Package 'serosv'

Description

An easy-to-use and efficient tool to estimate infectious diseases parameters using serological data. Implemented models include SIR models (basic_sir_model(), static_sir_model(), mseir_model(), sir_subpops_model()), parametric models (polynomial_model(), fp_model()), nonparametric models (lp_model()), semiparametric models (penalized_splines_model()), hierarchical models (hierarchical_bayesian_model()). The package is based on the book "Modeling Infectious Disease Parameters Based on Serological and Social Contact Data: A Modern Statistical Perspective" (Hens, Niel & Shkedy, Ziv & Aerts, Marc & Faes, Christel & Damme, Pierre & Beutels, Philippe., 2013) doi:10.1007/978-1-4614-4072-7.

Author(s)

Maintainer: Anh Phan Truong Quynh [email protected] (ORCID)

Authors:

• Nguyen Pham Nguyen The [email protected] (ORCID)

• Long Bui Thanh

• Tuyen Huynh [email protected]

• Thinh Ong [email protected] (ORCID)

• Marc Choisy [email protected] (ORCID)

See Also

Useful links:

• https://oucru-modelling.github.io/serosv/

• https://github.com/OUCRU-Modelling/serosv

• Report bugs at https://github.com/OUCRU-Modelling/serosv/issues

Description

Visualize positive threshold at different dilution factors

Usage

add_thresholds(dilution_factors, positive_threshold = 0.1, shift_text = 0.15)

Arguments

Description

Fit age-stratified seroprevalence across multiple time points. Also try to monotonize age (or birth cohort) - specific seroprevalence.

Usage

age_time_model(
  data,
  age_col = "age",
  status_col = "status",
  pos_col = "pos",
  tot_col = "tot",
  time_col = "date",
  grouping_col = "group",
  age_correct = F,
  le = 512,
  ci = 0.95,
  monotonize_method = "pava"
)

Arguments

Value

a list of class time_age_model with 4 items

Description

Generate table of metrics for model comparison

Usage

compare_models(data, method = "AIC/BIC", ...)

Arguments

Details

Built-in comparison methods include:

• computing AIC and BIC, which returns AIC, BIC values of the model if available

• cross validation (perform k-fold validation), which returns MSE and logloss (negative log Binomial likelihood) for aggregated data, or AUC and logloss (negative log Bernoulli likelihood) for linelisting data

Value

a data.frame with the following columns

Examples

comparison_table <- suppressWarnings(
  compare_models(
    data = hav_bg_1964,
    method = "CV",
    polynomial_mod = ~polynomial_model(.x, k=1),
    penalized_spline = penalized_spline_model,
    farrington = ~farrington_model(.x, start=list(alpha=0.3,beta=0.1,gamma=0.03))
  )
)
# view table of metrics
comparison_table
# view the model fitted with the whole dataset
comparison_table$plots

Description

Compute confidence interval for time age model

Usage

## S3 method for class 'age_time_model'
compute_ci(x, ci = 0.95, le = 100, ...)

Arguments

Value

confidence interval dataframe with n_group x 3 cols, the columns are 'group', 'sp_df', 'foi_df'

Description

Compute confidence interval for a model of serosv

Usage

## Default S3 method:
compute_ci(x, ci = 0.95, le = 100, ...)

Arguments

Value

confidence interval dataframe with 4 variables, x and y for the fitted values and ymin and ymax for the confidence interval

Description

Compute confidence interval for fractional polynomial model

Usage

## S3 method for class 'fp_model'
compute_ci(x, ci = 0.95, le = 100, ...)

Arguments

Value

confidence interval dataframe with 4 variables, x and y for the fitted values and ymin and ymax for the confidence interval

Description

Compute 95% credible interval for hierarchical Bayesian model

Usage

## S3 method for class 'hierarchical_bayesian_model'
compute_ci(x, ...)

Arguments

Value

list of confidence interval for seroprevalence and foi. Each confidence interval dataframe with 4 variables, x and y for the fitted values and ymin and ymax for the confidence interval

Description

Compute confidence interval for local polynomial model

Usage

## S3 method for class 'lp_model'
compute_ci(x, ci = 0.95, ...)

Arguments

Value

confidence interval dataframe with 4 variables, x and y for the fitted values and ymin and ymax for the confidence interval

Description

Compute confidence interval for mixture model

Usage

## S3 method for class 'mixture_model'
compute_ci(x, ci = 0.95, ...)

Arguments

Value

list of confidence interval for susceptible and infected. Each confidence interval is a list with 2 items for lower and upper bound of the interval.

Description

Compute confidence interval for penalized_spline_model

Usage

## S3 method for class 'penalized_spline_model'
compute_ci(x, ci = 0.95, ...)

Arguments

Value

list of confidence interval for seroprevalence and foi Each confidence interval dataframe with 4 variables, x and y for the fitted values and ymin and ymax for the confidence interval

Description

Compute confidence interval for Weibull model

Usage

## S3 method for class 'weibull_model'
compute_ci(x, ci = 0.95, ...)

Arguments

Value

confidence interval dataframe with 4 variables, x and y for the fitted values and ymin and ymax for the confidence interval

Description

Estimate the true sero prevalence using Frequentist/Bayesian estimation

Usage

correct_prevalence(
  data,
  bayesian = TRUE,
  age_col = "age",
  pos_col = "pos",
  tot_col = "tot",
  status_col = "status",
  init_se = 0.95,
  init_sp = 0.8,
  study_size_se = 1000,
  study_size_sp = 1000,
  chains = 1,
  warmup = 1000,
  iter = 2000
)

Arguments

Value

a list of 3 items

Examples

data <- rubella_uk_1986_1987
correct_prevalence(data)

Description

Estimate force of infection

Usage

est_foi(t, sp)

Arguments

Value

computed foi vector

Description

Estimate age-specific seroprevalence and FOI given a fitted mixture model (generated by [serosv::mixture_model()])

Usage

estimate_from_mixture(
  age,
  antibody_level,
  threshold_status = NULL,
  mixture_model,
  s = "ps",
  sp = 83,
  monotonize = TRUE
)

