prevtoinc:

Description

The prevtoinc package implements functionality to simulate point-prevalence studies (PPSs) for healtcare-associated infections (HAIs) and estimate incidence based on the PPS data. It is a companion package to the preprint Willrich et al., From prevalence to incidence - a new approach in the hospital setting; <doi:10.1101/554725> , where methods are explained in detail.

function to transform the distribution of stays to a fixed point to the distribution of the staying times

Description

function to transform the distribution of stays to a fixed point to the distribution of the staying times

Usage

A_to_X_dist(dist.point)

Arguments

Value

vector of probabilities of being at the hospital for 1:length(dist.point) days at random time of observation

Examples

# generate vector of probabilities for truncated Poisson distribution for 
# distribution of times of stay X
dist.X <- dpois(1:70, 4)
plot(dist.X)
# transform to distribution of distribution of staying-time up to observation point under
# assumption of steady state
dist.A <- X_to_A_dist(dist.X)
plot(dist.A)
# transform back to get original distribution
dist.X.2 <- A_to_X_dist(dist.A)
plot(dist.X.2)

Function to calculate confidence intervals I.pp for gren estimator with bootstrap method based on Grenander estimator

Description

Implements a bootstrap procedure for estimation of confidence intervals for I.pp based on boostrapping from the length of stay/infection distributions estimated by the gren method.

Usage

CI_np_bs(data, n_bs = 1000, alpha = 0.05)

Arguments

Value

single-row tibble with columns CI.lower.Ipp and CI.upper.Ipp

Examples

example.dist <- create_dist_vec(function(x) dpois(x-1, 7), max.dist = 70)
example.dist.los <- create_dist_vec(function(x) dpois(x-1, lambda = 12),
                                    max.dist = 70)
data.pps.fast <- simulate_pps_fast(n.sample=5000,
                                   P=0.05,
                                   dist.X.loi = example.dist,
                                   dist.X.los = example.dist.los)
gren_est <- calculate_I_smooth(data = data.pps.fast, method = "gren")
gren_est
CI_np_bs(data.pps.fast, n_bs = 500)

Transform a distribution of times of stay to a distribution of staying-time up to observation point under assumption of steady state.

Description

Transform a distribution of times of stay to a distribution of staying-time up to observation point under assumption of steady state.

Usage

X_to_A_dist(dist.stays)

Arguments

Value

vector of probabilities of staying 1:length(dist.point) days

Examples

# generate vector of probabilities for truncated Poisson distribution for 
# distribution of times of stay X
dist.X <- dpois(1:70, 4)
plot(dist.X)
# transform to distribution of distribution of staying-time up to observation point under
# assumption of steady state
dist.A <- X_to_A_dist(dist.X)
plot(dist.A)
# transform back to get original distribution
dist.X.2 <- A_to_X_dist(dist.A)
plot(dist.X.2)

Calculate confidence intervals for Grenander estimator of Ipp based on asymptotics

Description

Asymptotic or bootstrap approximation of confidence intervals for estimates of Ipp with gren method Can use output of calculate_I_* functions as input. The asymptotic method uses the asymptotic normality of the estimator of I.pp to calculate the confidence interval and the method "bs" uses a parametric bootstrap approximation based on the "naive" estimator.

Usage

calculate_CI_I_pp(data, method = "asymptotic", alpha = 0.05,
  n_bs = 10000)

Arguments

Value

tibble with columns CI.lower.Ipp and CI.upper.Ipp

Examples

example.dist <- create_dist_vec(function(x) dpois(x-1, 7), max.dist = 70)
example.dist.los <- create_dist_vec(function(x) dpois(x-1, lambda = 12),
                                    max.dist = 70)
data.pps.fast <- simulate_pps_fast(n.sample=5000,
                                   P=0.05,
                                   dist.X.loi = example.dist,
                                   dist.X.los = example.dist.los)
gren_est <- calculate_I_smooth(data = data.pps.fast, method = "gren")
gren_est
calculate_CI_I_pp(gren_est, method = "asymptotic", alpha = 0.05)

Function to calculate different estimators for I from PPS data.

Description

Function to calculate different estimators for I from PPS data.

