A Structural FHMM for Interpretable Disease Trajectories in T2DM

Alessandro Mari; Ekaterina Krymova; Guillaume Obozinski; Maria Luisa Marques de Sa Faquetti; Adrian Martinez de la Torre; Andrea Burden

cs.LGAug 25, 2026

A Structural FHMM for Interpretable Disease Trajectories in T2DM

Authors: Alessandro Mari, Ekaterina Krymova, Guillaume Obozinski, Maria Luisa Marques de Sa Faquetti, Adrian Martinez de la Torre, Andrea Burden

Organizations: Swiss Data Science Center (SDSC), Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Switzerland · Swiss Data Science Center (SDSC), ETH Zürich, Switzerland · Pharmacoepidemiology Group, Institute of Pharmaceutical Sciences, Zurich, Switzerland

Abstract

In this work, we propose a structural variant of the Factorial Hidden Markov Model (FHMM) for the analysis of disease trajectories in patients with Type 2 diabetes mellitus (T2DM). The model represents a patient's latent health state as a combination of multiple independent, simultaneously evolving components, associated with comorbidities and lab results. This structured latent representation facilitates the identification of clinically meaningful patient states and clustering of common disease trajectories. We evaluate the proposed approach using The IQVIA Medical Research Data incorporating data from THIN, a Cegedim database of anonymized electronic health records (EHR), identifying patients with a first-ever prescription for a non-insulin antidiabetic drug (NIAD) between January 2006 and December 2019. The model identifies multiple clinically coherent latent components corresponding to known patterns of diabetes-related complications and reveals heterogeneous progression pathways, including distinct microvascular-dominant and multi-organ trajectories associated with elevated comorbidity burden and mortality. These results demonstrate that the proposed framework captures meaningful longitudinal structure in EHR data and provides interpretable insights into the evolution of T2DM and its comorbidities.

Figures & tables

Figure 1: Graphical representation of the preprocessing steps.

Comorbidities	Lab Values	Drugs (with ATC code)
• Stroke • Myocardial infarction (MI) • Congestive heart failure (CHF) • Peripheral vascular disease (PVD) • Diabetic retinopathy (DR) • Hypertension (HT) • Chronic kidney disease (CKD) • Osteoporosis • Chronic obstructive pulmonary disease (COPD) • Chronic liver disease (CLD)	• Glycated hemoglobin (Hb A1c) in % • Low-density Lipoprotein (LDL) cholesterol in mmol/L • High-density Lipoprotein (HDL) cholesterol in mmol/L • Triglycerides (TG) in mmol/L • Blood pressure (Systolic/Diastolic) in mmHg • Body Mass Index (BMI) in kg/m 2 • Glomerular filtration rate (GFR) in mL/min/1.73m 2	• Diabetes Drugs 1 1 1 Including Gliclazide, Glimepiride, Glipizide, Metformin, Pioglitazone, Rosiglitazone, Sitagliptin, Dapagliflozin. • Antithrombotic agents (B01) • Cardiac therapy (C01) • Antihypertensives (C02) • Diuretics (C03) • Beta blocking agents (C07) • Calcium channels blockers (C08) • ACE inhibitors (C09) • Statins (C10) • Corticosteroids (H02) • Drugs for treatment of bone diseases (M05)

Table 1: List of variables that are included in the model.

Panel of Figure 2 — Figure 2: Directed graphical model of a FHMM with $M=3$ hidden chains. Arrows represent causal relationships and gray nodes are observed variables. White nodes are not observed. The variables $X_{t}$ are the drugs taken at time $t$ that influence the patient health state $H_{t}\stackrel{{\scriptstyle\rm def}}{{=}}(H_{t}^{(1)},\dots,H_{t}^{(M)})$ . The results of the lab tests $Y_{t}^{\text{LAB}}$ and the set of comorbidities $Y_{t}^{\text{COM}}$ are direct consequences of the health state $H_{t}$ at time $t$ .

Panel of Figure 3 — Figure 3: Possible transitions between states of a hidden chain with $5$ states and jumps of size $d=1$ .