Arguments

Details

Antibody level (denoted $Z$) is modeled using a 2-component Gaussian mixture model. Each component $Z_j$ ($j \in \{I, S\}$) represents the antibody level of the latent Infected and Susceptible sub-populations, following density $f_j(z_j|\theta_j)$

Let $\pi_{\text{TRUE}}(a)$ denotes the age-dependent mixing probability (i.e., the true prevalence), the density of the mixture is formulated as

$f(z|z_I, z_S,a) = (1-\pi_{\text{TRUE}}(a))f_S(z_S|\theta_S)+\pi_{\text{TRUE}}(a)f_I(z_I|\theta_I)$

The mean $E(Z|a)$ thus equals

$\mu(a) = (1-\pi_{\text{TRUE}}(a))\mu_S+\pi_{\text{TRUE}}(a)\mu_I$

From which true prevalence can be computed as

$\pi_{\text{TRUE}}(a) = \frac{\mu(a) - \mu_S}{\mu_I - \mu_S}$

And FOI can then be inferred as

$\lambda_{TRUE} = \frac{\mu'(a)}{\mu_I - \mu(a)}$

Function [serosv::mixture_model()] fits antibody level data to $f_S(z_S|\theta_S)$ and $f_I(z_I|\theta_I)$

Function [serosv::estimate_mixture()] will then estimate age-specific antibody level $\mu(a)$ and infer the estimation for $\pi_{\text{TRUE}}(a)$ and $\lambda_{TRUE}$

Refer to section 11.3. of the the book by Hens et al. (2012) for further details.

Value

a list of class estimated_from_mixture with the following items

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.

See Also

[mgcv::gam()] for more information about the fitted gam object

Description

Fit age-stratified seroprevalence data using the Farrington (1990) model, which assumes the force of infection increases linearly with age and subsequently decreases exponentially.

Usage

farrington_model(
  data,
  start,
  fixed = list(),
  age_col = "age",
  pos_col = "pos",
  tot_col = "tot",
  status_col = "status"
)

Arguments

Details

The force of infection is defined as followed

$\lambda(a) = (\alpha a - \gamma)e^{-\beta a} + \gamma$

Where $\gamma$ is called the long term residual for FOI, as $a \rightarrow \infty$ , $\lambda (a) \rightarrow \gamma$

The seroprevalence can thus be estimated using the non-linear model

$\pi(a) = 1 - exp\{ \frac{\alpha}{\beta}ae^{-\beta a} + \frac{1}{\beta}(\frac{\alpha}{\beta} - \gamma)(e^{-\beta a} - 1) -\gamma a \}$

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

Value

a list of class farrington_model with 5 items

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.

See Also

[stats4::mle()] for more information on the fitted mle object

Examples

df <- rubella_uk_1986_1987
model <- farrington_model(
  df,
  start=list(alpha=0.07,beta=0.1,gamma=0.03)
  )
plot(model)

Description

Return the best powers for a given degree

Usage

find_best_fp_powers(data, p, mc, degree, link = "logit")

Arguments

Value

list of 3 elements:

Description

Fractional polynomial model is a generalization of polynomial models where the power of the terms can be fractions, allowing more flexibility and better fit for data where asymptotic behavior is expected.

Usage

fp_model(
  data,
  p,
  monotonic = FALSE,
  link = "logit",
  age_col = "age",
  pos_col = "pos",
  tot_col = "tot",
  status_col = "status"
)

Arguments

Details

Instead of a polynomial, the linear predictor is now defined as

$\eta_m(a, \beta, p_1, p_2, ...,p_m) = \Sigma^m_{i=0} \beta_i H_i(a)$

Where $m$ is an integer, $p_1 \le p_2 \le... \le p_m$ is a sequence of powers, and $H_i(a)$ is a transformation given by

$H_i = \begin{cases} a^{p_i} & \text{ if } p_i \neq p_{i-1}, \\ H_{i-1}(a) \times log(a) & \text{ if } p_i = p_{i-1}, \end{cases}$

Refers to section 6.2. of the the book by Hens et al. (2012) for further details.

Value

a list of class fp_model with 5 items

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.

See Also

[stats::glm()] for more information on glm object

[polynomial_models()]

Examples

df <- hav_be_1993_1994
model <- fp_model(
  df,
  p=c(1.5, 1.6), link="cloglog")
plot(model)

Description

A study of the prevalence of HAV antibodies conducted in the Flemish Community of Belgium in 1993 and early 1994

Usage

hav_be_1993_1994

Format

A data frame with 3 variables:

age

Age group

pos

Number of seropositive individuals

tot

Total number of individuals surveyed

Source

Beutels, M., Van Damme, P., Aelvoet, W. et al. Prevalence of hepatitis A, B and C in the Flemish population. Eur J Epidemiol 13, 275-280 (1997). doi:10.1023/A:1007393405966

Examples

with(hav_be_1993_1994,
  plot(
    age, pos / tot,
    pty = "s", cex = 0.34 * sqrt(tot), pch = 16, xlab = "age",
    ylab = "seroprevalence", xlim = c(0, 86), ylim = c(0, 1)
  )
)

Description

A subset of the serological dataset of Varicella-Zoster Virus (VZV) and Parvovirus B19 in Belgium where only individuals living in Flanders were selected

Usage

hav_be_2002

Format

A data frame with 2 variables:

age

Age of individual

seropositive

If the individual is seropositive or not

Source

Thiry, N., Beutels, P., Shkedy, Z. et al. The seroepidemiology of primary varicella-zoster virus infection in Flanders (Belgium). Eur J Pediatr 161, 588-593 (2002). doi:10.1007/s00431-002-1053-2

Examples

library(dplyr)
df <- hav_be_2002 %>%
  group_by(age) %>%
  summarise(pos = sum(seropositive), tot = n())

with(
  df,
  plot(
    age, pos / tot,
    pty = "s", cex = 0.34 * sqrt(tot), pch = 16, xlab = "age",
    ylab = "seroprevalence", xlim = c(0, 86), ylim = c(0, 1)
  )
)

Description

A cross-sectional survey conducted in 1964 in Bulgaria. Samples were collected from schoolchildren and blood donors.

