Inferring Chronic Treatment Onset from ePrescription Data: A Renewal Process Approach

This paper proposes a probabilistic framework that models outpatient ePrescription dynamics as a renewal process with change-point detection to infer chronic treatment onset more accurately than rule-based methods, particularly in the presence of left-censored diagnosis data.

The Gist

Imagine you are trying to figure out exactly when a person started having a chronic health problem, like high blood pressure or diabetes. You have access to their medical records, but there's a big catch: the records are messy and incomplete.

In many countries, including Slovenia (where this study took place), doctors started using digital systems for diagnoses only recently. Before that, records were on paper, scattered, or never digitized. So, if you look at the "diagnosis" date in the computer, it might just be the day the doctor finally typed it in, not the day the patient actually got sick. It's like trying to guess when a movie started by looking at the timestamp on the DVD case you bought three years later.

The Problem with "Diagnosis" Dates
The researchers found that relying on diagnosis dates is like trying to find a needle in a haystack that's been moved around. Sometimes the date is wrong, sometimes it's missing, and sometimes it's just a typo. For example, they found cases where people were labeled as having two types of diabetes at the same time, which is extremely rare in real life but common in the messy data.

The Solution: The "Prescription Rhythm"
Instead of looking at the diagnosis, the researchers decided to listen to the patient's prescription rhythm.

Think of a patient's medication history like a music track:

• Sporadic (Random) Music: At first, a patient might get a prescription here and there. Maybe they have a cold, or they are trying a new vitamin. These are random, one-off notes. In math terms, this is a "Poisson process"—like raindrops hitting a roof randomly.
• Sustained (Rhythmic) Music: Then, the patient gets sick with a chronic condition. Now, they need to refill the same medicine every 3 months or every year, like clockwork. This is a steady beat, a drum loop. In math terms, this is a "Weibull renewal process."

The researchers built a smart computer program that acts like a music producer. It listens to the patient's prescription history and tries to find the exact moment the music switched from "random raindrops" to a "steady drum beat." That moment is the onset of the chronic treatment.

How the "Smart Producer" Works

1. The Baseline: The program knows what "random" looks like. If a patient gets a pill once a year, that's noise.
2. The Switch: The program watches for a change. When a patient starts getting the same pill regularly (e.g., every 90 days), the program says, "Aha! The rhythm has changed. This person has likely started a long-term treatment."
3. The Filter: The program is very strict. It won't declare a chronic condition just because someone got one pill. It waits until it sees a clear, repeating pattern. This prevents the computer from making up false stories about when a disease started.

Why This is Better
The researchers tested their "Smart Producer" against a simple, dumb rule: "If the doctor writes 'chronic' on the prescription, assume the disease started today."

• The Dumb Rule: It often said the disease started years before the patient even existed in the digital system (because the system was just being set up). It was like a smoke detector that goes off because someone burned toast.
• The Smart Producer: It figured out the start date much more accurately. For a disease like COVID-19 (which didn't exist before 2020), the dumb rule said people got it in 2016. The Smart Producer correctly said, "Nope, no one was getting these specific regular prescriptions before 2020."

The Catch (The "Signal" Problem)
The study also found a limitation. This method works great for diseases where people take pills every single day or every month (like heart disease or diabetes). It's like trying to hear a steady drum beat—it's easy to spot.

However, for diseases where people only take medicine occasionally (like an allergy that flares up once a year), the "beat" is too quiet. The computer can't hear the rhythm, so it can't tell when the treatment started. The more prescriptions a patient has, the clearer the signal, and the better the computer works.

The Big Picture
In short, this paper teaches us that how we take medicine tells us more about when we got sick than the doctor's notes do. By treating prescription data like a musical rhythm and using math to find the beat, we can reconstruct a patient's health history much more accurately, even when the official records are missing or wrong. It's a new way to listen to the story of a patient's life, one pill at a time.

Technical Summary

1. Problem Statement

Longitudinal Electronic Health Record (EHR) data is frequently left-censored, meaning historical records are incomplete due to the gradual adoption of digital systems. This makes diagnosis records unreliable for determining the true onset of chronic diseases, as they are often recorded only once, contain coding errors, or reflect system adoption rates rather than true incidence.

In contrast, outpatient prescription data offers a continuous, renewal-based signal of disease management because medications must be periodically re-issued. However, existing phenotyping approaches often rely on naive, rule-based heuristics (e.g., triggering onset at the first prescription with a "chronic" label). These methods ignore prescribing dynamics, leading to:

• Implausible early detections: Inferring disease onset years before the patient actually entered the system.
• Data leakage: Creating cohorts where treatment signals precede recorded diagnoses, biasing downstream AI/ML models.
• Inability to distinguish noise: Failing to differentiate between sporadic/acute prescribing and sustained chronic therapy.

2. Methodology

The authors propose a probabilistic framework that models prescription timing as a stochastic temporal point process to detect the transition from sporadic prescribing to sustained therapy.

