Statistical Methods in Clinical
Research
Dr Ranjith P
DNB Resident ACME Pariyaram ,
Kerala
www.dnbpediatrics.com
Overview
 Data types
 Summarizing data using descriptive statistics
 Standard error
 Confidence Intervals
www.dnbpedia...
Overview
 P values
 Alpha and Beta errors
 Statistics for comparing 2 or more groups with
continuous data
 Non-paramet...
Overview
 Regression and Correlation
 Risk Ratios and Odds Ratios
 Survival Analysis
 Cox Regression
www.dnbpediatrics...
 Forest plot
 PICOT
overview
www.dnbpediatrics.com
Types of Data
 Discrete Data-limited number of choices
 Binary: two choices (yes/no)
 Dead or alive
 Disease-free or n...
Types of data
 Continuous data
 Theoretically infinite possible values (within
physiologic limits) , including fractiona...
Types of Data
 Why important?
 The type of data defines:
 The summary measures used
 Mean, Standard deviation for cont...
Descriptive Statistics
 Characterize data set
 Graphical presentation
 Histograms
 Frequency distribution
 Box and wh...
Histogram
Continuous Data
No segmentation of data into groups
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Frequency Distribution
Segmentation of data into groups
Discrete or continuous data
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Box and Whiskers Plots
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Box and Whisker Plots
Popular in Epidemiologic Studies
Useful for presenting comparative data graphically
www.dnbpediatric...
Numeric Descriptive Statistics
 Measures of central tendency of data
 Mean
 Median
 Mode
 Measures of variability of
...
Mean
 Most commonly used measure of central tendency
 Best applied in normally distributed continuous data.
 Not applic...
 Eg mean Height of 6 adolescent
children 146 ,142,150,148,156,140
 Ans ?
 882/6 =147
www.dnbpediatrics.com
Median
 Used to indicate the “average” in a
skewed population
 Often reported with the mean
 If the mean and the median...
 It is the middle value from an ordered
listing of the values
 If an odd number of values, it is the middle
value 1.2.3....
Mode
 Infrequently reported as a value in studies.
 Is the most common value eg. 1,3,8,9,5,8,5,6
 mode = 5
.
www.dnbped...
Interquartile range
 Is the range of data from the 25th percentile
to the 75th percentile
 Common component of a box and...
www.dnbpediatrics.com
Mean deviation(standard
deviation )
 Mean deviation(SD) = £I X- Ẍ I / n
 n is the no of observations Ẍ is the mean ,
X e...
Variance
 Square of SD(standard deviation )
Coefficient of variance = SD/ mean x 100
Eg. If sd is 3 mean is 150
Variance ...
Standard Error
 A fundamental goal of statistical analysis is to
estimate a parameter of a population based
on a sample
...
Standard Error
 Standard error of the mean
 Standard deviation / square root of (sample
size)
 (if sample greater than ...
Clarification
 Standard Deviation measures the
variability or spread of the data in an
individual sample.
 Standard erro...
Standard Error
 Significance:
 Is the basis of confidence intervals
 A 95% confidence interval is defined by
 Sample m...
 Mean +/- 1 sd = 68.27% value
Mean +/- 2 sd = 95.49% value
 Mean +/- 3 sd = 99.7% value
 Mean +/- 4 sd = 99.9% value
ww...
Confidence Intervals
 May be used to assess a single point
estimate such as mean or proportion.
 Most commonly used in a...
Confidence Intervals
Commonly reported in studies to provide an estimate of the precision
of the mean.
www.dnbpediatrics.c...
P Values
 The probability that any observation is
due to chance alone assuming that the
null hypothesis is true
 Typical...
 The P value used is an arbitrary value
 P value of 0.05 equals 1 in 20
chance
 P value of 0.01 equals 1 in 100
chance
...
Errors
 Type I error
 Claiming a difference between two
samples when in fact there is none.
 Remember there is variabil...