Usage

hav_bg_1964

Format

A data frame with 3 variables:

age

Age group

pos

Number of seropositive individuals

tot

Total number of individuals surveyed

Source

Keiding, Niels. "Age-Specific Incidence and Prevalence: A Statistical Perspective." Journal of the Royal Statistical Society. Series A (Statistics in Society) 154, no. 3 (1991): 371-412. doi:10.2307/2983150

Examples

with(
  hav_bg_1964,
  plot(
    age, pos / tot,
    pty = "s", cex = 0.6 * sqrt(tot), pch = 16, xlab = "age",
    ylab = "seroprevalence", xlim = c(0, 86), ylim = c(0, 1)
  )
)

Description

A seroprevalence study conducted in St. Petersburg (more information in the book)

Usage

hbv_ru_1999

Format

A data frame with 4 variables:

age

Age group

pos

Number of seropositive individuals

tot

Total number of individuals surveyed

gender

Gender of cohort (unsure what 1 and 2 means)

Source

Mukomolov, S., L. Shliakhtenko, I. Levakova, and E. Shargorodskaya. Viral hepatitis in Russian federation. An analytical overview. Technical Report 213 (3), 3rd edn. St Petersburg Pasteur Institute, St Petersburg, 2000.

Examples

library(dplyr)
hbv_ru_1999$age <- trunc(hbv_ru_1999$age / 1) * 1
hbv_ru_1999$age[hbv_ru_1999$age > 40] <- trunc(
  hbv_ru_1999$age[hbv_ru_1999$age > 40] / 5
) * 5
df <- hbv_ru_1999 %>%
  group_by(age) %>%
  summarise(pos = sum(pos), tot = sum(tot))

plot(
  df$age, df$pos / df$tot,
  cex = 0.32 * sqrt(df$tot), pch = 16, xlab = "age",
  ylab = "seroprevalence", xlim = c(0, 72)
)

Description

A study of HCV infection among injecting drug users. All injecting drug users were interviewed by means of a standardized face-to-face interview and information on their socio-demographic status, drug use history, drug use, and related risk behavior was recorded

Usage

hcv_be_2006

Format

A data frame with 3 variables:

dur

Duration of injection/Exposure time (years)

seropositive

If the individual is seropositive or not

Source

Mathei, C., Shkedy, Z., Denis, B., Kabali, C., Aerts, M., Molenberghs, G., Van Damme, P. and Buntinx, F. (2006), Evidence for a substantial role of sharing of injecting paraphernalia other than syringes/needles to the spread of hepatitis C among injecting drug users. Journal of Viral Hepatitis, 13: 560-570. doi:10.1111/j.1365-2893.2006.00725.x

Examples

library(dplyr)
# snapping age to aggregated age group
# (credit: https://stackoverflow.com/a/12861810)
groups <- c(0.5:24.5)
range <- 0.5
low <- findInterval(hcv_be_2006$dur, groups)
high <- low + 1
low_diff <- hcv_be_2006$dur - groups[ifelse(low == 0, NA, low)]
high_diff <- groups[ifelse(high == 0, NA, high)] - hcv_be_2006$dur
mins <- pmin(low_diff, high_diff, na.rm = TRUE)
pick <- ifelse(!is.na(low_diff) & mins == low_diff, low, high)
hcv_be_2006$dur <- ifelse(
  mins <= range + .Machine$double.eps, groups[pick], hcv_be_2006$dur
)
hcv_be_2006 <- hcv_be_2006 %>%
  group_by(dur) %>%
  summarise(tot = n(), pos = sum(seropositive))

with(hcv_be_2006,
  plot(
    dur, pos / tot,
    cex = 0.42 * sqrt(tot), pch = 16,
    xlab = "duration of injection (years)",
    ylab = "seroprevalence", xlim = c(0, 25), ylim = c(0, 1)
  )
)

Description

Fit age-stratified seroprevalence to parametric hierarchical Bayesian models. Supported models including Farrington model (2 and 3 parameters variants) and Log Logistic model

Usage

hierarchical_bayesian_model(
  data,
  age_col = "age",
  pos_col = "pos",
  tot_col = "tot",
  status_col = "status",
  type = "far3",
  chains = 1,
  warmup = 1500,
  iter = 5000
)

Arguments

Details

Consider a model for prevalence that has a parametric form $\pi(a_i, \alpha)$ where $\alpha$ is a parameter vector

Under a Bayesian framework, we can constraint the parameter space of the prior distribution $P(\alpha)$ to achieve monotonicity of the posterior distribution $P(\pi_1, \pi_2, ..., \pi_m|y,n)$

Where:

- $n = (n_1, n_2, ..., n_m)$ and $n_i$ is the sample size at age $a_i$

- $y = (y_1, y_2, ..., y_m)$ and $y_i$ is the number of infected individual from the $n_i$ sampled subjects

For Farrington model with 3 parameters, prevalence is formulated as follow

$\pi (a) = 1 - exp\{ \frac{\alpha_1}{\alpha_2}ae^{-\alpha_2 a} + \frac{1}{\alpha_2}(\frac{\alpha_1}{\alpha_2} - \alpha_3)(e^{-\alpha_2 a} - 1) -\alpha_3 a \}$

The likelihood model is defined as $y_i \sim Bin(n_i, \pi_i), \text{ for } i = 1,2,3,...m$

The constraint on the parameter space can be incorporated by assuming truncated normal distribution for the components of $\alpha$, $\alpha = (\alpha_1, \alpha_2, \alpha_3)$ in $\pi_i = \pi(a_i,\alpha)$

The flat hyperpriors are defined as $\mu_j \sim \mathcal{N}(0, 10000)$ and $\tau^{-2}_j \sim \Gamma(100,100)$

For Farrington model with 2 parameters, it is equivalent to the previous model with $\alpha_3 = 0$

For Log logistic model, seroprevalence is instead defined as

$\pi(a) = \frac{\beta a^\alpha}{1 + \beta a^\alpha}, \text{ } \alpha, \beta > 0$

The likelihood is similarly defined as $y_i \sim Bin(n_i, \pi_i))$

The prior model of $\alpha_1$ is specified as $\alpha_1 \sim \text{truncated } \mathcal{N}(\mu_1, \tau_1)$ with flat hyperpriors as in Farrington model

$\beta$ is constrained to be positive by specifying $\alpha_2 \sim \mathcal{N}(\mu_2, \tau_2)$

Refer to section Chapter 10.3 of the the book by Hens et al. (2012) for further details.

