1.
Understanding the Concept of
Contingency Table
By
Weam Banjar. DDS., MS in Clinical Research

2.
Overview
• Contingency tables, also called cross-tabs or two-way table are used in
statistics to summarize relationships between several categorical variables
• A special type of frequency table, where two variables are presented
simultaneously
• Data arrays containing counts of observations that are recorded in cross-
classification by a number of discrete factors predictors
• Contingency tables are summaries of response data where predictor
variables (exposure, confounder) are discrete factors or categorical
variables and where the response are counts

3.
Factors and Contingency Tables
• a categorical (discrete) variable taking a small number of values that
represent the levels of the factor.
• Examples:
• Gender: Two levels; 0= male ad 1= female
• Marital status: Five levels; 0= single, 1= married, 2= divorced, 3= widow, and 4=
separated
• Data description:
• Frequencies of factor levels and their combinations
• To assess whether factors are related

4.
Factors and Contingency Tables
• Data summary:
• Categorical data are often summarized by reporting the proportion or
percentage in each category
• Alternatively, a summary of the relative proportion (odds) in each
category might be calculated (relative to a baseline category)
• Testing:
• Assessing the relation between the factors could be achieved using
2 test.

5.
Factors and Contingency Tables
• Dependent variable:
• Outcome of interest
• What do you intend to measure?
• Independent variable:
• Exposure of interest
• What do you intend to investigate?
• Confounder:
• Any factors other than dependent and independent variables that
may influence the results

6.
Factors and Contingency Tables
• Example:
• A total of 30 subjects where enrolled; 20 male and 10 female, to
assess the effect of electronic smoking on development of
ginigivitis.
• Identify:
Dependent variable Development of gingivitis
Independent variable Electronic smoking use
Confounder Gender

7.
Outcome

8.
Exposure

9.
• Count: number of observation within the cell
• Row percentage:

10.
• Count: number of observation within the cell
• Row percentage:
• Column percentage:

11.
• Count: number of observation within the cell
• Row percentage
• Column percentage:
• Total percentage:

12.
Risk Comparison
By
Weam Banjar. DDS., MS in Clinical Research

13.
Absolute Risk
• Concept: The absolute risk of an event is the likelihood of occurrence of
that event in the population at risk.
• Calculation: The absolute risk of an event is estimated as the number of
persons who actually experience the event divided by the total number of
persons exposed to the risk of that event. This figure is usually expressed
as a percentage, though it can also be expressed in other ways, such as per
1,000 or per 100,000 persons in the population at risk. It can also be
expressed in terms of person-years of exposure to the risk factor.

14.
Absolute Risk
• Example:

15.
Absolute Risk
• Because 40 patients took venlafaxine and because 8 of them developed sexual
dysfunction, the absolute risk of sexual dysfunction with venlafaxine is 8/40, or
20.0%. Similarly, the absolute risk of developing sexual dysfunction with placebo
is 3/36, or 8.3%.
• 20.0% of patients who receive venlafaxine (as administered in this trial) and 8.3%
of those who receive placebo (as administered in this trial) can expect to
experience new-onset sexual dysfunction during the first 8 weeks of treatment.
Presumably, sexual dysfunction resulting from venlafaxine treatment involves
specific drug-related mechanisms, whereas sexual dysfunction with placebo
involves nocebo mechanisms, illness-related factors, or other causes.

16.
Absolute Risk (Risk Difference)
• The attributable risk is the risk of an event that is specifically due to the risk
factor of interest.
• It is estimated as the difference in the absolute risk (of the event of interest)
between persons exposed to the risk factor and persons not exposed to the
risk factor. It is usually expressed as a percentage.

17.
Attributable Risk (Risk Difference)
• Example:

18.
Attributable Risk (Risk Difference)
• The absolute risk of sexual dysfunction with venlafaxine is 8/40, or 20.0%.
• The absolute risk of developing sexual dysfunction with placebo is 3/36, or
8.3%.
• The risk of sexual dysfunction attributable specifically to venlafaxine is the
absolute risk of sexual dysfunction with venlafaxine minus that with placebo;
that is, 20.0% – 8.3%= 11.7%.

19.
Attributable Risk (Risk Difference)
• 20% of patients who receive venlafaxine (as administered in this trial) can
expect to develop sexual dysfunction. However, in only 11.7% of the
patients is the adverse event specifically attributable to venlafaxine; in the
remaining 8.3%, other causes are probably responsible (eg, nocebo
mechanisms, illness-related factors).

