cells: Cellular Differentiation

In Fahrmeir: Data from the Book "Multivariate Statistical Modelling Based on Generalized Linear Models", First Edition, by Ludwig Fahrmeir and Gerhard Tutz

Description

The effect of two agents of immuno-activating ability that may induce cell differentiation was investigated.

Usage

data(cells)

Format

A data frame with 16 observations on the following 3 variables.

y

number of cells differentiating

TNF

dose of TNF, U/ml

IFN

dose of IFN, U/ml

Details

The effect of two agents of immuno-activating ability that may induce cell differentiation was investigated. As response variable the number of cells that exhibited markers after exposure was recorded. It is of interest if the agents TNF (tumor necrosis factor) and IFN (interferon) stimulate cell differentiation independently, or if there is a synergetic effect. 200 cells were examined at each dose combination.

Author(s)

Kjetil Halvorsen

Source

Ludwig Fahrmeir, Gerhard Tutz (1994): Multivariate Statistical Modelling Based on Generalized Linear Models. Springer Series in Statistics. Springer Verlag. New-York Berlin Heidelberg

Examples

str(cells)
cells.poisson <- glm(y~TNF+IFN+TNF:IFN, data=cells, 
                    family=poisson)
summary(cells.poisson)
confint(cells.poisson)
# Now we follow the book, example 2.6, page 51:
# there seems to be overdispersion?
cells.quasi <- glm(y~TNF+IFN+TNF:IFN, data=cells, 
                    family=quasipoisson)
summary(cells.quasi)
anova(cells.quasi)
confint(cells.quasi)
# We follow the book, example 2.7, page 56:
with(cells, tapply(y, factor(TNF), function(x) c(mean(x), var(x))))
# which might indicate the use of a negative binomial model

Example output

'data.frame':	16 obs. of  3 variables:
 $ y  : int  11 18 20 39 22 38 52 69 31 68 ...
 $ TNF: int  0 0 0 0 1 1 1 1 10 10 ...
 $ IFN: int  0 4 20 100 0 4 20 100 0 4 ...

Call:
glm(formula = y ~ TNF + IFN + TNF:IFN, family = poisson, data = cells)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.6824  -2.8179  -0.8222   1.9183   4.4728  

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept)  3.436e+00  6.377e-02  53.877  < 2e-16 ***
TNF          1.553e-02  8.308e-04  18.689  < 2e-16 ***
IFN          8.946e-03  9.669e-04   9.253  < 2e-16 ***
TNF:IFN     -5.670e-05  1.348e-05  -4.205 2.61e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 707.03  on 15  degrees of freedom
Residual deviance: 142.39  on 12  degrees of freedom
AIC: 243.69

Number of Fisher Scoring iterations: 4

Waiting for profiling to be done...
                    2.5 %        97.5 %
(Intercept)  3.308307e+00  3.558360e+00
TNF          1.390603e-02  1.716434e-02
IFN          7.043823e-03  1.083599e-02
TNF:IFN     -8.318686e-05 -3.031362e-05

Call:
glm(formula = y ~ TNF + IFN + TNF:IFN, family = quasipoisson, 
    data = cells)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-4.6824  -2.8179  -0.8222   1.9183   4.4728  

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  3.436e+00  2.184e-01  15.727 2.26e-09 ***
TNF          1.553e-02  2.846e-03   5.456 0.000146 ***
IFN          8.946e-03  3.312e-03   2.701 0.019273 *  
TNF:IFN     -5.670e-05  4.619e-05  -1.227 0.243176    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for quasipoisson family taken to be 11.73534)

    Null deviance: 707.03  on 15  degrees of freedom
Residual deviance: 142.39  on 12  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 4

Analysis of Deviance Table

Model: quasipoisson, link: log

Response: y

Terms added sequentially (first to last)


        Df Deviance Resid. Df Resid. Dev
NULL                       15     707.03
TNF      1   468.60        14     238.43
IFN      1    78.27        13     160.16
TNF:IFN  1    17.78        12     142.39
Waiting for profiling to be done...
                    2.5 %       97.5 %
(Intercept)  2.9786721160 3.838424e+00
TNF          0.0100046341 2.121871e-02
IFN          0.0023374841 1.540787e-02
TNF:IFN     -0.0001481632 3.358201e-05
$`0`
[1]  22.0000 143.3333

$`1`
[1]  45.2500 400.9167

$`10`
[1]   74.000 1608.667

$`100`
[1]  161.5 1655.0

Fahrmeir documentation built on May 2, 2019, 12:37 p.m.