Arterial pressure data of crossover design

Description

Data of a crossover experiment with three treatments to control arterial pressure: treatment A is a placebo, treatments B and C are 20 and 40 mg doses of a test drug. Thus, there were six three-period sequences: ABC, ACB, BCA, BAC, CAB and CBA, each one of them was applied to two individuals lasting six weeks each. Due to ethical reasons, there was no washout period between the treatments. In each period, 10 consecutive measurements of diastolic arterial pressure were taken: 30 and 15 minutes before, and 15, 30, 45, 60, 75, 90, 120 and 240 minutes after the administration of the treatment

Usage

Arterial

Format

A data frame with 360 rows and 5 columns:

Subject

The unique identifier of each of the patients

Period

The period of application of each treatment

Treatment

A is a placebo, treatments B and C are 20 and 40 mg doses of a test drug

Pressure

diastolic arterial pressure

Time

Measurement time

Source

Jones, B. and Kenward, M. G. (2015). Design and Analysis of Cross-Over Trials Third Edition. Chapman & Hall/CRC, Boca Raton

Run a GEE model for data from a crossover experiment

Description

Provides a GEE model for the data of a crossover design with S sequences of T periods. There must be one observation of each experimental unit in each period.

Usage

CrossGEE(
  response,
  period,
  treatment,
  id,
  carry,
  covar = NULL,
  data,
  family = gaussian(),
  correlation = "independence",
  formula = NULL,
  Mv = 1
)

Arguments

Value

QIC The QIC of the models: The model are fitted by geeglm

model The model fitted by geeglm.

Source

https://doi.org/10.1111/stan.12295

References

Cruz, N. A., López Pérez, L. A., & Melo, O. O. (2023). Analysis of cross-over experiments with count data in the presence of carry-over effects. Statistica Neerlandica, 77(4), 516-542.

Examples

data(Water)
model <- CrossGEE(response="LCC", covar=c("Age"), period="Period",
                  treatment = "Treatment", id="ID", carry="Carry_Agua",
                  family=gaussian(),correlation ="AR-M", Mv=1 ,data=Water)

model$QIC
model$model

## Aproximate p-values
(pvalues <- 2 * pnorm(abs(coef(summary(model$model))[,5]), lower.tail = FALSE))

summary(model$model)

Run a GEE model for data from a crossover experiment with repeated measures

Description

Provides a GEE model for the data of a crossover design with S sequences of T periods. There must be at least two observations of each experimental unit in each period.

Usage

CrossGEEKron(
  response,
  period,
  treatment,
  id,
  time,
  carry,
  covar = NULL,
  data,
  family = gaussian(),
  correlation = "independence",
  formula = NULL,
  tol = 1e-04,
  niter = 100,
  Mv
)

Arguments

Value

QIC The QIC of the model: The model are fitted by geeglm

model The model fitted by geeglm.

Within The estimated correlation matrix within the period with the structure determined by correlation.

Between The estimated correlation matrix between periods

Source

https://doi.org/10.1007/s00362-022-01391-z

References

Cruz, N.A., Melo, O.O. & Martinez, C.A. A correlation structure for the analysis of Gaussian and non-Gaussian responses in crossover experimental designs with repeated measures. Statistical Papers 65, 263–290 (2024)

Examples

data(Arterial)

carrydata <- createCarry(data=Arterial, treatment = "Treatment",
 period = "Period",id="Subject")

data <- carrydata$data
carry <- carrydata$carryover
model <- CrossGEEKron(response = "Pressure", treatment = "Treatment",
period = "Period", id="Subject", time="Time",
 carry=c("Carry_B","Carry_C"),data=data, correlation = "AR-M", Mv=1)

model$QIC
model$Within
model$Between
summary(model$model)

## Aproximate p-values for model
(pvalues <- 2 * pnorm(abs(coef(summary(model$model))[,5]), lower.tail = FALSE))

model2 <- CrossGEEKron(response = "Pressure", treatment = "Treatment",
 period = "Period", id="Subject", time="Time",
 carry=c("Carry_B","Carry_C"), data=data,
 correlation = "AR-M", Mv=1,formula=Pressure ~ Treatment+
 Period+ Carry_B+Carry_C)

model2$QIC
model2$Within
model2$Between
summary(model2$model)

Run a semi-parametric GEE model for data from a crossover experiment with repeated measures

Description

Provides a GEE model for the data of a crossover design with S sequences of T periods. There must be at least two observations of each experimental unit in each period. The effect of time within period and the possible carryover effects are modeled by means of splines.

Usage

CrossGEESP(
  response,
  period,
  treatment,
  id,
  time,
  carry,
  covar = NULL,
  data,
  family = gaussian,
  correlation = "independence",
  formula = NULL,
  tol = 1e-04,
  niter = 100,
  nodes = NULL,
  Mv = 1
)

Arguments

Value

QIC The QIC of the model: The model are fitted by geeglm

model The model fitted by geeglm.

graphs The graphs estimated by splines. In position 1 the graph of the effect of time appears and from then on, it appears one for each carryover effect declared in the carry option. The graphs are built with ggplot2, therefore they allow manipulation of axes and other graphic parameters of that library.