Value

a list of class hierarchical_bayesian_model with 6 items

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 <- mumps_uk_1986_1987
model <- hierarchical_bayesian_model(df, type="far3")
model$info
plot(model)

Description

Fit the age-specific seroprevalence to a local polynomial model, where the linear predictor is approximated locally at one particular age.

Usage

lp_model(
  data,
  kern = "tcub",
  nn = 0,
  h = 0,
  deg = 2,
  age_col = "age",
  pos_col = "pos",
  tot_col = "tot",
  status_col = "status"
)

Arguments

Details

Consider a linear predictor $\eta(a)$ approximated locally at one particular value $a_0$.

For a general degree $p$, the linear predictor for a neighbor of $a_0$, labeled $a_i$ is equivalent to the Taylor approximation

$\eta(a_i) = \eta(a_0) + \eta^{(1)}(a_0)(a_i - a_0) + \frac{\eta^{(2)}(a_0)}{2}(a_i - a_0)^2 + ... + \frac{\eta^{(p)}(a_0)}{p!}(a_i - a_0)^p$

$\eta(a_i)$ can be estimated by maximizing

$\Sigma_{i=1}^{N} \ell_i \{Y_i, g^{-1} (\beta_0 + \beta_1(a_i-a_0)+ \beta_2(a_i-a_0)^2 ... + \beta_p(a_i-a_0)^p) \} K_h(a_i - a_0)$

The estimator for the $k$-th derivative of $\eta(a_0)$, for $k = 0,1,…,p$ (degree of local polynomial) is thus:

$\hat{\eta}^{(k)}(a_0) = k!\hat{\beta}_k(a_0)$

The estimator for the prevalence at age $a_0$ is then given by

$\hat{\pi}(a_0) = g^{-1}\{ \hat{\beta}_0(a_0) \}$

Where $g$ is the link function

The estimator for the force of infection at age $a_0$ by assuming $p \ge 1$ is as followed

$\hat{\lambda}(a_0) = \hat{\beta}_1(a_0) \delta \{ \hat{\beta}_0 (a_0) \}$

Where $\delta \{ \hat{\beta}_0(a_0) \} = \frac{dg^{-1} \{ \hat{\beta}_0(a_0) \} } {d\hat{\beta}_0(a_0)}$

Refer to section 7.1 and 7.2. of the the book by Hens et al. (2012) for further details.

Value

a list of class lp_model with 6 items

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.

See Also

[locfit::locfit()] for more information on the fitted locfit object

Examples

df <- mumps_uk_1986_1987
model <- lp_model(
  df,
  nn=0.7, kern="tcub"
  )
plot(model)

Description

Fit the antibody level data to a 2-component Gaussian mixture model

Usage

mixture_model(
  antibody_level,
  breaks = 40,
  pi = c(0.2, 0.8),
  mu = c(2, 6),
  sigma = c(0.5, 1)
)

Arguments

Details

Antibody level (denoted $Z$) is modeled using a 2-component Gaussian mixture model. Each component $Z_j$ ($j \in \{I, S\}$) represents the antibody level of the latent Infected and Susceptible sub-populations, following density $f_j(z_j|\theta_j)$

Let $\pi_{\text{TRUE}}(a)$ denotes the age-dependent mixing probability (i.e., the true prevalence), the density of the mixture is formulated as

$f(z|z_I, z_S,a) = (1-\pi_{\text{TRUE}}(a))f_S(z_S|\theta_S)+\pi_{\text{TRUE}}(a)f_I(z_I|\theta_I)$

The mean $E(Z|a)$ thus equals

$\mu(a) = (1-\pi_{\text{TRUE}}(a))\mu_S+\pi_{\text{TRUE}}(a)\mu_I$

From which true prevalence can be computed as

$\pi_{\text{TRUE}}(a) = \frac{\mu(a) - \mu_S}{\mu_I - \mu_S}$

And FOI can then be inferred as

$\lambda_{TRUE} = \frac{\mu'(a)}{\mu_I - \mu(a)}$

Function [serosv::mixture_model()] fits antibody level data to $f_S(z_S|\theta_S)$ and $f_I(z_I|\theta_I)$

Function [serosv::estimate_mixture()] will then estimate age-specific antibody level $\mu(a)$ and infer the estimation for $\pi_{\text{TRUE}}(a)$ and $\lambda_{TRUE}$

Refer to section 11.3. of the the book by Hens et al. (2012) for further details.

Value

a list of class mixture_model with the following items

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 <- vzv_be_2001_2003[vzv_be_2001_2003$age < 40.5,]
data <- df$VZVmIUml[order(df$age)]
model <- mixture_model(antibody_level = data)
model$info
plot(model)

Description

a large survey of prevalence of antibodies to mumps and rubella viruses in the UK. The survey, covering subjects from 1 to over 65 years of age, provides information on the prevalence of antibody by age

Usage

mumps_uk_1986_1987

Format

A data frame with 3 variables:

age

Midpoint of the age group (e.g. 1.5 = 1-2 years old, 2.5 = 2-3 years old)

pos

Number of seropositive individuals

tot

Total number of individuals surveyed

Source

Morgan-Capner P, Wright J, Miller C L, Miller E. Surveillance of antibody to measles, mumps, and rubella by age. British Medical Journal 1988; 297 :770 doi:10.1136/bmj.297.6651.770

Examples

with(mumps_uk_1986_1987,
  plot(age, pos / tot,
    cex = 0.1 * sqrt(tot), pch = 16, xlab = "age", ylab = "seroprevalence",
    xlim = c(0, 45), ylim = c(0, 1)
  )
)

Description

A seroprevalence survey testing for parvovirus B19 IgG antibody, performed on large representative national serum banks in Belgium, England and Wales, Finland, Italy, and Poland. The sera were collected between 1995 and 2004 and were obtained from residual sera submitted for routine laboratory testing.

