Asthma Reassessment Model¶

An asthma diagnosis is not permanent. A person who was diagnosed with asthma may later be reassessed as not having it — either because the original diagnosis was incorrect, or because their underlying symptoms resolved. The reassessment model estimates the probability that a person with an asthma diagnosis at time \(t=0\) retains that diagnosis at time \(t=1\), stratified by age, sex, timepoint, and province.

Derivation¶

Rather than fitting \(\rho\) from individual-level data, we derive it analytically from population-level asthma prevalence and incidence predictions provided by the Occurrence Model.

Let:

• \(P_0\) = prevalence of asthma at time \(t=0\) (i.e., at age \(a\), timepoint \(t\))

• \(P_1\) = prevalence of asthma at time \(t=1\) (i.e., at age \(a+1\), timepoint \(t+1\))

• \(I_1\) = incidence of asthma at time \(t=1\) (probability of a new diagnosis at age \(a+1\), timepoint \(t+1\))

• \(\rho\) = probability that a person with an asthma diagnosis at \(t=0\) retains it at \(t=1\)

The prevalence at \(t=1\) can be decomposed into two groups:

1. People who had asthma at \(t=0\) and retained their diagnosis: \(P_0 \cdot \rho\)

2. People who did not have asthma at \(t=0\) but received a new diagnosis: \((1 - P_0) \cdot I_1\)

This gives:

Solving for \(\rho\):

This is computed by calculate_reassessment_probability() in leap/data_generation/reassessment_data.py. The result is clamped to \([0, 1]\) to handle edge cases where the formula yields values outside that range due to model uncertainty.

Age range¶

Reassessment applies only to people who already have an asthma diagnosis, so the earliest possible reassessment is at age 4 (one year after the minimum diagnosis age of 3).

For ages greater than 62, incidence and prevalence are assumed to remain constant at the rates predicted for age 62, so reassessment probabilities are also held constant beyond that age.

Data Source¶

The prevalence and incidence inputs \(P_0\), \(P_1\), and \(I_1\) come from the asthma occurrence predictions in Model 1 of the Occurrence Model.

Processed Data¶

The reassessment probabilities are generated by generate_reassessment_data() in leap/data_generation/reassessment_data.py and saved to:

• leap/processed_data/time_delta_365/asthma_reassessment.csv