Antigenicity Accelerated Stability Data

Description

An example dataset containing antigenicity concentration data at different temperatures over a period of up to 407 days. Two points over 180 days are to be used for validation instead of fitting.

Usage

data(antigenicity)

Format

An object of class "data.frame" with 56 rows and 6 variables

time

Number of days in years for which the datapoints are gathered.

Celsius

The temperature in celsius.

K

The temperature in Kelvin.

conc

The concentration at a time.

N.days

Number of days for which the datapoints are gathered.

validA

Whether the data point is to be used for validation or fitting.

Temperature Excursion

Description

Predict a temperature excursion for a product.

Usage

excursion(
  step1_down_object,
  temp_changes,
  time_changes,
  CI = TRUE,
  PI = TRUE,
  draw = 10000,
  confidence_interval = 0.95,
  intercept = NULL,
  ribbon = TRUE,
  xname = NULL,
  yname = NULL,
  plot_simulations = FALSE
)

Arguments

Details

Use the output from step1.down to run a temperature excursion prediction.

Value

An SB class object, a list including the following elements:

• prediction - A data frame containing the predictions with the confidence and prediction intervals.

• simulations - Matrix of the simulations.

• excursion plot - A plot with predictions and statistical intervals.

• user_parameters - List of users input parameters which is utilised by other functions in the package.

Examples

#load antigenicity
data(antigenicity)

#run step1.down fit
fit1 <- step1_down(data = antigenicity, y = "conc", .time = "time",
 C = "Celsius", max_time_pred = 3)

#run excursion function with fixed intercept.
excursion <- excursion(step1_down_object = fit1,
                       temp_changes = c(5,15,10),
                       time_changes = c(0.5,1.5,3),
                       CI = TRUE, PI = TRUE, draw = 4000,
                       confidence_interval = 0.95,
                       intercept = 80,
                       xname = "Time in years", yname = "Concentration",
                       ribbon = TRUE, plot_simulations = TRUE)

excursion$excursion_plot

Potency Accelerated Stability Data

Description

An example dataset containing potency data at different temperatures..

Usage

data(potency)

Format

An object of class "data.frame" with 78 rows and 3 variables

Time

Time for which the datapoints are gathered.

Potency

Measured potency at a time.

Celsius

The temperature in celsius.

Step1 Down Model

Description

Fit the one-step Šesták–Berggren kinetic model.

Usage

step1_down(
  data,
  y,
  .time,
  K = NULL,
  C = NULL,
  validation = NULL,
  draw = 10000,
  parms = NULL,
  temp_pred_C = NULL,
  max_time_pred = NULL,
  confidence_interval = 0.95,
  by = 101,
  reparameterisation = FALSE,
  zero_order = FALSE,
  ...
)

Arguments

Details

Fit the one-step Šesták–Berggren kinetic (non-linear) model using accelerated stability data that has been stored in an R data frame. Additionally, predictions of the mean at each tested temperature are returned, including associated confidence and prediction intervals, which can be subsequently visualised with step1_plot_pred(), step1_plot_CI(), step1_plot_PI() and step1_plot_T(). Kinetic parameters (k1, k2 and, if used, k3) are retained in the model even if one or more of these parameters turn out to be non-significant. Further arguments relating to model fitting, such as setting lower bounds for one or more model parameters, may be passed.

Value

An SB class object, a list including the following elements:

• fit - The non-linear fit.

• data - The data set.

• prediction - A data frame containing the predictions with the confidence and prediction intervals.

• user_parameters - List of users input parameters which is utilised by other functions in the package.

• sample_coefficients - A matrix containing the coefficients sampled during bootstrapping.

