Fig 1.
Diagram visualising the doubly interval-censoring method [19], highlighting the data typically observed, but accounting for the fact that infection and symptom onset times are not observed exactly and intervals of possible times must be considered.
Table 1.
The Burr distributions valid over (0, ∞) and previously trialled distributions [4] with their corresponding p.d.f and c.d.f.
Table 2.
Results from fitting the gamma and four Burr distribution models to the Melbourne incubation-period data using both the standard and DI likelihood fitting methods.
Fig 2.
A plot of the Melbourne case data with the four fitted Burr distributions included, which offer a visual representation of the incubation-period distributions trialled.
Fig 3.
Plots of the Melbourne data with the standard model fits in red and the doubly interval-censored model fit as a step function in yellow.
Each step of the function is a horizontal line from t ∈ (a, b] where a = ⌊t⌋ and b = ⌈t⌉.
Table 3.
Comparing Burr, log-normal and Weibull models with the gamma model on anthrax, salmonellosis and campylobacteriosis datasets.
For brevity, we define the datasets as A, S or C to represent anthrax, salmonellosis and campylobacteriosis datasets respectively. The numbers in the dataset column indicate which dataset for a given disease is being referred to, as we have multiple incubation-period datasets for Salmonella and Campylobacter. The value provided is the difference between the recorded AIC between a given model and the gamma distribution. Negative values indicate lower AIC, which is preferable. Similarly, positive values indicate higher AIC, which implies a worse model fit.
Fig 4.
Heatmaps of the results from the first simulation.
The sub-figures (a), (c) and (e) (left column panels) represent the results from the standard likelihood fitting simulation, whereas (b), (d) and (f) (right column panels) represent the results from the DI likelihood fitting simulation. The sub-figures (a) and (b) represent the αD estimates obtained. Next, (c) and (d) represent the βD estimates obtained. Finally, (e) and (f) represent the TD estimates obtained.
Fig 5.
Bias and appropriate coverage of 95% confidence intervals obtained from fitting the derived Burr distribution using DI methods to doubly-censored incubation periods generated from the derived Burr distribution.
The sub-figures (a), (b) and (c) represent the bias from the αD, βD and TD-varying simulations respectively. Further, the sub-figures (d), (e) and (f) represent the appropriate coverage from the αD, βD and TD-varying simulations respectively.