This document provides an overview of basic statistical concepts and techniques for analyzing data that are important for oncologists to understand. It covers topics such as types of data, measures of central tendency and variability, theoretical distributions, sampling, hypothesis testing, and basic techniques for analyzing categorical and numerical data, including t-tests, ANOVA, chi-square tests, correlation, and regression. The goal is to equip oncologists with fundamental statistical knowledge for handling, describing, and making inferences from medical data.

1. STATISTICS
Basics for Oncologist
DR.KIRAN KUMAR BR

2. Outline:
• Handling Data
• Sampling and Estimation
• Study Design
• Hypothesis testing
• Basic Techniques for Analyzing Data

3. 1.Types of data
Categorical (qualitative) data
Nominal data – Examples blood group (A, B, AB and O)
Ordinal data – Examples disease staging systems (advanced, moderate,
mild, none) and degree of pain (severe, moderate, mild, none).
Numerical (quantitative) data
Discrete data –
the number of visits to a GP in a particular year or the number of episodes
of illness in an individual over the last five years.
Continuous data – It occur when there is no limitation on the values
that the variable can take, e.g. weight or height.

4. Derived data
• Percentages.
• Ratios or quotients –For example, body mass index (BMI).
• Rates.
• Scores.

5. 2.Data entry
• A more flexible approach is to have your data available as an ASCII
or text file.
• ASCII format simply consists of rows of text that you can
view on a computer screen.
• Usually, each variable in the file is separated
from the next by some delimiter, often a space or a comma. This is
known as free format.

6. 3.Displaying data diagrammatically
• Bar or column chart
• Pie chart
• Histogram
• Dot plot
• Stem-and-leaf plot
• Box plot

9. 4.Describing data: the ‘average’
Measures of Central Tendency
• The mean
• The median
• The mode

10. • 5.Describing data: the ‘spread’
Measures of Variability
Range
Standard Deviation
Inter-quartile range

11. The range
The range is the difference between the largest and smallest observations
in the data set.
The standard deviation
Most common and most appropriate measure of dispersion.
The standard deviation is the square root of the variance in a sample
of n observations.
Standard deviation (SD) is used for data which are "normally distributed",
to provide information on how much the data vary around their mean.

12. Interpretation of SD:
Large SD: Data points are far from the mean.
Small SD: Data points are clustered closely around the mean.
Uses of SD:
Helps in finding suitable sample size.
Helps in finding Standard Error( It is the measure of
difference between sample and population).
It summarizes the deviation of a large distribution from mean.

13. Theoretical distributions: the Normal (Gaussian) distribution
One of the most important distributions in statistics is the Normal
distribution.
• bell-shaped .
• It is based on Mean and SD.
• Mean = Median = Mode.
• shifted to the right if the mean is increased and to the left if the mean
• is decreased .
• flattened as the variance is increased but becomes more peaked as the
variance is decreased .
• The Standard Normal distribution has a mean of zero and a SD of one.

14. +/- 1SD includes 68.2% of the data.
+/- 2SD includes 95.4% of the data.
+/- 3SD includes 99.7% of the data.

16. Theoretical distributions: other distributions
• The t-distribution
• The Chi-squared (c2) distribution
• The F-distribution
• The Lognormal distribution

17. Sampling and sampling distributions
We collect data on a sample of individuals who we believe
are representative of the population.
Random Sampling
( Probability sampling)
Nonrandom Sampling
( Non-probability sampling)
Simple Random Sampling Convenience Sampling
Systemic Random Sampling Quota Sampling
Stratified Random Sampling Snow-ball Sampling
Cluster Random Sampling Clinical Trial Sampling

18. Confidence intervals:
• Confidence intervals (CI) are typically used when, instead
of simply wanting the mean value of a sample, we want a
range that is likely to contain the true population value.
Eg: The average systolic BP before treatment in study, of a group of 100
hypertensive patients, was 170 mmHg. After treatment with the new drug
the mean BP dropped by 20 mmHg.
If the 95% CI is 15–25, this means we can be 95% confident that the true
effect of treatment is to lower the BP by 15–25 mmHg.

19. The P (probability) value :
• It is used when we wish to see how likely it is that a
hypothesis is true.
• The hypothesis is usually that there is no difference
between two treatments, known as the “null hypothesis”.
• The P value gives the probability of any observed
difference happened by chance.
• P = 0.5 means that the probability of the difference
having happened by chance is 0.5 in 1, or 50:50.