Usage

calculate_I(data, data.theo = NULL)

Arguments

Value

data frame with following columns

• n - number of patients sampled

• n.noso - number of HAIs

• P.hat - estimate of prevalence P

• I.hat - estimate of incidence rate I

• I.pp.hat - estimate of incidence proportion per admission I.pp

• x.loi.hat - estimate of x.loi

• x.los.hat - estimate of x.los

• method - name of the method

and rows for the estimators gren, rear, pps.median, pps.mean, pps.mixed, rhame.theo, L.full (for a description of the estimators see vignette).

Examples

# create example data for PPS
example.dist <- create_dist_vec(function(x) dpois(x-1, 7), max.dist = 70)
example.dist.los <- create_dist_vec(function(x) dpois(x-1, lambda = 12),
                                    max.dist = 70)
data.pps.fast <- simulate_pps_fast(n.sample=200,
                                   P=0.05,
                                   dist.X.loi = example.dist,
                                   dist.X.los = example.dist.los)
head(data.pps.fast)

# estimate incidence based on Rhame-Sudderth formula
calculate_I(data = data.pps.fast)

Function to calculate incidence from PPS data using a mix of two estimators

Description

A sigmoid function with parameters a and b (see below) is used to get weights for a combination of the two estimator for x.loi and x.los.

Usage

calculate_I_mixed(I.pps.1, I.pps.2, a = 0.01, b = 500,
  method = "pps.mixed")

Arguments

Details

is achieved in the following way for estimation of x.loi alpha = exp(a*(n.noso-b))/(1+exp(a*(n.noso-b))) x.loi.hat.mixed = alpha*x.loi.hat.1 + (1-alpha)*x.loi.hat.2

alpha = exp(a*(n-b))/(1+exp(a*(n-b))) x.los.hat.mixed = alpha*x.los.hat.1 + (1-alpha)*x.los.hat.2

Value

one-row data frame with following columns

• n - number of patients sampled

• n.noso - number of HAIs

• P.hat - estimate of prevalence P

• I.hat - estimate of incidence rate I

• I.pp.hat - estimate of incidence proportion per admission I.pp

• x.loi.hat - estimate of x.loi

• x.los.hat - estimate of x.los

• method - name of the method

Examples

# create example data for PPS
example.dist <- create_dist_vec(function(x) dpois(x-1, 7), max.dist = 70)
example.dist.los <- create_dist_vec(function(x) dpois(x-1, lambda = 12),
                                    max.dist = 70)
data.pps.fast <- simulate_pps_fast(n.sample=200,
                                   P=0.05,
                                   dist.X.loi = example.dist,
                                   dist.X.los = example.dist.los)
head(data.pps.fast)

# estimate of incidence
I.1 <- calculate_I_smooth(data = data.pps.fast,
                   method = "gren")
                   
# estimate incidence based on Rhame-Sudderth formula
I.2 <- calculate_I_rhame(data = data.pps.fast,
                   x.loi.hat = 8,
                   x.los.hat = 13)

# mixed estimator                                      
calculate_I_mixed(I.1, I.2)

Function to calculate incidence from PPS data using a Rhame-Sudderth like approach with estimates for x.loi and x.los supplied.

Description

Function to calculate incidence from PPS data using a Rhame-Sudderth like approach with estimates for x.loi and x.los supplied.

Usage

calculate_I_rhame(data, x.loi.hat, x.los.hat = NA, method = "rhame")

Arguments

Value

one-row data frame with following columns

• n - number of patients sampled

• n.noso - number of HAIs

• P.hat - estimate of prevalence P

• I.hat - estimate of incidence rate I

• I.pp.hat - estimate of incidence proportion per admission I.pp

• x.loi.hat - estimate of x.loi

• x.los.hat - estimate of x.los

• method - name of the method

Examples

# create example data for PPS
example.dist <- create_dist_vec(function(x) dpois(x-1, 7), max.dist = 70)
example.dist.los <- create_dist_vec(function(x) dpois(x-1, lambda = 12),
                                    max.dist = 70)
data.pps.fast <- simulate_pps_fast(n.sample=200,
                                   P=0.05,
                                   dist.X.loi = example.dist,
                                   dist.X.los = example.dist.los)
head(data.pps.fast)

# estimate incidence based on Rhame-Sudderth formula
calculate_I_rhame(data = data.pps.fast,
                   x.loi.hat = 8,
                   x.los.hat = 13)

Estimate the incidence based on PPS data using monotone estimators for the distribution of A.

