Introduction to medical statistics

Introduction to Medical Statistics
Mohamed Magdy Alhelaly

Why do we use statistics in medical
research?

We use statistical methods to:
collect,
summarize,
analyze,
and draw conclusions from our sample data.
medical statistics at a glance, 3rd edition

Before we start you should know…
• Variable: any quantity that varies from patient
to another in the collected data. for example;
if we collected data about age, sex, and
disease duration.
• Data (variables) may be either categorical
(qualitative) or numerical (quantitative).

categorical (qualitative) data
variables take names (categories)
• Nominal data, the categories have names but
not in an order. As blood groups (A, B, …) and
marital status (single, married, divorced).
• Ordinal data, the categories have names and
ordered in degrees of severity as example;
Pain severity and disease degree. (mild,
moderate, and severe).

numerical (quantitative) data
variables take numbers
(how many?)
• Discrete, variables are restricted to whole
certain numerical values.(often counts of
number of events) As number of visits to
physician, side effect incidence, and disease
episodes. (we cannot have a half visit!)
• Continuous, can contain any numerical value
without limitations. Age, weight, and results
of statistical tests.

In this module we will discuss…..
• Statistics that describe data.
- Percentages.
- Mean.
- Median.
- Mode.
- Standard Deviation.
• Statistics that test confidence.
- Confidence interval.
- P-value.

Percentages
• Frequency and Percentages usually describes
the categorical data, but it can be used in
descriptive statistics of numerical data.
• Frequency, is the number of patients in the
group expressing the event (variable) or have
the character of interest (variable) .
• Percentage, is described simply as number of
subjects in the group to the total number of
subjects multiplied by 100.

Example: (qualitative, ordinal variable)
we collected data about patients with Hypertension.
We collected data about severity of disease in these
patients.
PercentageFrequencyParameter
30%300Mild Hypertension
62%620Moderate
Hypertension
8%80Severe
Hypertension
100%1000Total

For numerical data (specially continous) we
usually use two types of statistical forms to
describe it. (to give a statistical summary)
- Measures of central tendency.(Mean,
Median, and mode)
- Measures of Dispersion (Spread): standard
deviation and inter-quartile range.

Measures of central tendency
(Mean, Median, and Mode)
• Mean (average or arithmetic mean): Sum of
all data divided by their number.
• Median: middle value of numbers ordered
from least to greatest.
• Mode: the most frequent number within
group of numbers.
1,2,3,4,5 and 1,1,1,2,2,3,11

Try to solve this..
Example: we collected data
about age of ten patients, and it
was:
54,33,87,55,96,33,54,44,21,33
Find; mean, median, and mode.

Example: we collected data about age
of ten patients, and it was:
54,33,87,55,96,33,54,44,21,33
• Mean= sum of data/their number
(54+33+87+55+96+33+54+44+21+33)/10=51
• Median= middle value of ordered values. 1st we
will order values from least to greatest
21,33,33,33,44,54,54,55,87,96 Then we get the
middle value = n/2=10/2=5, but the number is
even so there will be two middle values n/2,
(n/2)+1 = values 5,6= 44,54. To obtain the median
of two middle values, we calculate their mean=
(44+54)/2=49
• Mode: the most frequent value= 33

Measures of Dispersion
• Standard deviation (SD): We use it to show how far is the
data from the mean. Indicates variation of data around
their mean. Only if the data is normally distributed. We
can conclude that SD is the mean of individual values
deviation from the mean.
• Inter-quartile range (IQR): Usually given with median to
indicate the range of values in between it the middle half
of the sample lies. (The 1st quartile point has the ¼ of the
data below it, and the 3rd quartile point has ¾ of the data
below it) usually presented by ‘’box and whisker’’ plot.
• Range: Interval of values between maximum and minimum
values.

Normal (Gaussian) distribution and SD
If we collected data from population (large sample) about biological
or natural event and plotted the data on a curve, it will result in
normally distributed data curve. (normal distribution curve)
 Characters of normally distributed data;
 can be described by mean and SD.
 if plotted on curve, will result in bell shaped curve.
 symmetrically presented around the mean.
 curve will shift to right if the mean increased and to left if the
mean decreased.
 mean, median, and mode (symmetry result) are equal.
 area represented by mean±1SD (one SD above and below mean)
contains 68.2% of values, mean±2SD= 95.4%, and mean±3SD=
99.7%.