Figure 4: Filtering of patients based on missing laboratory data during the four years preceding NIAD initiation. A total of 100325 patients were excluded. Abbreviations are defined in Table 1 .

Sex	Men		Women
Age group	$<65$	$65+$	$<65$	$65+$
Number of patients	27191	21989	20792	18229
Average age at NIAD (y) $\pm$ SD	54.0 $\pm$ 8.0	73.7 $\pm$ 6.3	52.5 $\pm$ 9.3	74.9 $\pm$ 6.7
Median follow-up duration in years post-NIAD [IQR]	4.5 [5.0]	4.0 [4.5]	4.0 [5.0]	4.0 [4.5]
Average BMI at NIAD (kg/m 2 ) $\pm$ SD	32.9 $\pm$ 6.3	30.1 $\pm$ 5.1	35.4 $\pm$ 7.9	31.0 $\pm$ 6.4
Average HbA1c at NIAD (%) $\pm$ SD	7.4 $\pm$ 1.7	7.1 $\pm$ 1.4	7.2 $\pm$ 1.6	7.0 $\pm$ 1.3

Table 2: Patient characteristics at the index date (NIAD initiation) for the cohort after preprocessing. Comorbidities are reported as percentages of the cohort population. Laboratory measurements are summarized as mean values, with the proportion of missing observations reported in parentheses. Abbreviations are defined in Table 1 . SD denotes standard deviation and IQR denotes interquartile range.

	Men $<65$		Women $<65$		Men $65+$		Women $65+$
Model	BIC	AIC	BIC	AIC	BIC	AIC	BIC	AIC
$\text{HMM}(27)_{8}$	329077	314469	236219	221959	234704	220497	212736	198738
$\text{FHMM}(3,3)_{1}$	310663	307445	225526	222385	229629	226500	203633	200550
$\text{FHMM}(4,4)_{2}$	292039	286438	216236	210769	221682	216235	195206	189839
$\text{FHMM}(4,6)_{2}$	293949	285052	211923	203239	220663	212010	195312	186787
$\text{FHMM}(6,4)_{2}$	264231	256136	190847	182946	201848	193976	181320	173563

Table 3: Comparison between models with various number of chains. Metrics are evaluated on the validation set and drugs are not used as input.

Panel of Figure 5 — Figure 5: Top: Emission parameters $\eta$ modeling the risk of developing a comorbidity for a given state. Larger values indicate a higher probability of having the comorbidity. The values are reported on a logarithmic scale. Bottom: Mean value of lab tests with respect to the intercept (i.e., state 0). Red (resp. blue) indicates an increase (resp. decrease) in $\mathbb{E}[Y_{t}|H_{t}]$ relative to the intercept. The model includes 8 chains with 4 states per chain and is fitted on on Women $<65$ .

Figure 6: Estimated contribution of drug prescriptions to initial latent state allocation ( $W^{\text{init}}$ ), based on a model with 8 chains and 4 states per chain fitted to the Women $<65$ subgroup. Higher values indicate a greater probability of starting in a more severe latent state. These estimates capture baseline correlations, not causal effects, since they describe state assignment rather than counterfactual deviation.