Examples

#load antigenicity and potency data.
data(antigenicity)
data(potency)

#Basic use of the step1_down function with C column defined.
fit1 <- step1_down(data = antigenicity, y = "conc", .time = "time", C = "Celsius", draw = 5000)

#Basic use of the step1_down function with K column defined & Validation data segmented out.
fit2 <- step1_down(data = antigenicity, y = "conc", .time = "time", K = "K",
validation = "validA", draw = 5000)

#When zero_order = FALSE, the output suggests using zero_order = TRUE for Potency dataset.
fit3 <- step1_down(data = potency, y = "Potency", .time = "Time",C = "Celsius",
  reparameterisation = FALSE, zero_order = TRUE, draw = 5000)

#reparameterisation is TRUE.
fit4 <- step1_down(data = antigenicity, y = "conc", .time = "time",C = "Celsius",
  reparameterisation = TRUE, draw = 5000)

#Use a custom lower bound for k1 (default is 0).
fit5 <- step1_down(data = potency, y = "Potency", .time = "Time",C = "Celsius",
  reparameterisation = TRUE, zero_order = TRUE, draw = 5000, lower = c(-Inf, 0, 0))

Basic version Step1 Down Model

Description

Quickly fit the one-step Šesták–Berggren kinetic model.

Usage

step1_down_basic(
  data,
  y,
  .time,
  K = NULL,
  C = NULL,
  validation = NULL,
  parms = NULL,
  reparameterisation = FALSE,
  zero_order = FALSE,
  ...
)

Arguments

Details

Fit the one-step Šesták–Berggren kinetic (non-linear) model using accelerated stability data that has been stored in an R data frame. Only the model fit object is returned and a summary of the model fit is printed in the console, allowing for more rapid testing than step1_down(). Kinetic parameters (k1, k2 and, if used, k3) are retained in the model even if one or more of these parameters turn out to be non-significant. Further arguments relating to model fitting, such as setting lower bounds for one or more model parameters, may be passed.

Value

The fit object

Examples

#load antigenicity and potency data.
data(antigenicity)
data(potency)

#Use of the step1_down_basic function with C column defined.
fit1 <- step1_down_basic(data = antigenicity, y = "conc", .time = "time", C = "Celsius")

#Basic use of the step1_down_basic function with K column defined & Validation data segmented out.
fit2 <- step1_down_basic(data = antigenicity, y = "conc", .time = "time", K = "K",
validation = "validA")

#When zero_order = FALSE, the output suggests using zero_order = TRUE for Potency dataset.
fit3 <- step1_down_basic(data = potency, y = "Potency", .time = "Time",C = "Celsius",
  reparameterisation = FALSE, zero_order = TRUE)

#reparameterisation is TRUE.
fit4 <- step1_down_basic(data = antigenicity, y = "conc", .time = "time",C = "Celsius",
  reparameterisation = TRUE)

#Use a custom lower bound for k1 (default is 0).
fit5 <- step1_down_basic(data = potency, y = "Potency", .time = "Time", C = "Celsius",
  reparameterisation = TRUE, zero_order = TRUE, lower = c(-Inf, 0, 0))

Step1 Down Model Root Mean Square Error Calculation

Description

Calculate Root Mean Square Error (RMSE) for the one-step Šesták–Berggren kinetic model.

Usage

step1_down_rmse(
  data,
  y,
  .time,
  K = NULL,
  C = NULL,
  parms,
  reparameterisation = FALSE
)

Arguments

Details

Calculate RMSE for the one-step Šesták–Berggren kinetic (non-linear) model using user provided parameters.

Value

A data frame containing one row for each RMSE calculation

Examples

#load antigenicity and potency data.
data(antigenicity)
data(potency)

#Basic use of the step1_down_rmse function with C column defined.
rmse1 <- step1_down_rmse(data = antigenicity, y = "conc", .time = "time",
 C = "Celsius", parms = list(c0 = c(96,98,100), k1 = c(42,45),
  k2 = c(12000,12500), k3 = c(8,9,10)))

#Basic use of the step1_down_rmse function with K column defined.
rmse2 <- step1_down_rmse(data = antigenicity, y = "conc", .time = "time",
 K = "K", parms = list(c0 = c(98), k1 = c(42,45), k2 = c(12500), k3 = c(8,9)))

#reparameterisation is TRUE.
rmse3 <- step1_down_rmse(data = antigenicity, y = "conc", .time = "time",
 C = "Celsius", parms = list(c0 = c(100,95), k1 = c(2,2.5), k2 = c(12000,13000),
  k3 = c(9,10)), reparameterisation = TRUE)

Plot Confidence Intervals

Description

Plot the stability data and visualise the predictions with confidence intervals.