A. Modeling Prescription Dynamics (Renewal Processes)

The framework treats prescription events as a sequence of inter-arrival times ($\tau$) and models them using two distinct regimes:

1. Baseline Regime (Sporadic/Noise): Modeled as a Homogeneous Poisson Process.
   • Assumes constant hazard ($h(t) = \lambda$).
   • Inter-arrival times follow an exponential distribution.
   • Represents acute treatments, administrative noise, or sporadic prescribing.
2. Chronic Regime (Sustained Therapy): Modeled as a Weibull Renewal Process.
   • Inter-arrival times follow a Weibull distribution $p(\tau) = \frac{k}{\lambda}(\frac{\tau}{\lambda})^{k-1}e^{-(\tau/\lambda)^k}$.
   • Shape parameter ($k$): Indicates regularity. $k \approx 1$ is Poisson-like; $k > 1$ indicates regular, sustained refill behavior (typical of chronic therapy).
   • Scale parameter ($\lambda$): Represents the characteristic refill interval.
   • Note: Parameters are estimated separately for renewable and non-renewable prescriptions to account for different dispensing policies.

B. Change-Point Detection

The core inference task is to identify the transition point ($c$) where a patient's prescribing behavior shifts from the Poisson regime to the Weibull regime.

• Likelihood Function: The log-likelihood $\ell(c)$ is calculated by summing the probabilities of the Poisson model for events before $c$ and the Weibull model for events after $c$.
• Optimization: The estimated change-point $\hat{c}$ is the location that maximizes $\ell(c)$.
• Thresholding: A change-point is accepted only if the log-likelihood improvement over the null (all Poisson) model exceeds a user-specified threshold ($\epsilon$). This acts as a minimum evidence requirement to avoid false positives.
• Constraint: Inference is restricted to a single change-point per patient-drug trajectory, focusing on the onset of long-term treatment.

C. Disease-Level Phenotype Construction

To move from drug-level to disease-level (ICD-10) onset:

1. Empirical Association: Drug-disease links are learned via temporal co-occurrence between inferred treatment onsets and recorded diagnoses within a specific window (3 months prior to 12 months post-onset).
2. Aggregation: For each patient and ICD code, the disease onset is defined as the earliest inferred onset among the top-ranked drugs associated with that disease.
3. Baseline Comparison: A naive baseline is defined as the date of the first prescription carrying an administrative "chronic" label.

3. Key Contributions

• Probabilistic Framework: Introduces a renewal-process-based approach to distinguish sporadic noise from sustained chronic therapy, moving beyond simple rule-based triggers.
• Robustness to Left-Censoring: Demonstrates that modeling dynamics reduces "implausible early detections" (e.g., inferring disease onset in 2016 when the system started in 2016) significantly better than naive methods.
• Regime-Specific Modeling: Explicitly accounts for the difference between renewable and non-renewable prescriptions, showing they operate on distinct time scales and regularity levels.
• Empirical Drug-Disease Mapping: Develops a method to infer drug-disease associations directly from the data without relying on pre-existing, potentially noisy ontologies.

4. Results

The study utilized a nationwide Slovenian dataset (2.4 million patients, 101 million prescriptions, 2016–2022).

• Parameter Recovery: The Weibull shape parameter ($k$) estimated from all prescriptions strongly correlated ($r=0.86$) with estimates from only "chronic" labeled prescriptions, proving the model can recover structure even when administrative labels are noisy.
• Temporal Plausibility:
  • The Naive Method frequently predicted onset dates years before the recorded diagnosis (e.g., predicting COVID-19 onset in 2016, before the virus existed).
  • The Change-Point Method produced distributions centered near zero (agreement with diagnosis dates) and successfully avoided these early artifacts.
• Detection Performance:
  • Recall: The change-point method had lower recall than the naive baseline (which triggers on a single prescription). However, this is intentional; the method prioritizes precision and temporal validity over raw volume.
  • Prescription Density: Detection performance is strongly correlated with prescription density ($r \approx 0.67$). Diseases with dense, structured chronic trajectories are detected reliably, while sparse/episodic conditions remain challenging.
  • Conservative Triggering: The method requires sustained evidence (minimum 6 prescriptions) to trigger, filtering out noise that the naive method captures.

5. Significance

• Improved Cohort Construction: By providing more temporally plausible onset estimates, this method reduces data leakage in machine learning tasks where treatment signals might otherwise precede labels.
• Handling Incomplete EHRs: It offers a viable strategy for inferring disease history in systems with left-censored diagnosis data by leveraging the continuous signal of prescription renewals.
• Clinical Insight: The approach highlights that while treatment-based inference is powerful for chronic conditions (e.g., hypertension, diabetes), it has inherent limits for conditions with sparse prescribing patterns.
• Future Directions: The work motivates the integration of treatment switching dynamics and external biomedical knowledge to further refine phenotyping in complex EHR environments.