This prompt introduces the research article titled “Age-Period-Cohort Models: A Comparative Study of Available Methodologies“. Authored by Chris Robertson, Sara Gandini, and Peter Boyle, and published in the Journal of Clinical Epidemiology in 1999, this study provides a critical comparison of different approaches used to analyze trends in disease incidence and mortality.
Purpose and Context of the Study:
- The article focuses on age-period-cohort (APC) models, which are routinely employed in descriptive epidemiology to summarize disease rates classified by age group and time period.
- The primary goal of fitting these models is to assess and estimate the effects of three distinct factors on disease rates: age, time period, and birth cohort.
- The age effect reflects differing risks associated with various age groups.
- The time period effect signifies a change in rate affecting all age groups simultaneously, potentially due to factors like changes in treatment, exposure to carcinogens, or registration procedures.
- The birth cohort effect represents a change in rates across successive generations, often linked to long-term habits or exposures. The latter two effects are particularly crucial for understanding time trends in disease rates.
The Core Challenge: Identifiability Problem:
- A major hurdle in APC models is the exact linear dependency among the three factors, known as the identifiability problem. This means that the individual parameters for age, period, and cohort cannot be uniquely estimated without imposing additional constraints.
- The interpretation of age, period, and cohort effects critically depends on this unidentifiable parameter. Despite this being a well-known issue, there is a widespread application of various methodologies that attempt to solve it, often introducing bias.
Methodologies Under Comparison: The study comparatively evaluates several “solutions” to the identifiability problem, drawing on simulations with disease rates of known structure. These include:
- Penalty Function Approach: Methods that minimize a penalty function to derive the necessary extra linear constraint, such as the Decarli and La Vecchia solution.
- Individual Records Approach: Methods that use individual case records to construct a three-way age-period-cohort table, like the original Robertson and Boyle approach and its extended age model.
- Estimable Functions Approach: Methods that focus solely on estimable functions, specifically curvatures (second differences of parameter estimates) and deviations from linearity, exemplified by the approaches of Holford and Clayton and Schifflers.
- Nonparametric Testing Method: A method proposed by Tarone and Chu that compares rates within the same age group across different periods or cohorts to detect trends.
Key Findings and Recommendations: The findings of the study reveal significant biases in many commonly used methodologies:
- The research suggests that only methods based on estimable functions (such as curvatures and deviations) can be recommended for use in all circumstances. These methods are mathematically correct and always reveal the true input structure of the data, as they focus on identifiable contrasts without making extra assumptions.
- Other common approaches, while perhaps providing parameter estimates that are easier to interpret, all induce bias.
- Penalty function approaches (e.g., Decarli and La Vecchia) tend to bias results towards linear cohort effects when drift is present, potentially masking true period trends.
- Methods based on individual records (Robertson and Boyle) introduce severe bias, especially with strong age effects, pushing trends toward increasing period effects and decreasing cohort trends. This bias is persistent and more pronounced in the Robertson and Boyle approach.
- The nonparametric testing method (Tarone and Chu) has limited power in small tables and attributes strong drift in rates to both period and cohort trends. While it can detect nonlinear changes, it does not provide information on age effects.
- While all methods can correctly estimate nonlinear components (curvatures and nonlinear deviations), the study highlights that the turning point in the rates is not an identifiable parameter, making it impossible to definitively state which specific cohort or period experienced the maximum effect.
Conclusion and Implications: The authors conclude that the prevalent use of biased methods can lead to significant misinterpretations of disease trends, especially in analyses based on large populations. They strongly advise that only methods based on curvatures or other estimable functions should be used, despite their potentially less straightforward interpretation. The study explicitly recommends that interpretations of results from previous analyses based on the identified biased methods should be revised.
REFERENCE:Robertson, C., Gandini, S., & Boyle, P. (1999). Age-Period-Cohort Models: A Comparative Study of Available Methodologies. J Clin Epidemiol, 52(6), 569–583.