Usage

parvob19_be_2001_2003

Format

A data frame with 5 variables:

age

Age of individual

seropositive

If the individual is seropositive or not

year

Year surveyed

gender

Gender of individual

parvouml

Parvo B19 antibody units per ml

Source

MOSSONG, J., N. HENS, V. FRIEDERICHS, I. DAVIDKIN, M. BROMAN, B. LITWINSKA, J. SIENNICKA, et al. "Parvovirus B19 Infection in Five European Countries: Seroepidemiology, Force of Infection and Maternal Risk of Infection." Epidemiology and Infection 136, no. 8 (2008): 1059-68. doi:10.1017/S0950268807009661

Examples

library(dplyr)
df <- parvob19_be_2001_2003 %>%
  group_by(age) %>%
  summarise(pos = sum(seropositive), tot = n())
plot(df$age, df$pos / df$tot,
  cex = 0.3 * sqrt(df$tot), pch = 16, xlab = "age", ylab = "seroprevalence",
  xlim = c(0, 82), ylim = c(0, 1)
)

Description

A seroprevalence survey testing for parvovirus B19 IgG antibody, performed on large representative national serum banks in Belgium, England and Wales, Finland, Italy, and Poland. The sera were collected between 1995 and 2004 and were obtained from residual sera submitted for routine laboratory testing.

Usage

parvob19_ew_1996

Format

A data frame with 5 variables:

age

Age of individual

seropositive

If the individual is seropositive or not

year

Year surveyed

gender

Gender of individual

parvouml

Parvo B19 antibody units per ml

Source

MOSSONG, J., N. HENS, V. FRIEDERICHS, I. DAVIDKIN, M. BROMAN, B. LITWINSKA, J. SIENNICKA, et al. "Parvovirus B19 Infection in Five European Countries: Seroepidemiology, Force of Infection and Maternal Risk of Infection." Epidemiology and Infection 136, no. 8 (2008): 1059-68. doi:10.1017/S0950268807009661

Examples

# Note: This figure will look different to that of in the book, since we
# believe that the original authors has made some errors in specifying
# the sample size of the dots.

library(dplyr)
df <- parvob19_ew_1996 %>%
  mutate(age = round(age)) %>%
  group_by(age) %>%
  summarise(pos = sum(seropositive), tot = n())
plot(df$age, df$pos / df$tot,
  cex = 0.3 * sqrt(df$tot), pch = 16, xlab = "age", ylab = "seroprevalence",
  xlim = c(0, 82), ylim = c(0, 1)
)

Description

A seroprevalence survey testing for parvovirus B19 IgG antibody, performed on large representative national serum banks in Belgium, England and Wales, Finland, Italy, and Poland. The sera were collected between 1995 and 2004 and were obtained from residual sera submitted for routine laboratory testing.

Usage

parvob19_fi_1997_1998

Format

A data frame with 5 variables:

age

Age of individual

seropositive

If the individual is seropositive or not

year

Year surveyed

gender

Gender of individual

parvouml

Parvo B19 antibody units per ml

Source

MOSSONG, J., N. HENS, V. FRIEDERICHS, I. DAVIDKIN, M. BROMAN, B. LITWINSKA, J. SIENNICKA, et al. "Parvovirus B19 Infection in Five European Countries: Seroepidemiology, Force of Infection and Maternal Risk of Infection." Epidemiology and Infection 136, no. 8 (2008): 1059-68. doi:10.1017/S0950268807009661

Examples

# Note: This figure will look different to that of in the book, since we
# believe that the original authors has made some errors in specifying
# the sample size of the dots.

library(dplyr)
df <- parvob19_fi_1997_1998 %>%
  mutate(age = round(age)) %>%
  group_by(age) %>%
  summarise(pos = sum(seropositive), tot = n())
plot(df$age, df$pos / df$tot,
  cex = 0.4 * sqrt(df$tot), pch = 16, xlab = "age", ylab = "seroprevalence",
  xlim = c(0, 82), ylim = c(0, 1)
)

Description

A seroprevalence survey testing for parvovirus B19 IgG antibody, performed on large representative national serum banks in Belgium, England and Wales, Finland, Italy, and Poland. The sera were collected between 1995 and 2004 and were obtained from residual sera submitted for routine laboratory testing.

Usage

parvob19_it_2003_2004

Format

A data frame with 5 variables:

age

Age of individual

seropositive

If the individual is seropositive or not

year

Year surveyed

gender

Gender of individual

parvouml

Parvo B19 antibody units per ml

Source

MOSSONG, J., N. HENS, V. FRIEDERICHS, I. DAVIDKIN, M. BROMAN, B. LITWINSKA, J. SIENNICKA, et al. "Parvovirus B19 Infection in Five European Countries: Seroepidemiology, Force of Infection and Maternal Risk of Infection." Epidemiology and Infection 136, no. 8 (2008): 1059-68. doi:10.1017/S0950268807009661

Examples

library(dplyr)
df <- parvob19_it_2003_2004 %>%
  group_by(age) %>%
  summarise(pos = sum(seropositive), tot = n())
plot(df$age, df$pos / df$tot,
  cex = 0.32 * sqrt(df$tot), pch = 16, xlab = "age", ylab = "seroprevalence",
  xlim = c(0, 82), ylim = c(0, 1)
)

Description

A seroprevalence survey testing for parvovirus B19 IgG antibody, performed on large representative national serum banks in Belgium, England and Wales, Finland, Italy, and Poland. The sera were collected between 1995 and 2004 and were obtained from residual sera submitted for routine laboratory testing.