Cluster	0	1	2	3	4	5	6	7	8	9	10	11	12
# of patients	3373	1468	1549	792	2774	1491	1101	1431	1006	1421	594	1143	1362
Avg. age at NIAD (y) $\pm$ SD	47.01 $\pm$ 10.68	47.1 $\pm$ 10.3	54.01 $\pm$ 7.19	57.49 $\pm$ 6.09	54.27 $\pm$ 7.5	54.53 $\pm$ 8.24	54.61 $\pm$ 7.71	55.52 $\pm$ 7.38	56.12 $\pm$ 7.1	53.19 $\pm$ 7.93	57.12 $\pm$ 6.27	48.75 $\pm$ 9.98	55.23 $\pm$ 7.86
Avg. follow-up post-NIAD (y) $\pm$ SD	3.73 $\pm$ 2.68	4.52 $\pm$ 2.98	5.88 $\pm$ 3.15	4.87 $\pm$ 2.99	4.63 $\pm$ 3.13	5.23 $\pm$ 3.28	5.23 $\pm$ 3.19	6.21 $\pm$ 3.27	5.37 $\pm$ 3.24	5.81 $\pm$ 3.25	6.79 $\pm$ 3.23	5.08 $\pm$ 3.0	6.52 $\pm$ 3.35
Avg. BMI at NIAD (kg/m 2 ) $\pm$ SD	33.15 $\pm$ 7.55	37.25 $\pm$ 7.79	34.07 $\pm$ 6.16	35.74 $\pm$ 7.81	34.54 $\pm$ 6.94	34.31 $\pm$ 6.73	35.04 $\pm$ 6.93	40.96 $\pm$ 9.87	36.64 $\pm$ 7.38	38.35 $\pm$ 7.72	31.23 $\pm$ 6.45	32.96 $\pm$ 6.62	38.04 $\pm$ 8.34
Avg. HbA1c at NIAD (%) $\pm$ SD	6.83 $\pm$ 1.56	7.26 $\pm$ 1.66	7.48 $\pm$ 1.61	7.24 $\pm$ 1.47	6.89 $\pm$ 1.37	7.15 $\pm$ 1.49	7.25 $\pm$ 1.48	7.51 $\pm$ 1.61	7.35 $\pm$ 1.5	7.05 $\pm$ 1.46	7.16 $\pm$ 1.59	7.94 $\pm$ 1.83	6.92 $\pm$ 1.37
% Ever smoked	23.04	79.56	20.46	78.41	20.01	29.51	43.23	56.81	55.07	59.25	30.13	24.41	50.07

Table 4: Patient characteristics in each cluster for the Women

<65

cohort with average values and standard deviation where applicable. Comorbidities are presented as absolute counts at NIAD initiation, along with the number of new comorbidities developed post-NIAD. Proportions, expressed as percentages of the cohort population, are reported in parentheses.

Figure 7: Average cluster-specific probabilities and lab values for Women $<65$ . Values have been centered by subtracting the average at the time of NIAD initiation to improve readability. Red bars indicate increases, and blue bars indicate decreases relative to the average patient at NIAD. Comorbidity risks are shown as changes in probability (left axis), and lab values as percentage changes relative to the reference value (right axis). Annotated numbers indicate absolute changes in the original units (see Table 1 ). Error bars represent the standard error of the mean.

Figure 8: Distribution of the clusters over time.

Figure 9: Cumulative Incidence Function (CIF) for the time to first cluster transition in Women $<65$ , stratified by initial cluster assignment at 6 months post-NIAD. The estimates account for censoring due to loss to follow-up and study termination, computed using the Aalen nonparametric estimator [ 25 ] .

Figure 10: Transition graph. Red arrows (resp. blue) means an increase (resp. decrease) of the comorbidity risk ( Women $<65$ ). Arrow thickness is proportional to the number of observed transitions. Transitions with less than 1% probability are not shown.

Appendix figures & tables21 assets

Supplementary material from the paper’s appendix.

Appendix

Lab Value	High	Comment
Glomerular filtration rate	150	-
Hb A1C	16	-
High Density Lipoprotein	5	-
Low Density Lipoprotein	10	-
Triglycerides	15	-
BMI	80	-

Appendix

Table 5: Predefined thresholds used to remove outliers. Values are removed if they are not included in the lower and upper limits.

	Men $<65$			Men $65+$			Women $<65$			Women $65+$
	Train	Val	Test	Train	Val	Test	Train	Val	Test	Train	Val	Test
COPD	7.7	7.6	8.0	16.4	16.1	17.0	7.8	7.9	7.9	13.3	12.8	15.6
Diabetic retinopathy	32.8	33.4	32.9	34.8	36.3	36.4	30.4	31.5	31.1	34.6	33.8	35.7
Hypertension	59.5	59.7	61.3	71.2	71.0	71.9	56.9	57.0	57.1	78.6	79.9	79.2
Myocardial infarction	8.8	9.2	9.0	16.6	17.1	18.5	3.0	2.8	2.8	7.9	6.8	7.3
Peripheral vascular disease	4.2	3.8	4.5	11.0	11.1	10.5	1.7	1.8	1.6	5.5	6.2	5.7

Appendix

Table 6: Number of patient diagnosed with the comorbidity for each data split. Numbers are given in percentage.

