Joint modelling of PSA dynamics and prostate cancer risks: A population-based study

This population-based study demonstrates that a joint model linking PSA dynamics, retesting patterns, and prostate cancer diagnosis provides more accurate risk estimates and corrects for informative observation bias compared to traditional isolated analyses.

The Gist

Imagine you are trying to predict when a car engine is about to break down. You have a dashboard light (the PSA test) that flickers brighter as the engine gets older or hotter. But here's the tricky part: the driver doesn't just check the light randomly. If the light flickers a bit, the driver gets nervous and checks it again very soon. If it flickers a lot, they check it constantly.

This creates a confusing mess of data. If you just look at the light's brightness, you might think, "Oh, it's always bright, so the engine must be fine," or "It's getting brighter, so it's definitely broken," without realizing that the act of checking the light is actually changing the data you see.

This is exactly the problem doctors face with Prostate-Specific Antigen (PSA) tests for men.

The Old Way: Looking at the Light in Isolation

Traditionally, researchers have looked at PSA levels and cancer diagnoses separately. They would say, "Men with high PSA get cancer more often," or "Men get tested more often as they get older."

But this is like trying to understand a car engine by only looking at the dashboard light after the driver has already decided to check it. It misses the connection: The driver checks the light because the light is acting up. This creates a "feedback loop" that old models ignore, leading to inaccurate predictions.

The New Way: The "Three-Track" Joint Model

The authors of this paper built a new, smarter system called a Joint Model. Think of it as a super-sophisticated traffic control center that watches three things happening at the same time:

1. The Engine's Heat (PSA Trajectory): How the PSA level naturally rises and falls as a man ages.
2. The Driver's Anxiety (Retesting Pattern): How often a man decides to get tested based on his previous results.
3. The Breakdown (Cancer Diagnosis): When the actual disease is found.

Instead of treating these as three separate stories, the model weaves them together into one big story. It understands that if a man's PSA goes up, he is more likely to get tested again, and that higher PSA is also more likely to mean cancer.

What They Discovered

By using this "all-seeing" model, they found some surprising things:

• The "Double Trouble" Effect: When a man's PSA level doubles, the risk of actually having cancer isn't just slightly higher—it doubles (a 2x increase).

  • The Old Model said: "It's a 1.6x increase."
  • The New Model says: "It's a 2x increase."
  • Why the difference? The old model was confused by the fact that men with high PSA get tested more often, which muddied the water. The new model cleared that up.

• The "Nervous Driver" Effect: When PSA levels rise, men get tested more frequently. The new model showed this link is much stronger than previously thought. It's not just a random habit; it's a direct reaction to the numbers.

• The "Foggy Window": As men get older, their PSA levels become much more unpredictable. Some men have very stable levels, while others swing wildly. The new model accounts for this "fog," realizing that one size does not fit all when it comes to age and PSA.

Why This Matters for You

Imagine you are a doctor looking at a patient's history.

• Before: You might look at a single high PSA number and think, "Well, he's been tested a lot, maybe it's just noise," or "He's 60, so a little rise is normal."
• Now: You can use this new model to say, "This man's PSA isn't just high; it's rising faster than the average man his age, and his testing pattern suggests his body is reacting strongly to it. We need to look closer."

The Bottom Line

This study is like upgrading from a simple speedometer to a full GPS navigation system for prostate health. It doesn't just tell you how fast you are going (the PSA level); it tells you why you are going that fast, how often you are checking the map, and where you are likely to end up.

By understanding that testing, biology, and disease are all connected, doctors can stop guessing and start making much more precise, personalized decisions about who needs help and who doesn't. It turns a confusing jumble of numbers into a clear roadmap for better health.

Technical Summary

1. Problem Statement

Prostate-specific antigen (PSA) testing is a cornerstone of prostate cancer screening, yet its application in opportunistic (non-organized) settings creates complex data structures. In these settings, three critical processes are interdependent:

1. Longitudinal PSA Trajectories: How PSA levels change over a man's age.
2. Observational Process (Retesting): The timing and frequency of subsequent PSA tests, which are often driven by previous PSA results (informative observation).
3. Time-to-Event (Diagnosis): The time until a prostate cancer diagnosis.

The Core Issue: Conventional statistical analyses typically model these processes in isolation. For instance, standard linear mixed-effects models assume measurement times are independent of the outcome, while standard Cox proportional hazards models often fail to account for the fact that men with higher PSA levels are more likely to be retested. This "informative observation bias" leads to biased estimates of PSA dynamics and underestimates the strength of the association between PSA levels and cancer risk. There is a lack of population-level evidence linking these three processes simultaneously in men prior to diagnosis.