20. • P=0.05 means that the probability of the difference having
happened by chance is 0.05 in 1, i.e. 1 in 20.
• The lower the P value, the less likely it is that the
difference happened by chance and so the higher the
significance of the finding.
• Remember that P = 0.05 is usually classed as “significant”,
P= 0.01 as “highly significant” and P = 0.001 as “very
highly significant”.

21. Study design
Clinical trials.
Epidemiological Studies.

22. Clinical trials:
A clinical trial is any form of planned experimental study design, to
evaluate the effect of a new treatment on a clinical outcome in humans.

25. • Cohort studies
Advantages of cohort studies
• The time sequence of events can be assessed.
• They can provide information on a wide range of disease
outcomes.
• The incidence/risk of disease can be measured directly.
• They can be used to study exposure to factors that are rare.
• There is reduced recall and selection bias compared with
case–control studies

26. • Case–control studies
Advantages of case–control studies
• They are generally relatively quick, cheap and easy to perform.
• They are particularly suitable for rare diseases.
• A wide range of risk factors can be investigated in each study.
• There is no loss to follow-up.
Disadvantages of case–control studies
• Recall bias,
• If the onset of disease preceded exposure to the risk factor, causation
cannot be inferred.
• Case–control studies are not suitable when exposures to the risk
factor are rare.

28. Hypothesis testing :
Hypothesis testing (or significance testing) is used to
quantify our belief against a particular hypothesis.
We define five stages when carrying out a hypothesis test:
1 Define the null and alternative hypotheses under study.
2 Collect relevant data from a sample of individuals.
3 Calculate the value of the test statistic specific to the null
hypothesis.
4 Compare the value of the test statistic to values from a known
probability distribution.
5 Interpret the P-value and results

29. Obtaining the test statistic
After collecting the data, we substitute values from our sample into a
formula, specific to the test we are using, to determine a value for the
test statistic.
Obtaining the P-value
We relate the value of the test statistic obtained from the sample to the
known distribution to obtain the P-value.
The P-value is the probability of obtaining our results, or something
more extreme, if the null hypothesis is true.
The null hypothesis is either true or false and we cannot interpret the
P-value as the probability that the null hypothesis is true.

30. Using the P-value
We must make a decision about how much evidence we require to
enable us to decide to reject the null hypothesis in favor of the
alternative.
The smaller the P-value, the greater the evidence against the
null hypothesis.
• Conventionally, we consider that if the P-value is less than 0.05,We then
reject the null hypothesis and say that the results are significant at the
5% level.
• In contrast, if the P-value is equal to or greater than 0.05, We do not
reject the null hypothesis, and we say that the results are not
significant at the 5% level .
This does not mean that the null hypothesis is true; simply that we do not
have enough evidence to reject it.

31. Basic Techniques for Analyzing Data
(Tests of Statistical Significance)
Parametric Tests Non-Parametric Tests
Quantitative Data Qualitative Data
Compares Mean and SD Compares Percentage,
proportions and fractions.
Students t-Test, ANOVA test. Sign Test, Chi-Square test,
Wilcoxan signed rank test

32. Numerical data:
Two related groups ( In a same group before and after intervention):
• The paired t-test
E.g.: Mean serum albumin in dengue pts before treatment was 3.6g/Dl
and after treatment was 3.2g/Dl. Comparison of mean levels can be
done by Paired Students t-test.
• The Wilcoxon signed ranks test
Compares percentage proportions and fractions in a matched paired
data.

33. Two unrelated groups:
We have samples from two independent (unrelated) groups of individuals
and one numerical or ordinal variable of interest.
The unpaired (two-sample) t-test:
E.g.: Mean Hb levels of anemia pts was 9.5g/Dl and those of hookworm
pts was 7.4g/Dl , Comparison of Mean values can be done by
Unpaired t-test.
The Wilcoxon rank sum (two-sample) test.
Mann–Whitney U test.

34. Numerical data: more than two groups
ANOVA (analysis of variance) test
E.g.: Mean weight of students in class A is 50kg and those of
class B is 45kg, and of class c is 54 kg . Comparison of
mean weights can be done by ANOVA test.