Errors
 Type II error
 Claiming there is no difference between
two samples when in fact there is.
 Also called a  erro...
Errors
Null
Hypothesis
H0
Alternative
Hypothesis
H1
Null
Hypothesis
H0
No Error Type I

Alternative
Hypothesis
H1
Type II...
Sample Size Calculation
 Also called “power analysis”.
 When designing a study, one needs to
determine how large a study...
Sample Size Calculation
 Depends on:
 Level of Type I error: 0.05 typical
 Level of Type II error: 0.20 typical
 One s...
One-sided vs. Two-sided
 Most tests should be framed as a two-
sided test.
 When comparing two samples, we usually
canno...
Statistical Tests
 Parametric tests
 Continuous data normally distributed
 Non-parametric tests
 Continuous data not n...
Comparison of 2 Sample Means
 Student’s T test
 Assumes normally distributed continuous
data.
T value = difference betwe...
Paired T Tests
 Uses the change before
and after intervention in a
single individual
 Reduces the degree of
variability ...
Analysis of Variance(ANOVA)
 Used to determine if two or more
samples are from the same
population-
 If two samples, is ...
Non-parametric Tests
 Testing proportions
 (Pearson’s) Chi-Squared (2) Test
 Fisher’s Exact Test
 Testing ordinal var...
Use of non-parametric tests
 Use for categorical, ordinal or non-normally
distributed continuous data
 May check both pa...
(Pearson’s) Chi-Squared (2) Test
 Used to compare observed proportions of an
event compared to expected.
 Used with nom...
Non parametric test
For comparing 2 related samples
-Wilcoxon Signed Rank Test
For comparing 2 unrelated samples
-Mann- Wh...
Mann–Whitney U test
 Mann–Whitney–Wilcoxon (MWW), Wilcoxon
rank-sum test, or Wilcoxon–Mann–Whitney
test) is a non-paramet...
STUDENT T TEST
 A t-test is any statistical hypothesis
test in which the test statistic follows
a normal
distri bution if...
 The Kaplan–Meier estimator,also known
as the product limit estimator, is
an estimator for estimating the survival
functi...
 A plot of the Kaplan–Meier
estimate of the survival function is
a series of horizontal steps of
declining magnitude whic...
www.dnbpediatrics.com
www.dnbpediatrics.com
 ODDS RATIO
In case control study –
measure of the strength of the
association between risk factor
and out come
www.dnbpe...
Odds ratio
Lung
cancer(case
s)
No lung
cancer
(controls)
smokers 33 (a) 55 (b)
Non smokers 2 (c) 27 (d)
TOTAL 35(a+c) 82(b...
 Odds ratio =ad/bc
=33*27/55*2
=8.1
ie smokers have 8.1 times have the
risk to develop lung cancer than non
smokers
www.d...
RELATIVE RISK
 Measure of risk in a cohort
study
 RR=lncidence of disease
among exposed /
incidence among non exposed
ww...
Cigarette
smoking
Developo
d lung
cancer
Not
Developo
d lung
cancer
total
Yes 70 (a) 6930 (b) 7000
(a+b)
No 3 (c) 2997 (d)...
 Incidence among
smokers=70/7000=10/1000
 Incidence among non
smokers=3/3000=1/1000
 Total incidence= 73/10000=7.3/1000...
RR=lncidence of disease among exposed/
incidence among non exposed
Relative risk of lung cancer=10/1=10
Incidence of lung ...
Attributable risk
 It is the difference in incidence
rates of disease between exposed
group(EG) and non exposed
group(NEG...
 (Incidence of disease rate in EG-
Incidence of disease in NEG/incidence
rate in EG ) * 100
AR= 10-1/10=90%
I.e. 90% lung...
Population attributable Risk
 It is the incidence of the disease in total
population - the incidence of disease
among tho...