	Metric	BIC		AIC
Category	Model	Drugs	No Drugs	Drugs	No Drugs
Men $<65$	$\text{FHMM}(3,3)_{1}$	315914	310663	308086	307445
	$\text{FHMM}(4,4)_{2}$	308458	292039	294662	286438
	$\text{FHMM}(6,4)_{2}$	291660	264231	271273	256136
	$\text{FHMM}(8,4)_{2}$	280861	273337	253882	262748
	$\text{FHMM}(10,2)_{1}$	286149	276474	270171	270739

Appendix

Table 7: Comparison between models with drugs (

X_{t}

) and without drugs. Metrics are evaluated on the validation set.

Panel of Figure 11 — Figure 11: Top: Average effect of drugs on the transition matrix, estimated as $1/K\sum_{i=1}^{K}\left(W_{r,i}^{\text{drug}}-W_{l,i}^{\text{drug}}\right)$ . Red (resp. blue) means an increase of the probability to transition to a higher (resp. lower) state value. Bottom: Emission parameters $\eta$ modeling the risk of developing a comorbidity for a given state. Larger values indicate a higher probability of having the comorbidity. The model includes 8 chains with 4 states per chain and is fitted on Men $<65$ .

Figure 12: Cluster selection using Davies-Bouldin index and the prediction strength. The optimal number of cluster is indicated by the black dashed line. This is fitted on the population of Women $<65$ .

Panel of Figure 13 — Figure 13: Evolution of patient clusters 0 (healthy), 2 (pathway to multimorbidity), 3 (pulmonary-metabolic), 4 (isolated hypertension), 6 (hepatic), 8 (advanced nephropathy), 9 (obese hypertension), 10 (bone-vascular), 11 (isolated DR), and 12 (cardio-pulmonary multimorbidity) over time ( Women $<65$ ), conditional on the initial cluster assignment (6 months post-NIAD). The number of patients in each cluster is indicated alongside the corresponding bars. For clarity, flows representing less than 1% of the initial cluster size, as well as transitions to no available follow-up data, are not displayed. Clusters 1, 5, and 7 are excluded due to the low number of transitions observed from these clusters.

Cluster	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14
# of patients	6504	1788	1698	1166	3911	1522	360	1212	957	1534	1010	1511	1070	703	685
Avg. age at NIAD (y) $\pm$ SD	50.88 $\pm$ 8.68	53.66 $\pm$ 8.11	55.28 $\pm$ 6.95	57.41 $\pm$ 6.39	53.89 $\pm$ 7.32	56.18 $\pm$ 6.73	58.28 $\pm$ 5.63	53.21 $\pm$ 7.78	57.69 $\pm$ 5.92	57.42 $\pm$ 6.14	55.41 $\pm$ 7.21	51.53 $\pm$ 8.35	56.68 $\pm$ 6.42	55.89 $\pm$ 7.02	54.0 $\pm$ 7.97
Avg. follow-up post-NIAD (y) $\pm$ SD	4.28 $\pm$ 3.1	6.85 $\pm$ 3.25	5.78 $\pm$ 2.86	5.38 $\pm$ 3.11	4.72 $\pm$ 3.22	6.52 $\pm$ 3.27	4.49 $\pm$ 2.89	5.97 $\pm$ 3.06	5.46 $\pm$ 3.59	5.58 $\pm$ 3.57	3.63 $\pm$ 2.85	5.29 $\pm$ 2.75	6.25 $\pm$ 2.88	5.05 $\pm$ 3.08	6.29 $\pm$ 2.64
Avg. BMI at NIAD (kg/m 2 ) $\pm$ SD	30.85 $\pm$ 5.52	34.96 $\pm$ 6.67	31.58 $\pm$ 4.79	34.31 $\pm$ 6.68	32.47 $\pm$ 5.32	30.86 $\pm$ 4.48	32.25 $\pm$ 6.67	43.79 $\pm$ 5.7	32.82 $\pm$ 4.93	33.54 $\pm$ 4.23	33.08 $\pm$ 6.39	30.38 $\pm$ 4.95	36.46 $\pm$ 6.85	32.01 $\pm$ 6.18	34.96 $\pm$ 6.77
Avg. HbA1c at NIAD (%) $\pm$ SD	7.45 $\pm$ 1.73	7.39 $\pm$ 1.61	7.47 $\pm$ 1.59	7.31 $\pm$ 1.64	7.23 $\pm$ 1.56	7.19 $\pm$ 1.6	7.31 $\pm$ 1.61	7.44 $\pm$ 1.63	7.36 $\pm$ 1.7	7.2 $\pm$ 1.45	7.4 $\pm$ 1.71	7.69 $\pm$ 1.7	7.48 $\pm$ 1.59	7.47 $\pm$ 1.63	7.59 $\pm$ 1.65
% Ever smoked	43.48	53.75	32.63	62.86	39.43	34.82	71.67	39.69	53.81	44.72	55.15	39.38	44.11	70.13	53.87

