The Weibull model.

Model seroprevalence as a function of duration since vaccination using the Weibull model, where the force of infection is assumed to vary monotonically with duration.

Usage

weibull_model(
  data,
  t_lab = "t",
  pos_col = "pos",
  tot_col = "tot",
  status_col = "status"
)

Arguments

data: the input data frame, must either have columns for `t`, `pos`, `tot` (for aggregated data) OR `t`, `status` (for linelisting data)
t_lab: name of the `t` column (default t_lab="t").
pos_col: name of the `pos` column (default pos_col="pos").
tot_col: name of the `tot` column (default tot_col="tot").
status_col: name of the `status` column (default status_col="status").

Value

list of class weibull_model with the following items

datatype: type of datatype used for model fitting (aggregated or linelisting)
df: the dataframe used for fitting the model
info: fitted "glm" object
sp: seroprevalence
foi: force of infection

Details

For a Weibull model, the prevalence is given by $$ \pi (d) = 1 - e^{ - \beta_0 d ^ {\beta_1}} $$ Where $d$ is exposure time (difference between age of vaccination and age at test)

Which implies the force of infection to be the monotonic function $$ \lambda(d) = \beta_0 \beta_1 d^{\beta_1 - 1} $$

Refer to section 6.1.2. of the the book by Hens et al. (2012) for further details.

References

Hens, Niel, Ziv Shkedy, Marc Aerts, Christel Faes, Pierre Van Damme, and Philippe Beutels. 2012. Modeling Infectious Disease Parameters Based on Serological and Social Contact Data: A Modern Statistical Perspective. tatistics for Biology and Health. Springer New York. doi:10.1007/978-1-4614-4072-7 .

Examples

df <- hcv_be_2006[order(hcv_be_2006$dur), ]
df$t <- df$dur
df$status <- df$seropositive
model <- weibull_model(df, t_lab="dur", status_col="seropositive")
plot(model)