35. Categorical data: two proportions,percentages or fractions
Chi-square test:
E.g.: We have two independent groups of individuals (e.g.
homosexual men with and without a history of gonorrhea).
We want to know whether the proportions of individuals with
a characteristic (e.g. infected with human herpesvirus-8,
HHV-8) are the same in the two groups.

36. Correlation:
• Correlation analysis is concerned with measuring the
degree of association between two variables.
Pearson correlation coefficient (r):
• We measure how close the observations are to the straight
line that best describes their linear relationship by
calculating the Pearson correlation coefficient.
• Lies between -1 to +1.
• Represented by Scatter diagram.

37. Weak Positive Correlation r < 0.3
Moderate Positive Correlation r = 0.4-0.6
Strongly Positive Correlation r > 0.7

38. Regression:
• It is a change in measurement of a variable.
• Provides relation between two variables.
Regression Coefficient:
Measure of change of one dependant variable(y) with change
in independent variable(x) or variables.
y = a + b(x)
where y is dependant variable and x is independent variable.

39. Types of Regressions Equations
SIMPLE LINEAR RGRESSIONS Y = a + b(x)
MULTIPLE LINEAR
RGRESSIONS
Y = a + b(x1) + c(x2)
SIMPLE CURVILINEAR
REGRESSIONS
Y = a + b(x)6
MULTIPLE CURVILINEAR
REGRESSIONS
Y = a + b(x)2 + c(x)3

40. Binary outcomes and logistic regression
• Logistic regression is very similar to linear regression; we use it when
we have a binary outcome of interest (e.g. the presence/absence of a
symptom, or an individual who does/does not have a disease) and a
number of explanatory variables.
We perform a logistic regression analysis in order to do one or more of the
following:
• Determine which explanatory variables influence the outcome.
• Evaluate the probability that an individual with a particular covariate
pattern (i.e. a unique combination of values for the explanatory
variables) will have the outcome of interest.

41. • Bias and confounding
• Bias is said to have occurred when there is a systematic difference
between the results from a study and the true state of affairs.
• Selection bias
• Information bias
• Attention bias
• Berkesonian bias
• Lead time bias

42. Minimization of bias
• SINGLE BLINDING
• DOUBLE BLINDING
• TRIPLE BLINDING

43. • Confounding
Confounding occurs when we find a association between a
potential risk factor and a disease outcome
or miss a real association between them because we have
failed to adjust for any confounding variables.
Methods of Confounding:
Randamization
Restriction, Matching, Stratification

44. Systematic reviews and meta-analysis
• A systematic review is a formalized and stringent process of
combining the information from all relevant studies (both published
and unpublished) of the same health condition; these studies are
usually clinical trials of the same or similar treatments but may be
observational studies .
• A systematic review is an integral part of evidence-based medicine
which applies the results of the best available evidence, together with
clinical expertise, to the care of patients.

45. Meta-analysis
• A meta-analysis or overview is a particular type of systematic
review that focuses on the numerical results.
• The main aim of a metaanalysis is to combine the results from several
independent studies to produce, if appropriate, an estimate of the
overall or average effect of interest.

46. Survival analysis
• Survival data are concerned with the time it takes an individual to
reach an endpoint of interest.
• Statistical methods for analyzing longitudinal data on the occurrence of
events.
• Events may include death, injury, onset of illness, recovery from
illness (binary variables) or transition above or below the clinical
threshold of a meaningful continuous variable (e.g. CD4 counts).
• Accommodates data from randomized clinical trial or cohort study
design.

47. Characterized by the following two features:
• It is the length of time for the patient to reach the
endpoint, rather than whether or not she or he reaches the
endpoint, that is of primary importance.
• Data may often be censored.
• Censoring: Subjects are said to be censored if they are lost
to follow up or drop out of the study, or if the study ends
before they die or have an outcome of interest. They are
counted as alive or disease-free for the time they were
enrolled in the study.

48. Objectives of survival analysis:
– Estimate time-to-event for a group of individuals,
such as time until second heart-attack for a group of MI
patients.
– To compare time-to-event between two or more
groups, such as treated vs. placebo MI patients in a
randomized controlled trial.
– To assess the relationship of co-variables to time-to-
event, such as: does weight, insulin resistance, or
cholesterol influence survival time of MI patients

49. • THANK YOU.