Mortality rates & Ratios
 Crude Death rate
 No of deaths (from all cases )per 1000
estimated mid year population(MYP) in...
 CDR in Panchayath A is 15.2/1000
 Panchayath B is 8.2/1000 population
Health status of Panchayath B is better
than A
ww...
 Specific Death rate=(No of diseases due to
specific diseases during a calendar year/
MYP)*1,000
Can calculate death rate...
Case fatality rate(ratio)
 (Total no of deaths due to a particular
disease/Total no of cases due to same
disease)*100
 U...
Proportional mortality rate(ratio)
 Due to a specific disease=(No of
deaths from the specific disease in a
year/ Total de...
Survival rate
 (Total no of patients alive after 5yrs/Total
no of patients diagnosed or treated)*100
 Method of prognosi...
INCIDENCE
 No of new cases occurring in a defined
population during a specified period of time
 (No of new cases of spec...
Incidence-uses
 Can be expressed as Special incidence
rate , Attack rate , Hospital admission rate
, case rate etc
 Meas...
PREVALENCE
 Refers specifically to all current
cases (old & new) existing at a
given point of time, or a period of
time i...
 Point prevalence=(No of all currant cases
(old& new) of a specified disease existing
at a given point of time / Estimate...
jan1
dec 31 case1
3 4

5
case 6
case 7
case 8
www.dnbpediatrics.com
 Incidence - 3,4,5,8
 Point prevalence at jan 1- 1,2& 7
 Point prevalence at Dec 31- 1,3,5&8
 Period prevalence(jan-De...
Relationship b/n Incidence &
prevalence
 Prevalence=Incidence*Mean duration
 P=I*D I=P/D D=P/I
 Eg: Incidence=10 cases/...
PREVALENCE-USES
 Helps to estimate magnitude of
health/disease problems in the community,
& identify potential high risk ...
Statistical significance
 P value (hypothesis)
 95% CI (Interval)
www.dnbpediatrics.com
P value & its interpretation
“it is the probability of type 1 error”
 The chance that, a difference or
association is con...
 Study of prevalence of obesity in male &
female child in a classroom.
50 students
of 25 boys- 10 obese
of 25 girls - 16 ...
Null hypothesis: “no difference in obesity
among boys & girls in the classroom”
www.dnbpediatrics.com
study ,Bubble vs conventional CPAP for
prevention of extubation Failure( EF) in
preterm very low birth weight infants.
EF ...
Null hypothesis: “ no difference in EF
among preterm babies treated with
bCPAP &cCPAP.”
www.dnbpediatrics.com
95% CI
95%CI= Mean ‡1.96SD(2SD)
= Mean ‡ 2SE
1) 100 children attending pediatric OP.
mean wt=15kg SD=2
95%CI =?
www.dnbped...
Interpretation of 95%CI
 If a test is repeated 100times , 95 times
the mean value comes between this
value.
 If CI of 2 ...
Measures Of Risk
 case control study- Odds ratio
 Cohort study -RR,AR
www.dnbpediatrics.com
Chi-Squared (2) Test
 Chi-Squared (2) Formula
 Not applicable in small samples
 If fewer than 5 observations per cell...
BREAK
www.dnbpediatrics.com
Correlation
 Assesses the linear relationship between two variables
 Example: height and weight
 Strength of the associ...
Correlation
Source: Harris and Taylor. Medical Statistics Made Easy
www.dnbpediatrics.com
Correlation
Perfect Correlation
Source: Altman. Practical Statistics for Medical Research
www.dnbpediatrics.com
Regression
 Based on fitting a line to data
 Provides a regression coefficient, which is the slope of the
line
 Y = ax ...
Regression
 Types of regression
 Linear- uses continuous data to predict continuous
data outcome
 Logistic- uses contin...
Multiple Regression Models
 Determining the association between two
variables while controlling for the values of
others....
Multiple Regression Models
 In published papers, the multivariable models are
more powerful than univariable models and t...