Usage

step1_plot_CI(
  step1_down_object,
  xname = NULL,
  yname = NULL,
  xlim = NULL,
  ylim = NULL,
  ribbon = FALSE
)

Arguments

Details

Use the fit object obtained from the step1.down function to plot the data and visualise the predictions with confidence intervals applied. There is an option to view the confidence intervals as a ribbon. The confidence interval value is chosen in the step1.down function.

Value

Plot of stability data with prediction curves and confidence intervals.

Examples

#Load antigenciity data
data(antigenicity)

#Run step1.down fit
fit1 <- step1_down(data = antigenicity, y = "conc", .time = "time",
 C = "Celsius", max_time_pred = 3, confidence_interval = 0.9, validation = "validA")

#Plot raw data with prediction curves and confidence intervals.
step1_plot_CI(step1_down_object = fit1, xlim = NULL, ylim = NULL,
 xname = "Time (Years)", yname = "Concentration", ribbon = TRUE)

#Plot raw data with prediction curves and confidence intervals.
#Also limit x-axis to values between 0 and 1.5 and limit y-axis to values between 0 and 105.
step1_plot_CI(step1_down_object = fit1, xlim = c(0,1.5), ylim = c(0,105),
 xname = "Time (Years)", yname = "Concentration", ribbon = TRUE)

Plot Prediction Intervals

Description

Plot the stability data and visualise the predictions with prediction intervals.

Usage

step1_plot_PI(
  step1_down_object,
  xname = NULL,
  yname = NULL,
  xlim = NULL,
  ylim = NULL,
  ribbon = FALSE
)

Arguments

Details

Use the fit object obtained from the step1.down function to plot the stability data and visualise the predictions with prediction intervals applied. There is an option to view the prediction intervals as a ribbon. The prediction interval value is chosen in the step1.down function.

Value

Plot of stability data with prediction curves and prediction intervals.

Examples

#Load antigenicity data
data(antigenicity)

#Run step1.down fit
fit1 <- step1_down(data = antigenicity, y = "conc", .time = "time",
 C = "Celsius", max_time_pred = 3)

#Plot raw data with prediction curves and prediction intervals.
step1_plot_PI(step1_down_object = fit1, xlim = NULL, ylim = NULL,
 xname = "Time (Years)", yname = "Concentration", ribbon = TRUE)

#Plot raw data with prediction curves and confidence intervals.
#Also limit x-axis to values between 0 and 1.5 and limit y-axis to values between 0 and 105.
step1_plot_PI(step1_down_object = fit1, xlim = c(0,1.5), ylim = c(0,105),
 xname = "Time (Years)", yname = "Concentration", ribbon = TRUE)

Focus on Temperature

Description

Plot the stability data and visualise the predictions with focus on one temperature.

Usage

step1_plot_T(
  step1_down_object,
  focus_T = NULL,
  xname = NULL,
  yname = NULL,
  xlim = NULL,
  ylim = NULL,
  ribbon = FALSE
)

Arguments

Details

Plot the stability data and visualise the predictions focusing on one chosen temperature with confidence and prediction intervals.

Value

ggplot2 object with focus on chosen temperature.

Examples

#Load potency data
data(potency)

#Run step1_down fit
fit1 <- step1_down(data = potency, y = "Potency", .time = "Time",
 C = "Celsius", zero_order = TRUE)

#Plot raw data with prediction curves with focus on temperature in dataset.
#Also limit x-axis to values between 0 and 10 and limit y-axis to values between 0 and 12.
step1_plot_T(fit1, focus_T = 5,ribbon = TRUE, xlim = c(0,10), ylim = c(0,12),
 xname = "Time (Month)", yname = "Potency")

#Plot raw data with prediction curves with focus on temperature not in dataset.
#Also limit x-axis to values between 0 and 10 and limit y-axis to values between 0 and 12.
step1_plot_T(fit1, focus_T = -10,ribbon = TRUE, xlim = c(0,10), ylim = c(0,12),
 xname = "Time (Months)", yname = "Potency")

Plot Stability Data

Description

Plot raw accelerated stability data.