Usage

parvob19_pl_1995_2004

Format

A data frame with 5 variables:

age

Age of individual

seropositive

If the individual is seropositive or not

year

Year surveyed

gender

Gender of individual

parvouml

Parvo B19 antibody units per ml

Source

MOSSONG, J., N. HENS, V. FRIEDERICHS, I. DAVIDKIN, M. BROMAN, B. LITWINSKA, J. SIENNICKA, et al. "Parvovirus B19 Infection in Five European Countries: Seroepidemiology, Force of Infection and Maternal Risk of Infection." Epidemiology and Infection 136, no. 8 (2008): 1059-68. doi:10.1017/S0950268807009661

Examples

# Note: This figure will look different to that of in the book, since we
# believe that the original authors has made some errors in specifying
# the sample size of the dots.

library(dplyr)
df <- parvob19_pl_1995_2004 %>%
  mutate(age = round(age)) %>%
  group_by(age) %>%
  summarise(pos = sum(seropositive), tot = n())
plot(df$age, df$pos / df$tot,
  cex = 0.32 * sqrt(df$tot), pch = 16, xlab = "age", ylab = "seroprevalence",
  xlim = c(0, 82), ylim = c(0, 1)
)

Description

Monotonize seroprevalence

Usage

pava(pos = pos, tot = rep(1, length(pos)))

Arguments

Value

computed list of 2 items pai1 for original values and pai2 for monotonized value

Description

Fit age-specific seroprevalence to a semi-parametric model where predictor is modeled with penalized splines. The penalized splines can be estimated by either (1) penalized likelihood framework or (2) mixed model framework

Usage

penalized_spline_model(
  data,
  age_col = "age",
  pos_col = "pos",
  tot_col = "tot",
  status_col = "status",
  s = "bs",
  link = "logit",
  framework = "pl",
  sp = NULL
)

Arguments

Details

In the semi-parametric model, the predictor is formulated as a penalized spline with truncated power basis functions of degree $p$ and fixed knots $\kappa_1,..., \kappa_k$ as followed

$\eta(a_i) = \beta_0 + \beta_1a_i + ... + \beta_p a_i^p + \Sigma_{k=1}^ku_k(a_i - \kappa_k)^p_+$

- Where:

$(a_i - \kappa_k)^p_+ = \begin{cases} 0, & a_i \le \kappa_k \\ (a_i - \kappa_k)^p, & a_i > \kappa_k \end{cases}$

FOI can then be derived by

$\hat{\lambda}(a_i) = [\hat{\beta_1} , 2\hat{\beta_2}a_i, ..., p \hat{\beta} a_i ^{p-1} + \Sigma^k_{k=1} p \hat{u}_k(a_i - \kappa_k)^{p-1}_+] \delta(\hat{\eta}(a_i))$

Where $\delta(.)$ is determined by the link function used in the model

In matrix annotation, the mean structure model for $\eta(a_i)$ becomes

$\eta = \textbf{X}\beta + \textbf{Zu}$

Where $\eta = [\eta(a_i) ... \eta(a_N) ]^T$, $\beta = [\beta_0 \beta_1 .... \beta_p]^T$, and $\textbf{u} = [u_1 u_2 ... u_k]^T$ are the regression with corresponding design matrices

$\textbf{X} = \begin{bmatrix} 1 & a_1 & a_1^2 & ... & a_1^p \\ 1 & a_2 & a_2^2 & ... & a_2^p \\ \vdots & \vdots & \vdots & \dots & \vdots \\ 1 & a_N & a_N^2 & ... & a_N^p \end{bmatrix}, \textbf{Z} = \begin{bmatrix} (a_1 - \kappa_1 )_+^p & (a_1 - \kappa_2 )_+^p & \dots & (a_1 - \kappa_k)_+^p \\ (a_2 - \kappa_1 )_+^p & (a_2 - \kappa_2 )_+^p & \dots & (a_2 - \kappa_k)_+^p \\ \vdots & \vdots & \dots & \vdots \\ (a_N - \kappa_1 )_+^p & (a_N - \kappa_2 )_+^p & \dots & (a_N - \kappa_k)_+^p \end{bmatrix}$

Under penalized likelihood framework, the model is fitted by maximizing the following likelihood

$\phi^{-1}[y^T(\textbf{X}\beta + \textbf{Zu} ) - \textbf{1}^Tc(\textbf{X}\beta + \textbf{Zu} )] - \frac{1}{2}\lambda^2 \begin{bmatrix} \beta \\ \textbf{u} \end{bmatrix}^T D\begin{bmatrix} \beta \\ \textbf{u} \end{bmatrix}$

Where:

- $X\beta + Zu$ is the predictor

- $D$ is a known semi-definite penalty matrix [@Wahba1978], [@Green1993]

- $y$ is the response vector

- $\textbf{1}$ the unit vector, $c(.)$ is determined by the link function used

- $\lambda$ is the smoothing parameter (larger values –> smoother curves)

- $\phi$ is the overdispersion parameter and equals 1 if there is no overdispersion

Under the mixed model framework, the model instead treats the coefficients $\textbf{u}$ in the likelihood formulation as random effects with $\textbf{u} \sim N(\textbf{0}, \mathbf{\sigma}^2_u \textbf{I})$

Refer to section 8.1 and 8.2 of the the book by Hens et al. (2012) for further details.

Value

a list of class penalized_spline_model with 6 attributes

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.

See Also

[mgcv::gam()], [mgcv::gamm()] for more information the fitted gam and gamm model

Examples

data <- parvob19_be_2001_2003
data$status <- data$seropositive
model <- penalized_spline_model(data, framework="glmm")
model$info$gam
plot(model)

Description

Plot output for corrected_prevalence

Usage

plot_corrected_prev(x, y = NULL, facet = FALSE)

Arguments

Value

ggplot object

Description

Refers to section 7.2.

Usage

plot_gcv(age, pos, tot, nn_seq, h_seq, kern = "tcub", deg = 2)

Arguments

Value

plot of gcv value

Examples

df <- mumps_uk_1986_1987
plot_gcv(
  df$age, df$pos, df$tot,
  nn_seq = seq(0.2, 0.8, by=0.1),
  h_seq = seq(5, 25, by=1)
)

Description

Visualize standard curves for each plate

Usage

plot_standard_curve(
  x,
  facet = TRUE,
  xlab = "log10(concentration)",
  ylab = "Optical density",
  datapoint_size = 2
)

Arguments

Description

Visualize for each sample, whether titer estimates can be computed at the tested dilutions.

Usage

plot_titer_qc(x, n_plates = 18, n_samples = 22, n_dilutions = 3)

Arguments

Details

Each sample is represented by a 'n_estimates x n_dilutions' grid where cell color indicate estimate availability (green = estimate available, orange = result too low, red = result too high)

These sample grids are arranged in columns where each column represent samples from a plate

The figure below demonstrates the interpretation of the plot.