Appendix

Table 8: Patient characteristics in each cluster for the Men

<65

Figure 14: Average cluster-specific probabilities and lab values for Men $<65$ . Values have been centered by subtracting the average at the time of NIAD initiation to improve readability. Red bars indicate increases, and blue bars indicate decreases relative to the average patient at NIAD. Comorbidity risks are shown as changes in probability (left axis), and lab values as percentage changes relative to the reference value (right axis). Annotated numbers indicate absolute changes in the original units (see Table 1 ). Error bars represent the standard error of the mean.

Panel of Figure 15 — Figure 15: Evolution of patient clusters over time ( Men $<65$ ), conditional on the initial cluster assignment (6 months post-NIAD). The number of patients in each cluster is indicated alongside the corresponding bars. For clarity, only the most frequent transitions are shown (see Figure 16 for more details). Cluster 6 is excluded due to the low number of transitions observed from this cluster.

Figure 16: Cumulative Incidence Function (CIF) for the time to first cluster transition in Men $<65$ , stratified by initial cluster assignment at 6 months post-NIAD. The estimates account for censoring due to loss to follow-up and study termination, computed using the Aalen nonparametric estimator [ 25 ] .

Figure 17: Transition graph. Red arrows (resp. blue) means an increase (resp. decrease) of the comorbidity risk ( Men $<65$ ). Arrow thickness is proportional to the number of observed transitions. Transitions with less than 1% probability are not shown.

Cluster	0	1	2	3	4	5	6	7	8	9	10	11	12
# of patients	2732	1515	1813	838	1974	1430	1125	1214	1954	3028	769	762	1319
Avg. age at NIAD (y) $\pm$ SD	72.61 $\pm$ 6.01	72.22 $\pm$ 5.62	73.01 $\pm$ 5.74	75.48 $\pm$ 6.69	74.38 $\pm$ 6.09	74.57 $\pm$ 6.37	75.52 $\pm$ 6.54	73.3 $\pm$ 6.12	74.73 $\pm$ 6.57	72.0 $\pm$ 5.39	75.14 $\pm$ 6.76	73.46 $\pm$ 6.24	74.14 $\pm$ 6.3
Avg. follow-up post-NIAD (y) $\pm$ SD	4.4 $\pm$ 3.1	5.31 $\pm$ 2.86	5.08 $\pm$ 2.85	4.45 $\pm$ 2.8	4.9 $\pm$ 2.9	5.15 $\pm$ 3.28	4.37 $\pm$ 2.85	5.79 $\pm$ 3.08	4.04 $\pm$ 2.78	4.46 $\pm$ 3.1	4.89 $\pm$ 2.81	5.35 $\pm$ 2.73	4.96 $\pm$ 2.97
Avg. BMI at NIAD (kg/m 2 ) $\pm$ SD	28.68 $\pm$ 4.35	30.01 $\pm$ 4.87	29.41 $\pm$ 3.84	29.9 $\pm$ 5.1	30.54 $\pm$ 5.51	29.78 $\pm$ 3.97	30.13 $\pm$ 5.43	34.35 $\pm$ 6.26	29.0 $\pm$ 3.88	29.71 $\pm$ 4.17	32.81 $\pm$ 5.74	33.89 $\pm$ 6.31	28.94 $\pm$ 5.19
Avg. HbA1c at NIAD (%) $\pm$ SD	6.96 $\pm$ 1.33	7.33 $\pm$ 1.41	7.16 $\pm$ 1.36	7.09 $\pm$ 1.39	6.94 $\pm$ 1.33	6.95 $\pm$ 1.24	7.12 $\pm$ 1.36	6.87 $\pm$ 1.3	7.11 $\pm$ 1.37	6.92 $\pm$ 1.28	7.01 $\pm$ 1.36	7.21 $\pm$ 1.38	7.1 $\pm$ 1.36
% Ever smoked	29.61	31.22	26.86	27.92	45.54	27.48	56.44	27.68	41.91	27.87	34.72	29.27	48.6