Survivial Analysis
 Evaluation of time to an event (death,
recurrence, recover).
 Provides means of handling censored da...
Survival Analysis
Source: Altman. Practical Statistics for Medical Researchwww.dnbpediatrics.com
Kaplan-Meier Curve
Source: Wikipedia
www.dnbpediatrics.com
Kaplan-Meier Analysis
 Provides a graphical means of comparing the
outcomes of two groups that vary by intervention or
ot...
Cox Regression Model
 Proportional Hazards Survival Model.
 Used to investigate relationship between an event
(death, re...
Cox Regression Model
 Common use in long-term studies
where various factors might predispose
to an event.
 Example: afte...
True disease state vs. Test result
not rejected rejected
No disease
(D = 0)

specificity
X
Type I error
(False +) 
Disea...
Specific Example
Test Result
Pts with
disease
Pts without
the disease
www.dnbpediatrics.com
Test Result
Call these patients “negative” Call these patients “positive”
Threshold
www.dnbpediatrics.com
Test Result
Call these patients “negative” Call these patients “positive”
without the disease
with the disease
True Positi...
Test Result
Call these patients “negative” Call these patients “positive”
without the disease
with the disease
False
Posit...
Test Result
Call these patients “negative” Call these patients “positive”
without the disease
with the disease
True
negati...
Test Result
Call these patients “negative” Call these patients “positive”
without the disease
with the disease
False
negat...
Test Result
without the disease
with the disease
‘‘-’’ ‘‘+’’
Moving the Threshold: right
www.dnbpediatrics.com
Test Result
without the disease
with the disease
‘‘-’’ ‘‘+’’
Moving the Threshold: left
www.dnbpediatrics.com
TruePositiveRate
(sensitivity)
0%
100%
False Positive Rate
(1-specificity)
0% 100%
ROC curve
www.dnbpediatrics.com
TruePositiveRate
0
%
100%
False Positive Rate
0
%
100%
TruePositiveRate
0
%
100%
False Positive Rate
0
%
100%
A good test:...
Best Test: Worst test:
TruePositiveRate
0
%
100%
False Positive
Rate
0
%
100
%
TruePositive
Rate
0
%
100%
False Positive
R...
Best Test: Worst test:
TruePositiveRate
0
%
100%
False Positive
Rate
0
%
100
%
TruePositive
Rate
0
%
100%
False Positive
R...
FOREST PLOT
114www.dnbpediatrics.com
 An example forest plot of five odds ratios
(squares) with the summary measure
(centre line of diamond) and associated
co...
 A forest plot (or blobbogram[1]) is a
graphical display designed to illustrate
the relative strength of treatment effect...
117www.dnbpediatrics.com
 i. Probably a small study, with a wide CI,
crossing the line of no effect (OR = 1).
Unable to say if the intervention wo...
 iv. Large study, narrow confidence
intervals: entirely to left of OR = 1;
suggests intervention works
 v. Small study, ...
PICOT
 Used to test evidence based research
 Population
 Intervension or issue
 Comparison with another intervention
...