20.
Relative Risk
• The relative risk (RR) of an event is the likelihood of its occurrence after
exposure to a risk variable as compared with the likelihood of its occurrence
in a control or reference group.
• This measures how much more likely the event is to occur in one group
compared to another.

21.
Relative Risk
• The relative risk (RR) of an event is the likelihood of its occurrence after
exposure to a risk variable as compared with the likelihood of its occurrence
in a control or reference group.
• This measures how much more likely the event is to occur in one group
compared to another.

22.
Relative Risk

23.
Relative Risk
𝑹𝑹 =
𝐀/(𝑨 + 𝑩)
𝑪/(𝑪 + 𝑫)

24.
Relative Risk- Example
• A randomized controlled trial investigated mortality rates over a year for 300
patients with lung cancer. The first group received a new chemotherapy
treatment for lung cancer (New treatment) and the other the standard
chemotherapy treatment (Control treatment).

25.
Relative Risk- Example
• The relative risk is (Risk of dying in control group/ risk of dying in new
treatment group)= 0.25/0.1= 2.5
• This means that those in the control group were 2.5 times more likely to die
than those in the treatment group

26.
Relative Risk- Example

27.
Relative Risk- Example
• The absolute risk for sexual dysfunction with Tx= 0.2 (20.00%)
• The absolute risk for sexual dysfunction with placebo= 0.083 (8.33%)
• RR= 2.4

28.
Relative Risk- Example
• Vanlafaxine is associated with a more than double risk of sexual dysfunction
• The risk of sexual dysfunction with vanlafaxine is 2.4 times the placebo
• The risk of sexual dysfunction with venlafaxine is 240% that with placebo

29.
Odds Ratio
• A comparison of the odds of an event after exposure to a risk factor with the
odds of that event in a control or reference situation.
• 𝑂𝑅 =
A/𝐵
C/D

30.
Odds Ratio- Example

31.
Odds Ratio
• 𝑂𝑅 =
A/𝐵
C/D
=
8/32
3/33
=
0.25
0.09
=2.77

32.
Overview
• The absolute risk is the probability of an event in a sample or population of
interest. The relative risk (RR) is the risk of the event in an experimental
group relative to that in a control group. The odds ratio (OR) is the odds of
an event in an experimental group relative to that in a control group.

33.
Overview
• An RR or OR of 1.00 indicates that the risk is comparable in the two groups.
A value greater than 1.00 indicates increased risk; a value lower than 1.00
indicates decreased risk. The 95% confidence intervals and statistical
significance should accompany values for RR and OR.

34.
Overview
• As a measure of effect size, an RR value is generally considered clinically
significant if it is less than 0.50 or more than 2.00; that is, if the risk is at
least halved, or more than doubled. However, RR values that are closer to
1.00 can also be considered clinically significant if the event is serious or if it
is important to public health

35.
Overview
• RR and OR convey useful information about the effect of a risk factor on the
outcome of interest. However, the RR and OR must be interpreted in the
context of the absolute risk as well as the clinical importance of the outcome
in the individual patient.

36.
Overview
• The statistical significance of an RR value is usually provided. It is possible
for an RR value to be well below 1.00, or well above 1.00, and yet not
statistically significant, and it is possible for an RR value to be very close to
1.00 (ie, probably not clinically significant) but yet statistically significant
because the study was conducted on a large sample.

37.
Overview
• RR values are accompanied by their 95% confidence intervals (CIs). The
statistical significance of an RR value can be inferred from the 95% CI.
• If the CI includes the value 1.00, the RR is not statistically significant. For
example, if the RR is 1.70 and the CI is 0.90–2.50, then the elevation in risk
is not statistically significant because the value 1.00 (no difference in risk)
lies within the range of the confidence interval.

38.
Overview
• The OR is numerically different from the RR, even though both seek to
compare the same risk between the same groups. This is because the 2
statistics are based on different underlying concepts
• ORs and RRs are similar when the event being assessed is rare in the
control group (or population)
• ORs can substantially overestimate (if > 1.00) or underestimate (if < 1.00)
RRs when the event is commo

39.
Overview
• ORs are also less easy to express in plain English, and hence less easy to
understand
• The relationship between the OR and RR is nonlinear, but mathematical
methods exist to convert ORs to RRs