In this graph (m=80, SD=5); 68.2% of patients weigh between 75 and 85 Kgs.
95.4% of patients will weigh between 70 and 90 Kgs. 99.7% of patients will
weigh between 65 and 95 Kgs.
Michael Harris, Gordon Taylor. 2004. medical statistics made easy, Taylor & Francis Group.

Inferential statistics
• Statistics that test confidence.
- P-value.
- Confidence interval.

P-value
• P-value (probability value) is a numeric value used to
test if specific hypothesis is true or not, the hypothesis
is usually ‘’there is no difference between two
interventions’’ means the two interventions are equal
in efficacy, this hypothesis is called ‘’null hypothesis’’.
• P-value gives the probability that if any observed
difference has happened by chance.
• Null-hypothesis is always the opposite of what we are
trying to prove.
• Alternative hypothesis is the hypothesis against null
hypothesis.

• If we have 100 patients with specific observed
drug effect and p-value of 0.2, this means that
there is 20% probability that this observed
effect has happened by chance. Meaning
there is probability of the effect to be
happened by chance in 20 patients out of 100
patients. (so … is this enough to reject the
hypothesis stating that there is no difference
‘’the null’’?)

• For results to be statistically significant (to reject null
hypothesis), the p-value of the results must be ≤ 0.05,
this allows you to reject the null hypothesis and accept
the alternative hypothesis.
• P-value of 0.05 means there is 5% probability that the
differences have happened by chance, and we can
accept this difference as statistically significant
difference.
• The lower the p-value, the lower the probability of
chance, and the higher the significance of the results.

Example
Michael Harris, Gordon Taylor. 2004. medical statistics made easy, Taylor & Francis Group.

P-value and clinical relevance
• Distinction must be made between clinical
relevance and statistical significance.
• If the sample size is small it may result in high
p-value and statistically insignificant results
instead of observed clinical relevance, on the
other hand, a large sample size study may obtain
statistically significant (low p-value) results that
has no or very low clinical relevance.
• The confidence interval may be a better indicator
for clinical significance and the direct of the effect
in some circumstances.

Confidence interval
• It is the interval (two limits) within it we are
confident (by certain level) that it contains
the true population mean value.
• The population mean value is the mean of the
whole population values (so it is an imaginary
value) if we included all the population in the
study instead of taking a population sample.

Example (1)
• In a study on 500 patients with DM, we tried a
new anti-diabetic drug. Baseline mean fasting
blood glucose level was 190 mg/dl. After the
treatment, the fasting blood glucose level was
decreased by mean of 20 mg/dl( mean
difference=-20mg/dl), with 95% confidence
interval of (-15:-25).
Interpretation: we are 95% confident that the new
drug true effect of treatment can decrease blood
glucose level by 15-25 mg/dl.

Example (2)
• In another study with smaller sample size of 50 patients only,
and the same new anti-diabetic drug. Baseline mean fasting
blood glucose level was 190 mg/dl. After the treatment, the
fasting blood glucose level was decreased by mean of 20
mg/dl( mean difference=-20mg/dl), with wider 95% confidence
interval of (-50:+10).
Interpretation: this wide confidence interval includes zero (no
change), meaning that the drug has no effect in some patients
of the sample, even it has elevated blood glucose level in some
patients of the sample. So.. If the CI includes zero (no change,
null value) if we are using mean difference this means that
there is more than 5% chance (can not reject null hypothesis)
that the drug has no effect (results are not significant), and the
drug is not effective.

Null hypothesis and CI
• Null hypothesis assumes that there is no difference
between two interventions (equal). Or there is no
change from baseline.
• If the CI interval includes a null value at any point,
this means that results are not significant and the
null hypothesis has more than 5% probability to be
correct. (more than 5% probability that the results
have happened by chance and there is no effect)
• Null values are 1 if we are estimating the mean
difference and zero if we are estimating risk ratio or
odds ratio.

Null hypothesis and CI
forest plot

Introduction to medical statistics

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