Description

Estimate incidence from PPS by the method proposed in the companion paper. 'data' should be supplied as a data frame with at least a column named 'A.loi' giving lengths of infection up to date of PPS. Values of zero for 'A.loi' indicate absence of a HAI. Optionally, the data frame can also contain a column 'A.los' supplying lengths of stay up to PPS to estimate x.los with the same method as well. If 'correct.one' is 'TRUE', the number infections on their first day will be augmented to be at least as high as the number of infections on their second day for the estimation of x.loi .

Usage

calculate_I_smooth(data, method = "gren", correct.one.loi = "no",
  correct.one.los = "no")

Arguments

Value

one-row data frame with following columns

• n - number of patients sampled

• n.noso - number of HAIs

• P.hat - estimate of prevalence P

• I.hat - estimate of incidence rate I

• I.pp.hat - estimate of incidence proportion per admission I.pp

• x.loi.hat - estimate of x.loi

• x.los.hat - estimate of x.los

• method - name of the method

Examples

# create example data for PPS
example.dist <- create_dist_vec(function(x) dpois(x-1, 7), max.dist = 70)
example.dist.los <- create_dist_vec(function(x) dpois(x-1, lambda = 12),
                                    max.dist = 70)
data.pps.fast <- simulate_pps_fast(n.sample=200,
                                   P=0.05,
                                   dist.X.loi = example.dist,
                                   dist.X.los = example.dist.los)
head(data.pps.fast)

# estimate of incidence
calculate_I_smooth(data = data.pps.fast,
                   method = "gren")

Create vector of probabilities for a finite positive discrete distribution

Description

Cuts-off the (possibly unbounded) probability distribution at 'max.dist' and normalizes the resulting vector of probability to sum up to 1.

Usage

create_dist_vec(dist, max.dist)

Arguments

Value

vector of probabilites for values 1:max.dist

Examples

geom_dist_fct(1:70)
create_dist_vec(geom_dist_fct, max.dist = 70)

Function to simulate a single hospital bed trajectory

Description

Simulates the occupation of bed and incidence of HAIs of a single bed. Length of HAI is assumed to be additive to length of stay without HAI.

Usage

create_patient_history_add(X_los_dist, X_loi_dist, I, steps)

Arguments

Value

data frame with following columns

• pat_nbr - sequential patient number

• hai_nbr - sequential HAI number

• X_los - predicted total length of stay for patient on current day

• X_los_wo_hai -

• X_loi - total length of current HAI

• X_loi_tot - added total lengths of all HAIs up to day

• A_los - length of stay up to day

• X_lnint - length of stay after acquiring first HAI

Examples

example.dist <- create_dist_vec(function(x) dpois(x-1, 7), max.dist = 70)
example.dist.los <- create_dist_vec(function(x) dpois(x-1, lambda = 12),
                                    max.dist = 70)
bed_hist <- create_patient_history_add(example.dist.los, example.dist, I = 0.08, 1000)
tail(bed_hist)

Calculate empirical probability mass function for a discrete positive distribution starting at 1

Description

Calculate empirical probability mass function for a discrete positive distribution starting at 1

Usage

epmf(values)

Arguments

Value

vector of probabilities for epmf for the range 1:length(values)

Examples

# generate random sample of independent draws from Poisson distribution
x <- rpois(200,4)
# calculate empirical probability mass function and true probability mass function
y.emp  <- epmf(x)
y.theo <- dpois(1:max(x), 4)
plot(y.emp)
points(y.theo, col = "red")

Function to simulate PPS and data and calculate a number of estimators

Description

Function to simulate PPS and data and calculate a number of estimators

Usage

generate_I_fast(n.sample, P, dist.X.loi, data.theo = NULL,
  dist.X.los = NA, one.factor.loi = 1, one.factor.los = 1)

Arguments

Value

data frame with following columns

• n - number of patients sampled

• n.noso - number of HAIs

• P.hat - estimate of prevalence P

• I.hat - estimate of incidence rate I

• I.pp.hat - estimate of incidence proportion per admission I.pp

• x.loi.hat - estimate of x.loi

• x.los.hat - estimate of x.los

• method - name of the method

and rows for the estimators gren, rear, pps.median, pps.mean, pps.mixed, rhame.theo, L.full (for a description of the estimators see vignette).

