parfm (version 2.7.7)

mastitis: Correlated infection times in four cow udder quarters

Description

Mastitis, the infection of the udder, is economically the most important disease in the dairy sector of the western world. Mastitis can be caused by many organisms, most of them bacteria, such as Escherichia coli, Streptococcus uberis, and Staphylococcus aureus. Since each udder quarter is separated from the three other quarters, one quarter might be infected with the other quarters free of infection.

In an extensive study, 100 cows are followed up for infections. The objective of this observational study is to estimate the incidence of the different organisms causing mastitis in the dairy cattle population in Flanders. Also the correlation between the infection times of the four udder quarters of a cow is an important parameter to take preventive measures against mastitis. With high correlation, a lot of attention should be given to the uninfected udder quarters of a cow that has an infected quarter. From each quarter, a milk sample is taken monthly and is screened for the presence of different bacteria.

We model the time to infection with any bacteria, with the cow being the cluster and the quarter the experimental unit within the cluster. Observations can be right-censored if no infection occurs before the end of the lactation period, which is roughly 300-350 days but different for every cow, or if the cow is lost to follow-up during the study, for example due to culling. Due to the periodic follow-up, udder quarters that experience an event are interval-censored with lowerbound the time of the last milk sample with a negative result and upperbound the time of the first milk sample with a positive result. In some examples, the midpoint (average of lowerbound and upperbound of the interval) is used for simplicity; in other examples the interval-censored nature of the data is taken into account.

In the analysis, two types of covariates are considered. Cow level covariates take the same value for every udder quarter of the cow (e.g., number of calvings or parity). Several studies have shown that prevalence as well as incidence of intramammary infections increase with parity . Several hypotheses have been suggested to explain these findings, e.g., teat end condition deteriorates with increasing parity. Because the teat end is a physical barrier that prevents organisms from invading the udder, impaired teat ends make the udder more vulnerable for intramammary infections. For simplicity, parity is dichotomised into primiparous cows (heifer=1) and multiparous cows (heifer=0). Udder quarter level covariates change within the cow (e.g., position of the udder quarter, front or rear). The difference in teat end condition between front and rear quarters has also been put forward to explain the difference in infection status.

Usage

data(mastitis)

Format

A dataframe containing 400 observations.

Cowid:

Cow's identifyier.

Lower:

Lower bound of time to infection (in days).

Upper:

Upper bound of time to infection (in days).

Midpoint:

Midpoint between Lower and Upper (in days).

Status:

Censored (0) or observed (1) event time.

Heifer:

Multiparous cow (0) or primiparous cow (1).

Quarter:

Tthe udder quarter (LF=Left-Front, LR=Left-Rear, RF=Right-Front, RR=Right-Rear).

References

Duchateau L, Janssen P (2008). The frailty model. Springer. New York: Springer--Verlag.

Examples

# \donttest{
data(mastitis)
head(mastitis)

mastitis$timeto <- as.numeric((mastitis$Midpoint * 4 / 365.25))


################################################################################
# Example 4.4: The gamma frailty model for the udder quarter infection data    #
# Duchateau and Janssen (2008, page 136)                                       #
################################################################################
modParfm <- parfm(Surv(timeto, Status) ~ Heifer,
                  cluster = "Cowid",
                  dist = "weibull",
                  frailty = "gamma",
                  data = mastitis)
modParfm


################################################################################
# Example 4.7 The inverse Gaussian frailty model for the udder quarter         #
# infection data                                                               #
# Duchateau and Janssen (2008, page 156)                                       #
################################################################################
mastitis <- data.frame(mastitis, 
                       timeto = as.numeric((mastitis$Midpoint * 4 / 365.25)))
modParfm <- parfm(Surv(timeto, Status) ~ Heifer,
                  cluster = "Cowid",
                  dist = "weibull",
                  frailty = "ingau",
                  data = mastitis)
modParfm


################################################################################
# Example 4.10 The positive stable frailty model for the udder quarter         #
# infection data                                                               #
# Duchateau and Janssen (2008, page 169)                                       #
################################################################################
mastitis <- data.frame(mastitis, 
                       timeto = as.numeric((mastitis$Midpoint * 4 / 365.25)))
modParfm <- parfm(Surv(timeto, Status) ~ Heifer,
                  cluster = "Cowid",
                  dist = "weibull",
                  frailty = "possta",
                  data = mastitis)
modParfm
# }