Description

Plot output for age_time_model

Usage

## S3 method for class 'age_time_model'
plot(x, ...)

Arguments

Value

ggplot object

Description

plot() overloading for result of estimate_from_mixture

Usage

## S3 method for class 'estimate_from_mixture'
plot(x, ...)

Arguments

Value

ggplot object

Description

plot() overloading for Farrington model

Usage

## S3 method for class 'farrington_model'
plot(x, ...)

Arguments

Value

ggplot object

Description

plot() overloading for fractional polynomial model

Usage

## S3 method for class 'fp_model'
plot(x, ...)

Arguments

Value

ggplot object

Description

plot() overloading for hierarchical_bayesian_model

Usage

## S3 method for class 'hierarchical_bayesian_model'
plot(x, ...)

Arguments

Value

ggplot object

Description

plot() overloading for local polynomial model

Usage

## S3 method for class 'lp_model'
plot(x, ...)

Arguments

Value

ggplot object

Description

plot() overloading for mixture model

Usage

## S3 method for class 'mixture_model'
plot(x, ...)

Arguments

Value

ggplot object

Description

plot() overloading for penalized spline

Usage

## S3 method for class 'penalized_spline_model'
plot(x, ...)

Arguments

Value

ggplot object

Description

plot() overloading for polynomial model

Usage

## S3 method for class 'polynomial_model'
plot(x, ...)

Arguments

Value

ggplot object

Description

plot() overloading for Weibull model

Usage

## S3 method for class 'weibull_model'
plot(x, ...)

Arguments

Value

ggplot object

Description

Fit age-stratified seroprevalence data to serocatalytic models formulated as polynomials.

Usage

polynomial_model(
  data,
  k,
  link = "log",
  age_col = "age",
  pos_col = "pos",
  tot_col = "tot",
  status_col = "status"
)

Arguments

Details

The seroprevalence is assumed to follow the general format

$\pi(a) = 1 - e^{-\Sigma_{i=1}^k \beta_i a^i}$

Which implies the force of infection to be $\lambda(a) = \Sigma_{i=1}^k \beta_i i a^{i-1}$

Where:

- $\pi$ is the seroprevalence at age $a$

- $a$ is the variable age

- $k$ is the degree of the polynomial

The seroprevalence $\pi(a)$ is fitted using a GLM with log link with the linear predictor $\eta(a) = \Sigma_{i=1}^k \beta_i a^{i}$

Muench (1934) model is equivalent to a degree 1 ($k=1$) linear predictor

Griffith model is equivalent to a degree 2 ($k=2$) linear predictor

Grenfell & Anderson (1985) suggested a higher order polynomials ($k \geq 3$)

Refer to section 6.1.1. of the the book by Hens et al. (2012) for further details.

Value

a list of class polynomial_model with 5 items

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.

Grenfell, B. T., and R. M. Anderson. 1985. “The Estimation of Age-Related Rates of Infection from Case Notifications and Serological Data.” The Journal of Hygiene 95 (2): 419–36. doi:10.1017/s0022172400062859.

Muench, Hugo. 1934. “Derivation of Rates from Summation Data by the Catalytic Curve.” Journal of the American Statistical Association 29 (185): 25–38. doi:10.1080/01621459.1934.10502684.

Examples

data <- parvob19_fi_1997_1998[order(parvob19_fi_1997_1998$age), ]
aggregated <- transform_data(data, stratum_col = "age", status_col="seropositive")

# fit with aggregated data
model <- polynomial_model(aggregated, k = 1)
# fit with linelisting data
model <- polynomial_model(data,
    status_col = "seropositive",
    k = 1)
plot(model)

Description

Predict from the age_time_mdoel

Usage

## S3 method for class 'age_time_model'
predict(object, newdata, modtype = "monotonized", ...)

Arguments

Value

confidence interval dataframe with n_group x 3 cols, the columns are 'group', 'sp_df', 'foi_df'

Description

Prediction for serosv Farrington model

Usage

## S3 method for class 'farrington_model'
predict(object, newdata = NULL, ...)

Arguments

Value

prediction output

Description

Prediction for serosv fractional polynomial model

Usage

## S3 method for class 'fp_model'
predict(object, newdata = NULL, ...)

Arguments

Value

prediction output

See Also

[stats::predict.glm()] for more information on the predict function

Description

Predict from an hierarchical bayesian model

Usage

## S3 method for class 'hierarchical_bayesian_model'
predict(object, newdata = NULL, ...)

Arguments

Value

list of confidence interval for seroprevalence and foi. Each confidence interval dataframe with 4 variables, x and y for the fitted values and ymin and ymax for the confidence interval

Description

Prediction for serosv local polynomial model

Usage

## S3 method for class 'lp_model'
predict(object, newdata = NULL, ...)

Arguments

Value

prediction output

Description

Prediction for serosv penalized spline model

Usage

## S3 method for class 'penalized_spline_model'
predict(object, newdata = NULL, ...)

Arguments

Value

prediction output

See Also

[mgcv::predict.gam()] for more information on the predict function

Description

A wrapper of predict.glm for direct prediction from polynomial_model object

Usage

## S3 method for class 'polynomial_model'
predict(object, newdata = NULL, ...)

Arguments

Value

prediction output

See Also

[stats::predict.glm()] for more information on the predict function

Description

Prediction for serosv Weibull model

Usage

## S3 method for class 'weibull_model'
predict(object, newdata = NULL, ...)

Arguments

Value

prediction output

See Also

[stats::predict.glm()] for more information on the predict function

Description

Rubella - Mumps data from the UK (aggregated)

Usage

rubella_mumps_uk

Format

A data frame with 5 variables:

age

Age group

NN

Number of individuals negative to rubella and mumps

NP

Number of individuals negative to rubella and positive to mumps

PN

Number of individuals positive to rubella and negative to mumps

PP

Number of individuals positive to rubella and mumps

Source

Morgan-Capner P, Wright J, Miller C L, Miller E. Surveillance of antibody to measles, mumps, and rubella by age. British Medical Journal 1988; 297 :770 doi:10.1136/bmj.297.6651.770

Description

Prevalence of rubella in the UK, obtained from a large survey of prevalence of antibodies to both mumps and rubella viruses.

