Fitting models for Secondary Attack Rate with Chain Binomial response

Description

Fitting models for Secondary Attack Rate with Chain Binomial response

Usage

cbmod(
  y,
  s0,
  x = NULL,
  i0 = 1,
  generations = Inf,
  link = "identity",
  optim_method = "BFGS"
)

Arguments

Details

The following link functions are available: identity, log, logit, and cloglog.

Value

A list of class cbmod with the following components:

• parameters The point estimate of the regression coefficients.

• se Standard error of the regression coefficient estimates.

• vcov Variance-Covariance matrix of the regression coefficient estimates.

• p_values P-values of the null hypothesis that the regression regression coefficient estimate is 0.

• loglikelihood the log likelihood value at the point estimate.

• npar Number of parameters.

• sar_hat Vector of fitted secondary attack rates.

• fitted_values Vector of expected outbreak size (final attack rate).

• link Link function used by the regression model.

• null_model = Null model, fitted with estimate_sar(). This is equivalent to an intercept only model.

• warnings Warning_messages,

• est_time: Time used to fit the model.

• omitted_values Vector indicating data points that were ignored during estimation because of missing values.

See Also

Methods for cbmod objects:

• summary.cbmod()

• predict.cbmod()

• coef.cbmod()

• confint.cbmod()

• vcov.cbmod()

• tidy.cbmod()

• glance.cbmod()

Examples

set.seed(234)
mydata <- data.frame(infected = rchainbinom(n = 15, s0 = 5, sar = 0.2,
   i0 = 1, generations = Inf),
   s0 = 5, i0 = 1, generations = Inf)
xmat <- model.matrix(~ 1, data = mydata)
res <- cbmod(y = mydata$infected, s0 = mydata$s0, x = xmat, i0 = mydata$i0,
   generations = mydata$generations)
summary(res)

Extract Model Coefficient for cbmod Fits

Description

Extract Model Coefficient for cbmod Fits

Usage

## S3 method for class 'cbmod'
coef(object, ...)

Arguments

Value

Coefficients extracted from the cbmod object.

Confidence intervals for cbmod Object.

Description

Confidence intervals for cbmod Object.

Usage

## S3 method for class 'cbmod'
confint(object, parm = NULL, level = 0.95, ...)

Arguments

Value

A two-column matrix with the lower and upper end of the confidence intervals.

Confidence intervals for sar Object.

Description

Confidence intervals for sar Object.

Usage

## S3 method for class 'sar'
confint(object, parm = NULL, level = 0.95, method = "chisq", ...)

Arguments

Value

A numeric of length 2 with the lower and upper end of the confidence interval.

The Chain Binomial distribution

Description

Probability mass function, expected value, and random generation, for the chain binomial distribution, with parameters s0, sar, i0, and number of generations, for the number of infected cases in a population of size s0 after a given number of generations.

Usage

dchainbinom(x, s0, sar, i0 = 1, generations = Inf)

rchainbinom(n, s0, sar, i0 = 1, generations = Inf)

echainbinom(s0, sar, i0 = 1, generations = Inf)

Arguments

Value

dchainbinom gives the probability of x infected, given s0, i0, sar and generations. echainbinom gives the expected value. rchainbinom generates random data.

Examples

dchainbinom(x = 0:5, s0 = 5, sar = 0.2, i0 = 1, generations = Inf)
rchainbinom(n = 10, s0 = 5, sar = 0.2, i0 = 1, generations = Inf)
echainbinom(s0 = 5, sar = 0.2, i0 = 1, generations = Inf)

Estimate Secondary Attack Rate of the Chain Binomial Model

Description

Given data on the number of infected after a number of generation, initial number of susceptible, and initial number of infected, estimate the secondary attack rate (SAR) using maximum likelihood.

Usage

estimate_sar(infected, s0, i0 = 1, generations = Inf, se = TRUE)

Arguments

Value

A list of class sar with the following components:

• sar_hat The point estimate of the secondary attack rate.

• se Standard error of the estimate (if se = TRUE).

• loglikelihood The log likelihood value at the point estimate.

• data The input data.

See Also

confint.sar() for calculating confidence intervals.

Examples

set.seed(234)
mydata <- rchainbinom(n = 15, s0 = 5, sar = 0.2, i0 = 1, generations = Inf)
res <- estimate_sar(infected = mydata, s0 = 5, i0 = 1, generations = Inf)

Glance at a cbmod object

Description

Glance at a cbmod object

Usage

## S3 method for class 'cbmod'
glance(x, ...)

Arguments

Value

Returns a tibble with the following columns:

• logLik The model's log-likelihood.

