects the duration of the date of the first visit to death, in years. Survival rates are expressed as the percentage of patients surviving for 2 years calculated using the Kaplan-Meier method. All the analyses were carried out in SPSS version 29, considering a statistical significance of 0.05.Figure 4 presents the result of the survival analysis performed on the Lisbon ALS Clinic dataset. For ClusTric, the survival curve shows that the group FP was the one with the shortest survival rate of 24.6 months (ranging from 19 to 30 months), and a 2-year survival rate of 27% (95% CI of 16–39%). The SP group is the one with the longest survival rate, with a 2-year survival rate of 81% (95% CI of 77–85%) and a mean survival of 53.9 months (ranging from 50 to 57 months). The two moderate progressors groups have similar survival rates and mean survival time. This was confirmed by the pairwise statistical comparison, p = 0.955. All other survival curves were considered statistically different (see Table S3 of the Supplementary material).Fig. 4: Survival analysis on the Lisbon ALS cohort.A Kaplan–Meier curves showing up to 8 years follow-up for MoGP and ClusTric comparing the groups identified by each method and tables with the number of patients at risk, censored, and that died by year in each group. Log-rank test between survival curves and p-values of pairwise comparisons between curves in Table S3 of the Supplementary material. B Mean survival time (in months) and 95% of confidence interval for MoGP and ClusTric. C Survival rates as the percentage of patients surviving for 2 years calculated using the Kaplan–Meier method.Regarding MoGP, it identified 27 clusters in the Lisbon cohort, however, only the four most predominant clusters were considered for the survival analysis. The analysis showed that the three groups are quite similar and only group G3 diverges from the remaining. In particular, group G3 presented statistically significant differences when compared to any other group (see Table S3 of the Supplementary material). The mean survival time and the 2-year survival rate of group G3 are higher than in the remaining groups (Fig. 4).Prediction of group progressionDespite the specific disease progression identified by the proposed method, it is possible that, at a given moment, the progression changes for certain patients. Hence, we set to find out whether the patients always remained within the original cluster, or changed over time.To answer this question, we investigate the progression of the group assignment for each patient from appointments 1–3 (approximately, the first 6 months) to appointments 3–5 (approximately, the following 6 months). For this, we employed a Random Forests classifier, using the clustering labels obtained from the previous analysis as the target prediction. The classifier was trained using the transformed data of the initial three appointments. We then predicted the patient’s cluster considering the third to fifth appointments. The analysis is depicted in Fig. 5A indicates that the majority of patients (66.82%) remained in the same cluster during the 12 months of follow-up, whereas 33.18% of patients changed their cluster.Fig. 5: ClusTric clusters transition from 6 to 12 months follow up on the Lisbon ALS cohort.A Sankey diagram with patient’s transitions between ClusTric clusters and the number of patients that transition from one cluster to any other cluster. B Survival analysis of patients coming from group SP in the first 6 months to other progression groups (namely, SP, MPb, and MPs) in the following 6 months. Log-rank test between survival curves and p-values of pairwise comparisons between curves are in Table S4 of Supplementary material.Given the lack of ground truth to confirm the assignments obtained by the classifier, we decided to do a survival analysis of the patients belonging to one group (e.g., SP) found by the ClusTric method and were then classified in the second period of follow-up as belonging to different groups. Figure 5B presents the analysis for the patients coming from group SP (composed of 313 patients) that were later classified either as SP, MPb, and MPs. The new SP group is composed of 196 patients and is the one with a higher survival rate, with a 2-year survival rate of 93% (95% CI of 90–97%). The MPb in the second period is composed of 47 patients and has the lowest survival rate, in particular, a 2-year survival rate of 78% (95% CI of 66–90%). Finally, MPs is composed of 69 patients and has a 2-year survival rate of 83% (95% CI of 74–92%).Moreover, from the patient transition table in Fig. 5A, we notice that some transitions correspond to outliers, e.g., one patient shifted from SP to FP. Although a steep decline of 20 points in the ALSFRS-R score was observed for that patient in the second period, further conclusions could not be drawn from a single observation.Finally, the survival curves for the remaining transitions are not presented due to a small sample size. In particular, the transition from MPb to MPs includes only 27 patients, and the transition from MPs to FP has only 10 patients. Nonetheless, when analyzing the 2-year survival rate for such transitions, we noticed that patients who remain in the MPb group (a total of 130 patients) have a survival rate of 74% (95% CI of 66–81%), and the ones that shifted to FP coming from MPb (a total of 61 patients) have a survival rate of 51% (95% CI of 38–64%).