2. Methodology

The authors utilized a Joint Modeling Framework to analyze data from the Stockholm Prostate Cancer Diagnostics Register.

• Data Source: A population-based cohort of 506,761 men residing in Stockholm County who underwent at least one PSA test between 2003 and 2020.
  • Total tests recorded: 1,836,900.
  • Diagnoses: 30,199 men (6.0%).
  • Censoring: Follow-up was censored at the date of prostate cancer diagnosis to exclude post-diagnosis treatment effects.
• Statistical Model: A joint model linking three submodels via shared random effects (latent variables) representing the underlying individual PSA trajectory:
  1. Longitudinal Submodel: A linear mixed-effects model for log-transformed PSA values as a nonlinear function of attained age (using natural cubic splines). It included random intercepts and slopes to capture between-person heterogeneity.
  2. Time-to-Diagnosis Submodel: A left-truncated proportional hazards model where the hazard of diagnosis depends on the baseline age hazard and the underlying (latent) PSA trajectory.
  3. Time-to-Retesting Submodel: A recurrent-event proportional hazards model (counting-process formulation) where the hazard of a subsequent test depends on age and the underlying PSA trajectory.
• Implementation: The model was fitted using the VAJointSurv package in R (version 4.4.3) using variational approximations to handle the large dataset size.
• Comparison: The authors fitted standalone models (Linear Mixed-Effects, Cox PH, and Prentice-Williams-Peterson recurrent event models) to contrast the results with the joint model.

3. Key Contributions

• Novel Framework: This is one of the first large-scale population studies to jointly model PSA dynamics, retesting patterns, and cancer diagnosis simultaneously in a pre-diagnostic setting.
• Correction of Informative Bias: The study explicitly demonstrates how failing to account for the dependency between testing frequency and PSA levels (informative observation) leads to biased parameter estimates.
• Personalized Prediction: The model generates individual-specific trajectories and confidence intervals, allowing for the assessment of how a specific man's PSA evolution deviates from the population mean.
• Scalability: The use of variational approximations allows joint modeling to be applied to register-based datasets with hundreds of thousands of individuals and millions of observations.

4. Key Results

• PSA Dynamics:
  • PSA increases nonlinearly with age.
  • There is substantial heterogeneity between individuals (large random effect variances).
  • Heteroscedasticity: The unexplained variation in PSA levels increases significantly with age.
  • Correlation: Men with higher baseline PSA levels tend to have steeper age-related increases (correlation between random intercept and slope = 0.59).
• Hazard Ratios (Joint vs. Standalone Models):
  • Diagnosis Risk: Doubling of PSA was associated with a Hazard Ratio (HR) of 2.01 (95% CI: 1.99–2.02) in the joint model. In the standalone Cox model, this was significantly lower at 1.61.
  • Retesting Risk: Doubling of PSA was associated with an HR of 1.163 (95% CI: 1.161–1.165) for a subsequent test in the joint model, compared to 1.068 in the standalone PWP model.
  • Interpretation: The joint model revealed significantly stronger associations than isolated models, indicating that standard approaches substantially underestimate the predictive power of PSA dynamics due to unmodeled informative observation bias.
• Population Estimates: The joint model estimated slightly lower population-average PSA trajectories compared to the standalone linear mixed-effects model, suggesting that standard models overestimate population PSA levels by failing to adjust for the fact that high-PSA individuals are tested more frequently.

5. Significance and Implications

• Clinical Precision: The findings suggest that screening models should move beyond single PSA thresholds or isolated trajectory analyses. Integrating testing history and PSA trajectories into a joint framework can improve risk stratification and personalized decision-making (e.g., determining the need for MRI referral).
• Methodological Advancement: The study validates that joint modeling is essential for analyzing opportunistic screening data where the observation process is driven by the biomarker itself.
• Future Directions: The authors propose using this model to estimate detailed PSA dynamic profiles for screening simulations. Future work aims to incorporate changepoint models to explicitly account for trajectory shifts occurring at the moment of cancer onset.
• Limitations: The study is observational and lacks data on non-cancer factors elevating PSA (e.g., infections, BPH). It also does not explicitly model the PSA trajectory change after cancer onset, though follow-up was censored at diagnosis to mitigate this.

In conclusion, this study provides robust evidence that joint modeling corrects for informative observation bias, yielding more accurate population estimates and stronger, more reliable associations between PSA dynamics and prostate cancer risk compared to traditional isolated statistical approaches.