Usage

rubella_uk_1986_1987

Format

A data frame with 3 variables:

age

Midpoint of the age group (e.g. 1.5 = 1-2 years old, 2.5 = 2-3 years old)

pos

Number of seropositive individuals

tot

Total number of individuals surveyed

Source

Morgan-Capner P, Wright J, Miller C L, Miller E. Surveillance of antibody to measles, mumps, and rubella by age. British Medical Journal 1988; 297 :770 doi:10.1136/bmj.297.6651.770

Examples

with(rubella_uk_1986_1987,
  plot(age, pos / tot,
    cex = 0.2 * sqrt(tot), pch = 16, xlab = "age", ylab = "seroprevalence",
    xlim = c(0, 45), ylim = c(0, 1)
  )
)

Description

Helper to adjust styling of a plot

Usage

set_plot_style(
  sero = "blueviolet",
  ci = "royalblue1",
  foi = "#fc0328",
  sero_line = "solid",
  foi_line = "dashed",
  xlabel = "Age"
)

Arguments

Value

list of updated aesthetic values

Description

Validate and prepare raw serological test results for use with 'to_titer()'

Usage

standardize_data(
  df,
  plate_id_col = "PLATE_ID",
  id_col = "SAMPLE_ID",
  result_col = "RESULT",
  dilution_fct_col = "DILUTION_FACTORS",
  antitoxin_label = "Anti_toxin",
  negative_col = "^NEGATIVE_*"
)

Arguments

Value

a standardized data.frame that can be passed to 'to_titer()'

Description

A study of tuberculosis conducted in the Netherlands. Schoolchildren, aged between 6 and 18 years, were tested using the tuberculin skin test.

Usage

tb_nl_1966_1973

Format

A data frame with 5 variables:

age

Age group

pos

Number of seropositive individuals

tot

Total number of individuals surveyed

gender

Gender of cohort (unsure what 0 and 1 means)

birthyr

Birth year of cohort

Source

Nagelkerke, N., Heisterkamp, S., Borgdorff, M., Broekmans, J. and Van Houwelingen, H. (1999), Semi-parametric estimation of age-time specific infection incidence from serial prevalence data. Statist. Med., 18: 307-320. doi:10.1002/(SICI)1097-0258(19990215)18:3<307::AID-SIM15>3.0.CO;2-Z

Examples

with(tb_nl_1966_1973,
  plot(age, pos / tot,
    pch = 16, cex = 0.01 * sqrt(tot), xlab = "age",
    ylab = "prevalence", xlim = c(6, 18)
  )
)

with(tb_nl_1966_1973,
  plot(birthyr, pos / tot,
    pch = 16, cex = 0.01 * sqrt(tot), xlab = "year", ylab = "prevalence"
  )
)

Description

to_titer() converts raw assay readings (e.g., OD, fluorescence intensity) to titer by fitting a calibrating model

Usage

to_titer(
  df,
  model = "4PL",
  positive_threshold = NULL,
  ci = 0.95,
  negative_control = TRUE
)

Arguments

Value

a data.frame with 8 columns

Description

Generate a dataframe with 't', 'pos' and 'tot' columns from 't' and 'seropositive' vectors.

Usage

transform_data(data, stratum_col = "age", status_col = "status")

Arguments

Value

dataframe in aggregated format

Examples

df <- hcv_be_2006
hcv_df <- transform_data(df, stratum_col="dur", status_col="seropositive")
hcv_df

Description

Age-specific seroprevalence of VZV antibodies, assessed in Flanders (Belgium) between October 1999 and April 2000. This population was stratified by age in order to obtain approximately 100 observations per age group.

Usage

vzv_be_1999_2000

Format

A data frame with 3 variables:

age

Age group

pos

Number of seropositive individuals

tot

Total number of individuals surveyed

Source

Thiry, N., Beutels, P., Shkedy, Z. et al. The seroepidemiology of primary varicella-zoster virus infection in Flanders (Belgium). Eur J Pediatr 161, 588-593 (2002). doi:10.1007/s00431-002-1053-2

Examples

with(vzv_be_1999_2000,
  plot(age, pos / tot,
    cex = 0.1 * sqrt(tot), pch = 19, xlab = "age", ylab = "seroprevalence",
    xlim = c(0, 45), ylim = c(0, 1)
  )
)

Description

The survey is the same as the one used to study the seroprevalence of parvovirus B19 in Belgium, as described above.

Usage

vzv_be_2001_2003

Format

A data frame with 4 variables:

age

Age of individual

seropositive

If the individual is seropositive or not

gender

Gender of individual

VZVmIUml

VZV milli international units per ml

Source

MOSSONG, J., N. HENS, V. FRIEDERICHS, I. DAVIDKIN, M. BROMAN, B. LITWINSKA, J. SIENNICKA, et al. "Parvovirus B19 Infection in Five European Countries: Seroepidemiology, Force of Infection and Maternal Risk of Infection." Epidemiology and Infection 136, no. 8 (2008): 1059-68. doi:10.1017/S0950268807009661

Examples

library(dplyr)
df <- vzv_be_2001_2003 %>%
  mutate(age = round(age)) %>%
  group_by(age) %>%
  summarise(pos = sum(seropositive), tot = n())
plot(df$age, df$pos / df$tot,
  cex = 0.1 * sqrt(df$tot), pch = 19, xlab = "age", ylab = "seroprevalence",
  xlim = c(0, 45), ylim = c(0, 1)
)

Description

VZV and Parvovirus B19 serological data in Belgium (line listing)

Usage

vzv_parvo_be

Format

A data frame with 7 variables:

id

ID of individual

age

Age of individual

gender

Gender of individual

parvouml

Parvo B19 antibody units per ml

parvo_res

If an individual is positive for parvovirus B19

VZVmUIml

VZV milli international units per ml

vzv_res

If an individual is positive for VZV

Source

MOSSONG, J., N. HENS, V. FRIEDERICHS, I. DAVIDKIN, M. BROMAN, B. LITWINSKA, J. SIENNICKA, et al. "Parvovirus B19 Infection in Five European Countries: Seroepidemiology, Force of Infection and Maternal Risk of Infection." Epidemiology and Infection 136, no. 8 (2008): 1059-68. doi:10.1017/S0950268807009661

Description

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

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.

Value

list of class weibull_model with the following items

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.

See Also

[stats::glm()] for more information on the fitted "glm" object

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)