Appendix

Table 9: Patient characteristics in each cluster for the Men

65+

Figure 18: Average cluster-specific probabilities and lab values for Men $65+$ . Values have been centered by subtracting the average at the time of NIAD initiation to improve readability. Red bars indicate increases, and blue bars indicate decreases relative to the average patient at NIAD. Comorbidity risks are shown as changes in probability (left axis), and lab values as percentage changes relative to the reference value (right axis). Annotated numbers indicate absolute changes in the original units (see Table 1 ). Error bars represent the standard error of the mean.

Panel of Figure 19 — Figure 19: Evolution of patient clusters over time ( Men $65+$ ), conditional on the initial cluster assignment (6 months post-NIAD). The number of patients in each cluster is indicated alongside the corresponding bars. For clarity, only the most frequent transitions are shown (see Figure 20 for more details). Clusters 2,3,6,8,10,11 are excluded due to the low number of transitions observed from these clusters.

Figure 20: Cumulative Incidence Function (CIF) for the time to first cluster transition in Men $65+$ , stratified by initial cluster assignment at 6 months post-NIAD. The estimates account for censoring due to loss to follow-up and study termination, computed using the Aalen nonparametric estimator [ 25 ] .

Figure 21: Transition graph. Red arrows (resp. blue) means an increase (resp. decrease) of the comorbidity risk ( Men $65+$ ). Arrow thickness is proportional to the number of observed transitions. Transitions with less than 1% probability are not shown.

Cluster	0	1	2	3	4	5	6	7	8	9	10	11	12
# of patients	2604	857	1629	742	1626	1276	787	1258	681	3702	716	644	452
Avg. age at NIAD (y) $\pm$ SD	72.7 $\pm$ 5.8	72.98 $\pm$ 5.79	74.91 $\pm$ 6.32	74.08 $\pm$ 6.18	76.72 $\pm$ 6.69	79.47 $\pm$ 7.44	76.98 $\pm$ 7.06	73.32 $\pm$ 5.86	78.33 $\pm$ 7.13	73.24 $\pm$ 5.72	73.69 $\pm$ 6.0	77.85 $\pm$ 7.15	74.04 $\pm$ 6.35
Avg. follow-up post-NIAD (y) $\pm$ SD	4.7 $\pm$ 3.12	5.11 $\pm$ 2.68	5.07 $\pm$ 2.71	4.35 $\pm$ 2.77	5.52 $\pm$ 3.12	3.5 $\pm$ 2.66	3.79 $\pm$ 2.64	6.0 $\pm$ 3.23	4.04 $\pm$ 2.31	4.82 $\pm$ 3.24	5.7 $\pm$ 2.68	4.24 $\pm$ 2.78	4.91 $\pm$ 2.73
Avg. BMI at NIAD (kg/m 2 ) $\pm$ SD	30.24 $\pm$ 6.15	29.99 $\pm$ 5.92	29.84 $\pm$ 4.83	32.63 $\pm$ 6.74	28.96 $\pm$ 5.31	27.99 $\pm$ 4.72	29.53 $\pm$ 6.46	36.76 $\pm$ 7.37	30.7 $\pm$ 6.34	30.74 $\pm$ 4.8	36.67 $\pm$ 7.09	34.36 $\pm$ 7.83	31.65 $\pm$ 6.33
Avg. HbA1c at NIAD (%) $\pm$ SD	6.96 $\pm$ 1.27	7.24 $\pm$ 1.32	7.09 $\pm$ 1.29	7.08 $\pm$ 1.39	6.83 $\pm$ 1.3	7.08 $\pm$ 1.35	7.15 $\pm$ 1.42	6.98 $\pm$ 1.26	7.37 $\pm$ 1.49	6.9 $\pm$ 1.25	7.05 $\pm$ 1.18	7.09 $\pm$ 1.41	7.32 $\pm$ 1.37
% Ever smoked	30.72	32.79	24.86	64.56	18.02	31.03	43.96	24.24	37.0	21.47	25.56	33.7	23.67