• npar Numnber of parameters in the model.

Common Cold Data

Description

Data presented in Heasman & Reid (1961), originally gathered and analyzed by Brimblecombe et al (1958). The data set describes 664 outbreaks of the common cold in 72 families over two years. All families consists of two parents and three children. The data is available in aggregated form as presented in the paper, with counts of the number of outbreaks that belong to a given classification.

Usage

heasman_reid_1961_chains

heasman_reid_1961_crowding

heasman_reid_1961_intro_case_status

heasman_reid_1961_intro_case_status

heasman_reid_1961_crowding

Format

An object of class data.frame with 24 rows and 2 columns.

An object of class data.frame with 5 rows and 5 columns.

An object of class data.frame with 5 rows and 4 columns.

Chain Data

Each outbreak was classified to a specific chain suitable for analysis by the Chain Binomial model by Heasman & Reid (1961), Table V.

heasman_reid_1961_chains: A data frame with 24 rows and 2 columns:

chain

the number of infected in each generation, separated by '-', ie the Chain.

n

Number of outbreaks

Crowding

Each outbreak classified according to the degree of domestic overcrowding. Heasman & Reid (1961), Table IV. Overcrowded homes have either one or two rooms, crowded homes have three rooms, while uncrowded homes have more than three rooms.

heasman_reid_1961_crowding: A data frame with 5 rows and 4 columns:

further_cases

The number of cases in the outbreak, in addition to the primary case.

overcrowding

Number of outbreaks that belong to the overcrowded household category.

crowded

Number of outbreaks that belong to the crowded household category.

uncrowded

Number of outbreaks that belong to the uncrowded household category.

Index case status

Each outbreak classified according to who the the introducing case was. Heasman & Reid (1961), Table II.

heasman_reid_1961_intro_case_status: A data frame with 5 rows and 5 columns:

further_cases

The number of cases in the outbreak, in addition to the primary case.

father

Number of outbreaks with father as the index case.

mother

Number of outbreaks with mother as the index case.

school_child

Number of outbreaks with a school child as the index case.

pre_school_child

Number of outbreaks with a pre-school child as the index case.

References

• Heasman & Reid (1961) Theory And Observation In Family Epidemics Of The Common Cold. Brit. J. prev. soc. Med.

• Brimblecombe et al (1958) Family Studies Of Respiratory Infections. British Medical Journal.

Predict Method for cbmod Fits

Description

Predict Method for cbmod Fits

Usage

## S3 method for class 'cbmod'
predict(object, x, type = "identity", ...)

Arguments

Value

a vector of predictions.

Examples

set.seed(234)
mydata <- data.frame(infected = rchainbinom(n = 15, s0 = 5, sar = 0.2,
  i0 = 1, generations = Inf),
  s0 = 5, i0 = 1, generations = Inf)
xmat <- model.matrix(~ 1, data = mydata)
res <- cbmod(y = mydata$infected, s0 = mydata$s0, x = xmat, i0 = mydata$i0,
  generations = mydata$generations, link = 'identity')
summary(res)
predict(res, x = xmat, type = 'sar')

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

generics

glance, tidy

Summary of cbmod Object.

Description

Summary of cbmod Object.

Usage

## S3 method for class 'cbmod'
summary(object, ...)

Arguments

Value

Returns nothing, but displays a summary of the model fit.

Tidy a cbmod object

Description

Tidy a cbmod object

Usage

## S3 method for class 'cbmod'
tidy(x, conf.int = FALSE, conf.level = 0.95, ...)

Arguments

Value

Returns a tibble with the following columns:

• term The coefficients name.

• estimate The point estimates of the coefficients.

• std.error Standard error of the regression coefficient estimates.

• p.value P-values of the null hypothesis that the regression regression coefficient estimate is 0.

• conf.low If conf.int = TRUE, the lower end of the confidence interval.

• conf.highIf conf.int = TRUE, the upper end of the confidence interval.

Variance-Covariance Matrix of cbmod Object.

Description

Variance-Covariance Matrix of cbmod Object.

Usage

## S3 method for class 'cbmod'
vcov(object, ...)

Arguments

Value

A variance-covariance matrix.