Usage

step1_plot_desc(
  data,
  y,
  .time,
  K = NULL,
  C = NULL,
  validation = NULL,
  xname = NULL,
  yname = NULL,
  xlim = NULL,
  ylim = NULL
)

Arguments

Details

Plot the raw accelerated stability data by selecting the columns - response, time and temperature.

Value

Plot of raw accelerated stability data.

Examples

#Load example datasets
data(antigenicity)
data(potency)

step1_plot_desc(data=antigenicity, y="conc", .time="time", C = "Celsius")

step1_plot_desc(data=potency, y="Potency", .time="Time", C = "Celsius", xlim=c(0,10), ylim=c(0,12))

Create Diagnostic Plots

Description

Generate residual diagnostic plots from a step1_down fit.

Usage

step1_plot_diagnostic(step1_down_object, bins = 7, residuals = "classic")

Arguments

Details

Use the fit object obtained from the step1_down function to plot the residual diagnostic plots, assess the quality of fit and search for anomalies. Change the type of Residuals assessed. Plots created are: Residuals Histogram, QQ Plot of Residuals, Observed Vs Predicted results, Residuals Vs Predicted results and Residuals By Time.

Value

A list containing the five ggplot2 plots.

Examples

#load antigenicity data
data(antigenicity)

#run step1_down fit
fit1 <- step1_down(data = antigenicity, y = "conc", .time = "time",
 C = "Celsius", max_time_pred = 3)

#plot diagnostic plots to asses the fit
step1_plot_diagnostic(fit1)

Plot Model Predictions

Description

Plot the stability data and visualise the predictions.

Usage

step1_plot_pred(
  step1_down_object,
  xname = NULL,
  yname = NULL,
  xlim = NULL,
  ylim = NULL
)

Arguments

Details

Use the fit object from the step1.down function to plot the accelerated stability data and visualise the predictions.

Value

Plot of accelerated stability data with prediction curves.

Examples

#Load antigenicity data
data(antigenicity)

fit1 <- step1_down(data = antigenicity, y = "conc", .time = "time",
 C = "Celsius", max_time_pred = 3)

step1_plot_pred(step1_down_object = fit1, xlim = c(0,1.5), ylim = c(0,105),
 xname = "Time (Years)", yname = "Concentration")

Sample the Multivariate t Distribution

Description

Take a selected number of samples from the multivariate t distribution (mvt).

Usage

step1_sample_mvt(
  data,
  y,
  .time,
  K = NULL,
  C = NULL,
  validation = NULL,
  draw,
  parms = NULL,
  reparameterisation = FALSE,
  zero_order = FALSE,
  ...
)

Arguments

Details

Using the provided data the function creates a fit of the Šesták–Berggren kinetic model and then draws a selected number of samples from the mvt of the model parameters.

Value

A matrix containing parameter draws from the mvt distribution.

Examples

#load antigenicity data.
data(antigenicity)

#Basic use of the step1_sample_mvt function with C column defined and 1000 draws.
sample1 <- step1_sample_mvt(data = antigenicity, y = "conc", .time = "time",
 C = "Celsius", draw = 1000)

#Basic use of the step1_sample_mvt function with K column defined and 50000 draws
sample2 <- step1_sample_mvt(data = antigenicity, y = "conc", .time = "time",
 K = "K", draw = 50000)

#reparameterisation is TRUE and 10000 draws.
sample3 <- step1_sample_mvt(data = antigenicity, y = "conc", .time = "time",
C = "Celsius", reparameterisation = TRUE, draw = 10000)