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  1. 1. Statistical Methods in Clinical Research Dr Ranjith P DNB Resident ACME Pariyaram , Kerala www.dnbpediatrics.com
  2. 2. Overview  Data types  Summarizing data using descriptive statistics  Standard error  Confidence Intervals www.dnbpediatrics.com
  3. 3. Overview  P values  Alpha and Beta errors  Statistics for comparing 2 or more groups with continuous data  Non-parametric tests www.dnbpediatrics.com
  4. 4. Overview  Regression and Correlation  Risk Ratios and Odds Ratios  Survival Analysis  Cox Regression www.dnbpediatrics.com
  5. 5.  Forest plot  PICOT overview www.dnbpediatrics.com
  6. 6. Types of Data  Discrete Data-limited number of choices  Binary: two choices (yes/no)  Dead or alive  Disease-free or not  Categorical: more than two choices, not ordered  Race  Age group  Ordinal: more than two choices, ordered  Stages of a cancer  Likert scale for response  E.G. strongly agree, agree, neither agree or disagree, etc. www.dnbpediatrics.com
  7. 7. Types of data  Continuous data  Theoretically infinite possible values (within physiologic limits) , including fractional values  Height, age, weight  Can be interval  Interval between measures has meaning.  Ratio of two interval data points has no meaning  Temperature in celsius, day of the year).  Can be ratio  Ratio of the measures has meaning  Weight, height www.dnbpediatrics.com
  8. 8. Types of Data  Why important?  The type of data defines:  The summary measures used  Mean, Standard deviation for continuous data  Proportions for discrete data  Statistics used for analysis:  Examples:  T-test for normally distributed continuous  Wilcoxon Rank Sum for non-normally distributed continuous www.dnbpediatrics.com
  9. 9. Descriptive Statistics  Characterize data set  Graphical presentation  Histograms  Frequency distribution  Box and whiskers plot  Numeric description  Mean, median, SD, interquartile range www.dnbpediatrics.com
  10. 10. Histogram Continuous Data No segmentation of data into groups www.dnbpediatrics.com
  11. 11. Frequency Distribution Segmentation of data into groups Discrete or continuous data www.dnbpediatrics.com
  12. 12. Box and Whiskers Plots www.dnbpediatrics.com
  13. 13. Box and Whisker Plots Popular in Epidemiologic Studies Useful for presenting comparative data graphically www.dnbpediatrics.com
  14. 14. Numeric Descriptive Statistics  Measures of central tendency of data  Mean  Median  Mode  Measures of variability of data(dispersion)  Standard Deviation, mean deviation  Interquartile range, variance www.dnbpediatrics.com
  15. 15. Mean  Most commonly used measure of central tendency  Best applied in normally distributed continuous data.  Not applicable in categorical data  Definition:  Sum of all the values in a sample, divided by the number of values. www.dnbpediatrics.com
  16. 16.  Eg mean Height of 6 adolescent children 146 ,142,150,148,156,140  Ans ?  882/6 =147 www.dnbpediatrics.com
  17. 17. Median  Used to indicate the “average” in a skewed population  Often reported with the mean  If the mean and the median are the same, sample is normally distributed. www.dnbpediatrics.com
  18. 18.  It is the middle value from an ordered listing of the values  If an odd number of values, it is the middle value 1.2.3.4.5 ie 3  If even number of values, it is the average of the two middle values.1,2,3,4,5,6 ie 3+4/2 = 3.5  Mid-value in interquartile range www.dnbpediatrics.com
  19. 19. Mode  Infrequently reported as a value in studies.  Is the most common value eg. 1,3,8,9,5,8,5,6  mode = 5 . www.dnbpediatrics.com
  20. 20. Interquartile range  Is the range of data from the 25th percentile to the 75th percentile  Common component of a box and whiskers plot  It is the box, and the line across the box is the median or middle value  Rarely, mean will also be displayed. www.dnbpediatrics.com
  21. 21. www.dnbpediatrics.com
  22. 22. Mean deviation(standard deviation )  Mean deviation(SD) = £I X- Ẍ I / n  n is the no of observations Ẍ is the mean , X each observation  Square mean deviation= variance= £I X- Ẍ I² / n Root mean square deviation =√£I X- Ẍ I² / n www.dnbpediatrics.com