Examples

example.dist <- create_dist_vec(function(x) dpois(x-1, 7), max.dist = 70)
generate_I_fast(200, P = 0.05, example.dist )

Probability mass function for a geometric distribution shifted by one and resulting expected value 8

Description

Probability mass function for a geometric distribution shifted by one and resulting expected value 8

Usage

geom_dist_fct(x)

Arguments

Examples

plot(geom_dist_fct(1:100)) 

Calculate length-biased distribution from discrete length-unbiased distribution starting at 1

Description

Calculate length-biased distribution from discrete length-unbiased distribution starting at 1

Usage

length_biased_dist(dist)

Arguments

Value

vector of probabilities of transformed distribution

Examples

# geometric distribution starting in 1 and cutoff at 70 with mean at about 8.
geom.dist <- create_dist_vec(geom_dist_fct, max.dist = 70)
# calculate mean
sum(1:length(geom.dist)*geom.dist)
# plot original distribution
plot(geom.dist)
geom.dist.lb <- length_biased_dist(geom.dist)
# plot length biased distribution
plot(geom.dist.lb)

Calculate mean of length-unbiased distribution from discrete length-biased distribution starting at 1

Description

Calculate mean of length-unbiased distribution from discrete length-biased distribution starting at 1

Usage

length_unbiased_mean(dist)

Arguments

Value

mean of length-unbiased distribution

Examples

# geometric distribution starting in 1 and cutoff at 70 with mean at about 8.
geom.dist <- create_dist_vec(geom_dist_fct, max.dist = 70)
# calculate mean of distribution
sum(1:length(geom.dist)*geom.dist)
# create length-biased distribution in same format
geom.dist.lb <- length_biased_dist(geom.dist)

# recalculate mean of original distribution based on length-biased distribution
length_unbiased_mean(geom.dist.lb)

Calculate a monotone probability mass function estimate

Description

using a rearrangement or a Grenander estimator as described in Jankoswski, Wellner, 2009 <doi:10.1214/09-EJS526>

Usage

monotone_smoother(values, method = "rear", range = c(1, max(values)))

Arguments

Value

vector of estimated pmf (support of distribution is by default assumed to be min(values):max(values) )

Examples

# generate sample from geometric distribution
A <- rgeom(50, 0.2)
# plot empirical probability mass function
plot(epmf(A))
dist.A.gren <- monotone_smoother(A, method = "gren")
# plot estimated probability mass function
points(dist.A.gren, col = "red")

Probability mass function for a Poisson distribution shifted by one and resulting expected value 8

Description

Probability mass function for a Poisson distribution shifted by one and resulting expected value 8

Usage

pois_dist_fct(x)

Arguments

Examples

plot(pois_dist_fct(1:100))

Calculate theoretical values like x.los, x.loi and other characteristics of the patient population

Description

Calculate theoretical values like x.los, x.loi and other characteristics of the patient population

Usage

simulate_incidence_stats(hospital, steps = 365 * 10000,
  n.sim.pat = 5000)

Arguments

Value

list with following components

• x.los - average length of stay x_los

• x.loi - average length of infection x_loi

• x.los.noso.only - average length of stay for patients with HAI

• x.los.wo.noso - average length of stay for patients discounting time with HAI

• I - theoretical incidence rate per patient day

• I.pp - list of theoretical incidences for patient types

• patient.stats - list with 'x.los' and 'x.loi' for different patient types

• patient.risk.times - list of patient days at risk for different patient types

Examples

pat.1 <- list(dist.X.los = create_dist_vec(
                               function(x) dpois(x-1, lambda = 12), 70),
I.p = 0.008,
dist.X.loi = create_dist_vec(function(x) dpois(x-1, lambda = 10), 70))

pat.2 <- list(dist.X.los = 
                create_dist_vec(function(x) dpois(x-1, lambda = 10), 70),
              I.p = 0.02,
              dist.X.loi = 
                create_dist_vec(function(x) dpois(x-1, lambda = 7), 70))

patient.list <- list(pat.1, pat.2)