Appendix

Table 10: Patient characteristics in each cluster for the Women

65+

Figure 22: Average cluster-specific probabilities and lab values for Women $65+$ . Values have been centered by subtracting the average at the time of NIAD initiation to improve readability. Red bars indicate increases, and blue bars indicate decreases relative to the average patient at NIAD. Comorbidity risks are shown as changes in probability (left axis), and lab values as percentage changes relative to the reference value (right axis). Annotated numbers indicate absolute changes in the original units (see Table 1 ). Error bars represent the standard error of the mean.

Panel of Figure 23 — Figure 23: Evolution of patient clusters over time ( Women $65+$ ), conditional on the initial cluster assignment (6 months post-NIAD). The number of patients in each cluster is indicated alongside the corresponding bars. For clarity, only the most frequent transitions are shown (see Figure 24 for more details). Clusters 1,8 are excluded due to the low number of transitions observed from these clusters.

Figure 24: Cumulative Incidence Function (CIF) for the time to first cluster transition in Women $65+$ , stratified by initial cluster assignment at 6 months post-NIAD. The estimates account for censoring due to loss to follow-up and study termination, computed using the Aalen nonparametric estimator [ 25 ] .

Figure 25: Transition graph. Red arrows (resp. blue) means an increase (resp. decrease) of the comorbidity risk ( Women $65+$ ). Arrow thickness is proportional to the number of observed transitions. Transitions with less than 1% probability are not shown.

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Chronic disease management relies on regular patient-provider interactions to follow-up on disease progression and control. For Type 2 Diabetes (T2D), current guidelines prescribe fixed time intervals between subsequent primary care visits for all patients, overlooking heterogeneity in clinical trajectories and patient characteristics. This study introduces a Contextual Markov Decision Process (CMDP) model to optimize subpopulation-specific follow-up interval decisions using Electronic Health Record (EHR) data from 22,154 T2D patients across 10 primary care clinics. Contexts are identified by: i) dimensionality reduction of variables representing the individual health trajectories utilizing Principal Component Analysis, and ii) assigning patients to contexts via principal components and additional patient-level features using clustering. Two distinct contexts emerged, representing a lower- and a higher-risk subpopulation. CMDP-derived policies recommend: (i) follow-up within 1 month if lab value at current visit is unmeasured; (ii) up to 3 months for elevated lab values or recent hospitalizations; and (iii) 6 to 12 months for sustained glycemic control, with shorter follow-up intervals for patients in high-risk context. The optimal policies achieved lower expected cumulative cost than benchmarks (e.g., in the higher-comorbidity context, the CMDP policy reduced cost by about 34.8%, and in the lower-comorbidity context by about 6.4%, relative to an American Diabetes Association-like fixed interval follow-up policy. These findings demonstrate how context-aware approaches can inform adaptive follow-up strategies, and have the potential to advance chronic care management in primary care by synthesizing machine learning and probabilistic decision models.

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