Source

https://doi.org/10.1177/09622802231158736

References

Cruz Gutierrez NA, Melo OO, Martinez CA. Semiparametric generalized estimating equations for repeated measurements in cross-over designs. Statistical Methods in Medical Research, 2023;32(5):1033-1050.

Examples

data(Arterial)

carrydata <- createCarry(data=Arterial, treatment = "Treatment",
                         period = "Period",id="Subject", carrySimple = FALSE)
data <- carrydata$data
carry <- carrydata$carryover
model1 <- CrossGEESP(response = "Pressure", treatment = "Treatment",
                    period = "Period", id="Subject", time="Time",
                    carry=carrydata$carryover,data=data,
                    correlation = "exchangeable")


model2 <- CrossGEESP(response = "Pressure", treatment = "Treatment",
                     period = "Period", id="Subject", time="Time",
                     carry=carrydata$carryover,data=data, correlation = "AR-M")


model1$QIC
model2$QIC
summary(model1$model)
summary(model2$model)

## Aproximate p-values for model 2

(pvalues <- 2 * pnorm(abs(coef(summary(model2$model))[,5]), lower.tail = FALSE))

model1$graph[[1]]
model1$graph[[2]]
plot <- model1$graph[[1]] + ggplot2::xlab("Time in minutes")+
ggplot2::ylab("Change in systolic blood pressure")
plot

Water student data of crossover design

Description

A pilot study to investigate the impact of providing supplementary drinking water on the cognitive performance of pupils of two school grades (5 and 6) in water-scarce schools in rural Mali. 47 students were assigned to take the control treatment (normal conditions) on the first day and receive the treatment (controlled hydration) on the second day. 60 received the treatments in reverse (Hydration the first day and control the second day). One part of this test assesses visual attention. This test assesses visual attention. Pupils were given a grid containing target letters randomly dispersed among non-target letters and were given one minute to cross out as many target letters as possible. Scores were calculated by subtracting the number of non-target letters identified from the number of target letters identified; the maximum test score was 38.

Usage

Water

Format

A data frame with 214 rows and 10 columns:

ID

The unique identifier of each of the students

Age

The age in years of each of the students

LCS

Letter Cancel incorrect (raw score)

LCC

Letter Cancel correct (raw score)

LCI

Letter Cancel score (LCC-LCI)

sex

f=female, 1=male

school

school indicator A or B

Treatment

Condition indicator 0=Control 1=Water

Period

date of visit

Carry_Agua

Carry indicator 0=First period, 1=Water in the first period, -1 = Control in the first period

Source

<https://journals.plos.org/plosone/article/authors?id=10.1371/journal.pone.0210568>

Quasi Information Criterion

Description

Function for calculating the quasi-likelihood under the independence model information criterion (QIC), quasi-likelihood, correlation information criterion (CIC), and corrected QIC for one or several fitted geeglm model object from the geepack package.

Usage

computeqic(object)

Arguments

Details

QIC is used to select a correlation structure. The QICu is used to compare models that have the same working correlation matrix and the same quasi-likelihood form but different mean specifications. CIC has been suggested as a more robust alternative to QIC when the model for the mean may not fit the data very well and when models with different correlation structures are compared.

Models with smaller values of QIC, CIC, QICu, or QICC are preferred.

Value

A vector or matrix with the QIC, QICu, quasi likelihood, CIC, the number of mean effect parameters, and the corrected QIC for each GEE object

Author(s)

Alirio Cruz nelson-alirio.cruz@uib.es, Claus Ekstrom claus@rprimer.dk, Brian McLoone bmcloone@pdx.edu and Steven Orzack orzack@freshpond.org

References

Pan, W. (2001). Akaike's information criterion in generalized estimating equations. Biometrics, 57, 120-125. Hardin, J.W. and Hilbe, J.M. (2012). Generalized Estimating Equations, 2nd Edition, Chapman and Hall/CRC: New York.

Hin, L.-Y. and Wang, Y-G. (2009). Working-correlation-structure identification in generalized estimating equations, Statistics in Medicine 28: generalized estimating equations, Statistics in Medicine 28: 642-658. Thall, P.F. and Vail, S.C. (1990). Covariance Models for Longitudinal Count Data with Overdispersion. Biometrics, 46, 657-671.

Examples

library(gee)
data(Arterial)
fit <- gee(Pressure ~ Time + Treatment, id=Subject,
       data=Arterial, family=gaussian, corstr="AR-M")
computeqic(fit)

Add carryover dummy variables

Description

Create dummy variables associated with first-order carryover effect in a Crossover Design

Usage

createCarry(data, treatment, period, id, carrySimple = TRUE)

Arguments

Value

data A data frame with all the variables of the crossover experimental design and the carryover variables

carryover The new carryover variables

Examples

data(Water)
carryover <- createCarry(data=Water,
                         treatment = "Treatment", id = "ID",
                         period = "Period", carrySimple = FALSE)
carryover$carryover
carryover$data