# define distribution of patients
pat.1.prob <- 0.4; pat.2.prob <- 0.6
pat.dist.hosp <- c(pat.1.prob, pat.2.prob)
hospital.1 <- list(inc.factor = 1,
                   pat.dist = pat.dist.hosp,
                   patient.list = patient.list)
data.pps <- simulate_pps_data(n.sample=1000, steps=200, hospital=hospital.1) 
data.inc.theo <- simulate_incidence_stats(hospital.1, 365 * 1000)
# gives incidence rate I
data.inc.theo$I
# gives incidence proportion per admission
data.inc.theo$I.pp

Function to calculate theoretical value for x.loi and I

Description

Function to calculate theoretical value for x.loi and I

Usage

simulate_incidence_stats_fast(P, dist.X.loi, dist.X.los = NA)

Arguments

Value

list with following components

• x.loi - average length of infection

• x.los - average length of stay

• I - theoretical incidence rate per patient day

• I.pp - theoretical incidence proportion per admission

Examples

example.dist <- create_dist_vec(function(x) dpois(x-1, 7), 70)
data.fast.inc.theo <- simulate_incidence_stats_fast(P=0.05, dist.X.loi = example.dist)
data.fast.inc.theo$x.loi
data.fast.inc.theo$I

Function to simulate PPS data

Description

Simulates PPS data for a prespecified hospital according to a steady state model of incidence ( see vignette "Overview of prevtoinc-Package" for details.)

Usage

simulate_pps_data(n.sample, steps, hospital)

Arguments

Value

data frame with following columns

• A.loi - length of infection up to PPS

• L.loi - total length of infection

• A.los - length of stay up to PPS

• L.los - total length of stay

• patient.type - patient type

Examples

pat.1 <- list(dist.X.los = 
                   create_dist_vec(function(x) dpois(x-1, lambda = 12), 70),
              I.p = 0.008,
              dist.X.loi = 
                   create_dist_vec(function(x) dpois(x-1, lambda = 10), 70))

pat.2 <- list(dist.X.los = 
                   create_dist_vec(function(x) dpois(x-1, lambda = 10), 70),
              I.p = 0.02,
              dist.X.loi =
                   create_dist_vec(function(x) dpois(x-1, lambda = 7), 70))

patient.list <- list(pat.1, pat.2)


# define distribution of patients
pat.1.prob <- 0.4; pat.2.prob <- 0.6
pat.dist.hosp <- c(pat.1.prob, pat.2.prob)
hospital.1 <- list(inc.factor = 1,
                   pat.dist = pat.dist.hosp,
                   patient.list = patient.list)
data.pps <- simulate_pps_data(n.sample=1000, steps=200, hospital=hospital.1)                    

Faster method to generate data for PPS with only length of nosocomial infections as output

Description

The function 'simulate_pps_fast' can be used to generate PPS data. This functions simulates a PPS on the basis of a given prevalence 'P' using a vector of probabilities 'dist.X.loi' for the values 1:length(dist.X.loi) of X.loi. It directly samples the time of infection up to date based on 'dist.X.loi'. Optionally, the length of stay is sampled independently ( treating the marginal distributions of length of stay and length of infection as independent by assumption) using 'dist.X.los' which is in the same format as 'dist.X.loi'. Because of this non-joint sampling rows should not be interpreted as individual patients.

Usage

simulate_pps_fast(n.sample, P, dist.X.loi, dist.X.los = NA,
  one.factor.loi = 1, one.factor.los = 1)

Arguments

Value

data frame with a row for a each simulated patient and the following columns

• A.loi - length of infection up to PPS

• L.loi - total length of infection

• A.los - length of stay up to PPS

• L.los - total length of stay

• patient.type - patient type (fixed to 1 for fast method)

Examples

example.dist <- create_dist_vec(function(x) dpois(x-1, 7), 70)
data.pps.fast <- simulate_pps_fast(n.sample=5000,
                                  P=0.05,
                                  dist.X.loi = example.dist)
head(data.pps.fast)