  23. 23. Variance  Square of SD(standard deviation ) Coefficient of variance = SD/ mean x 100 Eg. If sd is 3 mean is 150 Variance is 9, coefficient of variance is 300/150 = 2 www.dnbpediatrics.com
  24. 24. Standard Error  A fundamental goal of statistical analysis is to estimate a parameter of a population based on a sample  The values of a specific variable from a sample are an estimate of the entire population of individuals who might have been eligible for the study.  A measure of the precision of a sample www.dnbpediatrics.com
  25. 25. Standard Error  Standard error of the mean  Standard deviation / square root of (sample size)  (if sample greater than 60)  Sd/ √n  Important: dependent on sample size  Larger the sample, the smaller the standard error. www.dnbpediatrics.com
  26. 26. Clarification  Standard Deviation measures the variability or spread of the data in an individual sample.  Standard error measures the precision of the estimate of a population parameter provided by the sample mean or proportion. www.dnbpediatrics.com
  27. 27. Standard Error  Significance:  Is the basis of confidence intervals  A 95% confidence interval is defined by  Sample mean (or proportion) ± 1.96 X standard error  Since standard error is inversely related to the sample size:  The larger the study (sample size), the smaller the confidence intervals and the greater the precision of the estimate. www.dnbpediatrics.com
  28. 28.  Mean +/- 1 sd = 68.27% value Mean +/- 2 sd = 95.49% value  Mean +/- 3 sd = 99.7% value  Mean +/- 4 sd = 99.9% value www.dnbpediatrics.com
  29. 29. Confidence Intervals  May be used to assess a single point estimate such as mean or proportion.  Most commonly used in assessing the estimate of the difference between two groups. www.dnbpediatrics.com
  30. 30. Confidence Intervals Commonly reported in studies to provide an estimate of the precision of the mean. www.dnbpediatrics.com
  31. 31. P Values  The probability that any observation is due to chance alone assuming that the null hypothesis is true  Typically, an estimate that has a p value of 0.05 or less is considered to be “statistically significant” or unlikely to occur due to chance alone. Null hypothesis rejected www.dnbpediatrics.com
  32. 32.  The P value used is an arbitrary value  P value of 0.05 equals 1 in 20 chance  P value of 0.01 equals 1 in 100 chance  P value of 0.001 equals 1 in 1000 chance. www.dnbpediatrics.com
  33. 33. Errors  Type I error  Claiming a difference between two samples when in fact there is none.  Remember there is variability among samples- they might seem to come from different populations but they may not.  Also called the  error.  Typically 0.05 is used www.dnbpediatrics.com
  34. 34. Errors  Type II error  Claiming there is no difference between two samples when in fact there is.  Also called a  error.  The probability of not making a Type II error is 1 - , which is called the power of the test.  Hidden error because can’t be detected without a proper power analysis www.dnbpediatrics.com
  35. 35. Errors Null Hypothesis H0 Alternative Hypothesis H1 Null Hypothesis H0 No Error Type I  Alternative Hypothesis H1 Type II  No Error Test result Truth www.dnbpediatrics.com
  36. 36. Sample Size Calculation  Also called “power analysis”.  When designing a study, one needs to determine how large a study is needed.  Power is the ability of a study to avoid a Type II error.  Sample size calculation yields the number of study subjects needed, given a certain desired power to detect a difference and a certain level of P value that will be considered significant.www.dnbpediatrics.com
  37. 37. Sample Size Calculation  Depends on:  Level of Type I error: 0.05 typical  Level of Type II error: 0.20 typical  One sided vs two sided: nearly always two  Inherent variability of population  Usually estimated from preliminary data  The difference that would be meaningful between the two assessment arms. www.dnbpediatrics.com
  38. 38. One-sided vs. Two-sided  Most tests should be framed as a two- sided test.  When comparing two samples, we usually cannot be sure which is going to be be better.  You never know which directions study results will go.  For routine medical research, use only two- sided tests. www.dnbpediatrics.com
