Logistic Regression in Case-Control study using – A

statistical tool

Satish Gupta

What is R?

The R statistical programming language is a free open

source package.

The language is very powerful for writing programs.

Many statistical functions are already built in.

Contributed packages expand the functionality to

cutting edge research.

Getting Started

Go to www.r-project.org

Downloads: CRAN (Comprehensive R Archive

Network)

Set your Mirror: location close to you.

Select Windows 95 or later, MacOS or UNIX

platforms

Getting Started

Basic operators and calculations

Comparison operators equal: == not equal: != greater/less than: > < greater/less than or equal: >= <=

Example: 1 == 1 # Returns TRUE

Basic operators and calculationsLogical operators AND: &

x <- 1:10; y <- 10:1  # Creates the sample vectors 'x' and 'y'.

x > y & x > 5  # Returns TRUE where both comparisons return TRUE.

OR: |

x == y | x != y # Returns TRUE where at least one comparison is TRUE. 

NOT: !

!x > y  # The '!' sign returns the negation (opposite) of a logical vector. 

Basic operators and calculationsCalculations Four basic arithmetic functions: addition, subtraction,

multiplication and division

1 + 1; 1 - 1; 1 * 1; 1 / 1 # Returns results of basic arithmetic calculations. 

Calculations on vectors

x <- 1:10; sum(x); mean(x), sd(x); sqrt(x) # Calculates for the vector x its sum, mean, standard deviation  and square root.  

x <- 1:10; y <- 1:10; x + y # Calculates the sum for each element in the vectors x and y.

R-Graphics

R provides comprehensive graphics utilities for visualizing and exploring scientific data. It includes:

Scatter plots Line plots Bar plots Pie charts Heatmaps Venn diagrams Density plots Box plots

Data handling in R Load data: mydata = read.csv(“/path/mydata.csv”) See data on screen: data(mydata) See top part of data: head(mydata) Specific number of rows and column of data: mydata[1:10,1:3] To get a type of data: class(mydata) Changing class of data: newdata = as.matrix(mydata) Summary of data: summary(mydata) Selecting (KEEPING) variables (columns)

newdata = mydata[c(1,3:5)]

Data handling in R

Selecting observations

newdata= subset(mydata, age>=20 | age <10, select=c(ID, weight)

newdata= subset(mydata, sex==“Male” & age >25, select=weight:income)

Excluding (DROPPING) variables (columns)

newdata = mydata[c(-3,-5)]

mydata$v3 = NULL

R-Library There are many tools defined as “package” are present in R for

different kind of analysis including data from genetics and genomics.

Depending upon the availability of library, it can be downloaded from two sources

Using CRAN (Comprehensive R Archive Network) as:

install.packages(“package_name”)

Using Bioconductor as:

source("http://bioconductor.org/biocLite.R")

biocLite(“package_name”)

R-Library

To load a package,

library() #Lists all libraries/packages that are available on a system.

library(genetics) #Package for genetics data analysis

library(help=genetics) #Lists all functions/objects of “genetics”

package

?function #Opens documentation of a function

What is Logistic Regression?

Logistic regression describes the relationship between a dichotomous response variable and a set of explanatory variables.

Logistic regression is often used because the relationship between the DV (a discrete variable) and a predictor is non-linear.

A General Model:

Logistic Regression

JJdisease

diseasedisease XX

p

pp

110)

1log()logit(

Where:

pdisease is the probability that an individual has a particular disease.

β0 is the intercept

β1, β2 … βJ are the coefficients (effects) of genetic factors

X1, X2 … XJ are the variables of genetic factors

Assumptions

Logistic regression does not make any assumptions of normality, linearity, and homogeneity of variance for the independent variables.

Because it does not impose these requirements, it is preferred to discriminant analysis when the data does not satisfy these assumptions.

Questions ??

What is the relative importance of each predictor variable? How does each predictor variable affect the outcome? Does a predictor variable make the solution better or

worse or have no effect? Are there interactions among predictors?

Does adding interactions among predictors (continuous or categorical) improve the model?

What is the strength of association between the outcome variable and a set of predictors?

Often in model comparison you want non-significant differences so strength of association is reported for even non-significant effects.

Types of Logistic Regression Unconditional logistic regression

Conditional logistic regression

** Rule of thumbs

Use conditional logistic regression if matching has been done, and unconditional if there has been no matching.

When in doubt, use conditional because it always gives unbiased results. The unconditional method is said to overestimate the odds ratio if it is not appropriate.

