Estimating a delay distribution from incomplete data, with application to reporting lags for AIDS cases

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Accurate statistical inference for reporting delays is crucial for disease surveillance.
• Traditional methods may be limited when data is only available after a specific time point (tau).

Purpose of the Study:

• To develop a statistical method for estimating probability distributions of reporting delays using data recorded before a certain time (tau).
• To assess the impact of including pre-tau data on the precision of these estimates.

Main Methods:

• Utilizing incidences recorded prior to time tau.
• Deriving explicit expressions for maximum likelihood estimates and standard errors.
• Applying the method to Australian AIDS diagnosis reporting delay data.

Main Results:

• Inclusion of pre-tau AIDS diagnosis data significantly improved the precision of reporting delay estimates.
• A simulation study showed minimal bias in the estimates.
• Large sample formulae for standard errors provided good estimates of the standard deviation.

Conclusions:

• The proposed statistical method effectively enhances the precision of reporting delay estimates.
• Incorporating historical data (pre-tau) is a valuable strategy in epidemiological surveillance.
• The method demonstrates practical utility and reliability in real-world data analysis.