Data FormatStatus Matset Se_Quartiles GPX1 GPX4 SEP15 TXN2

1 1 <60 CT TT AG AG

0 1 >60 – 70 CC CC GG GG

1 2 <60 TT CC AG AA

0 2 >70 – 80 CC CT GG GG

1 3 >80 CC CC AA AA

0 3 >60 – 70 CT TT GG GG

1 4 <60 CC CC AA AG

0 4 >70 – 80 TT TT GG GG

1 5 >80 CC CC AG AA

0 5 <60 CC CC GG GG

1 6 >70 – 80 CT TT AA AA

0 6 >80 CC CC GG AG

1 7 >60 – 70 TT CC AA AG

Data and Library loading

Load and use data in R (Using Lung cancer data from PLoS One 2013, 8(3):e59051).

lung = read.csv(“/path/lung.csv”, sep= “\t”, header = TRUE)

Load the library and use data for analysis

library(epicalc)

use(lung)

Data Analysis

Performing conditional logistic regression (Case vs. Control)

clogit_lung = clogit(Status ~ Se_Quartiles + strata(Matset), data = .data)

clogistic.display(clogit_lung)

  OR(95%CI) P(Wald's test) P(LR-test)

Quartiles: ref.=<60     <0.001

>60 – 70 0.4(0.15 – 1.09) 0.074  

>70 – 80 0.11(0.03 – 0.33) <0.001  

>80 0.10(0.03 – 0.34) <0.001  

Data Analysis

Performing conditional logistic regression (Case vs. Control),

clogit_lung = clogit(Status ~ GPX1+ strata(Matset), data = .data)

clogistic.display(clogit_lung)

  OR(95%CI) P(Wald's test) P(LR-test)

GPX1: ref.=CC     0.032

CT 0.44(0.22 – 0.86) 0.017  

TT 0.42(0.13 – 1.38) 0.151  

Data Analysis Performing conditional logistic regression (Case vs. Control),

clogit_lung = clogit(Status ~ Se_Quartiles + GPX1+ strata(Matset), data = .data)

clogistic.display(clogit_lung)

 

crude OR(95%CI)

adj. OR(95%CI)

P(Wald's test) P(LR-test)

Quartiles: ref.=<60       <0.001

>60 – 70 0.4(0.15 – 1.09) 0.32(0.11 – 0.96) 0.042  

>70 – 80 0.11(0.03 – 0.33) 0.09(0.02 – 0.3) <0.001  

>80 0.1(0.03 – 0.34) 0.05(0.01 – 0.23) <0.001  

       

GPX1:ref.=CC       0.006

CT 0.44(0.22 – 0.86) 0.26(0.11 – 0.65) 0.004  

TT 0.42(0.13 – 1.38) 0.44(0.09 – 2.18) 0.313  

Environmental Factor

Genetic Factor

Data Analysis

Performing unconditional logistic regression (Case vs. Control),

ulogit_lung = glm(Status ~ Se_Quartiles , family=binomial, data = .data)

logistic.display(ulogit_lung)

  OR(95%CI) P(Wald's test) P(LR-test)

Quartiles: ref.=<60     <0.001

>60 – 70 0.41 (0.17 – 1.02) 0.054  

>70 – 80 0.13 (0.05 – 0.34) <0.001  

>80 0.17 (0.07 – 0.42) <0.001  

Data Analysis

Performing unconditional logistic regression (Case vs. Control),

ulogit_lung = glm(Status ~ GPX1 , family=binomial, data = .data)

logistic.display(ulogit_lung)

  OR(95%CI) P(Wald's test) P(LR-test)

Quartiles: ref.=CC     0.034

CT 0.45 (0.24 – 0.85) 0.014  

TT 0.44 (0.14 – 1.36) 0.156  

Data Analysis Performing unconditional logistic regression (Case vs.

Control),

ulogit_lung = glm(Status ~ Se_Quartiles , family=binomial, data = .data)

logistic.display(ulogit_lung)

 crude

OR(95%CI)adj.

OR(95%CI) P(Wald's test) P(LR-test)

Quartiles: ref.=<60     <0.001

>60 – 70 0.41 (0.17 – 1.02) 0.43 (0.17 – 1.08) 0.074  

>70 – 80 0.13 (0.05 – 0.34) 0.13 (0.05 – 0.34) <0.001  

>80 0.17 (0.07 – 0.42) 0.15 (0.06 – 0.39) <0.001  

GPX1:ref.=CC 0.024

CT 0.45 (0.24 – 0.85) 0.40(0.20 – 0.80) 0.01

TT 0.44 (0.14 – 1.36) 0.42 (0.12 – 1.41) 0.161

Something More Changing the default reference

GPX1 = relevel(GPX1, ref = "TT")pack()

Saving the result

result = clogistic.display(clogit_lung)

write.csv(result$table, file=“path/result.csv“, sep = “\t”)

write.table(result$table, file=“path/result.xls“, sep = “\t”)

Summary: regression models

Regression models can be used to describe the average effect of predictors on outcomes in your data set.

They can tell how likely that the effect is just be due to chance.

They can look at each predictor “adjusting for” the others (estimating what would happen if all others were held constant.)

Thanks to,

Prof. Virasakdi Chongsuvivatwong

Epidemiology Unit,

Faculty of Medicine,

Prince of Songkla University, Thailand