  39. 39. Statistical Tests  Parametric tests  Continuous data normally distributed  Non-parametric tests  Continuous data not normally distributed  Categorical or Ordinal data www.dnbpediatrics.com
  40. 40. Comparison of 2 Sample Means  Student’s T test  Assumes normally distributed continuous data. T value = difference between means standard error of difference  T value then looked up in Table to determine significance www.dnbpediatrics.com
  41. 41. Paired T Tests  Uses the change before and after intervention in a single individual  Reduces the degree of variability between the groups  Given the same number of patients, has greater power to detect a difference between groups www.dnbpediatrics.com
  42. 42. Analysis of Variance(ANOVA)  Used to determine if two or more samples are from the same population-  If two samples, is the same as the T test.  Usually used for 3 or more samples. www.dnbpediatrics.com
  43. 43. Non-parametric Tests  Testing proportions  (Pearson’s) Chi-Squared (2) Test  Fisher’s Exact Test  Testing ordinal variables  Mann Whiney “U” Test  Kruskal-Wallis One-way ANOVA  Testing Ordinal Paired Variables  Sign Test  Wilcoxon Rank Sum Test www.dnbpediatrics.com
  44. 44. Use of non-parametric tests  Use for categorical, ordinal or non-normally distributed continuous data  May check both parametric and non- parametric tests to check for congruity  Most non-parametric tests are based on ranks or other non- value related methods  Interpretation:  Is the P value significant? www.dnbpediatrics.com
  45. 45. (Pearson’s) Chi-Squared (2) Test  Used to compare observed proportions of an event compared to expected.  Used with nominal data (better/ worse; dead/alive)  If there is a substantial difference between observed and expected, then it is likely that the null hypothesis is rejected.  Often presented graphically as a 2 X 2 Table www.dnbpediatrics.com
  46. 46. Non parametric test For comparing 2 related samples -Wilcoxon Signed Rank Test For comparing 2 unrelated samples -Mann- Whitney U Test For comparing >2groups -Kruskal Walli Test www.dnbpediatrics.com
  47. 47. Mann–Whitney U test  Mann–Whitney–Wilcoxon (MWW), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a non-parametric test especially that a particular population tends to have larger values than the other.  It has greater efficiency than the t-test on non- normal distributions, such as a mixture of normal distributions, and it is nearly as efficient as the t-test on normal distributions. www.dnbpediatrics.com
  48. 48. STUDENT T TEST  A t-test is any statistical hypothesis test in which the test statistic follows a normal distri bution if the null hypothesis is supported.  It can be used to determine if two sets of data are significantly different from each other, and is most commonly applied when the test statistic would follow a normal distribution www.dnbpediatrics.com
  49. 49.  The Kaplan–Meier estimator,also known as the product limit estimator, is an estimator for estimating the survival function from lifetime data.  In medical research, it is often used to measure the fraction of patients living for a certain amount of time after treatment.  The estimator is named after Edward L. Kaplan and Paul Meier. www.dnbpediatrics.com
  50. 50.  A plot of the Kaplan–Meier estimate of the survival function is a series of horizontal steps of declining magnitude which, when a large enough sample is taken, approaches the true survival function for that population. www.dnbpediatrics.com
  51. 51. www.dnbpediatrics.com
  52. 52. www.dnbpediatrics.com
  53. 53.  ODDS RATIO In case control study – measure of the strength of the association between risk factor and out come www.dnbpediatrics.com
  54. 54. Odds ratio Lung cancer(case s) No lung cancer (controls) smokers 33 (a) 55 (b) Non smokers 2 (c) 27 (d) TOTAL 35(a+c) 82(b+d) www.dnbpediatrics.com
  55. 55.  Odds ratio =ad/bc =33*27/55*2 =8.1 ie smokers have 8.1 times have the risk to develop lung cancer than non smokers www.dnbpediatrics.com
  56. 56. RELATIVE RISK  Measure of risk in a cohort study  RR=lncidence of disease among exposed / incidence among non exposed www.dnbpediatrics.com
  57. 57. Cigarette smoking Developo d lung cancer Not Developo d lung cancer total Yes 70 (a) 6930 (b) 7000 (a+b) No 3 (c) 2997 (d) 3000 (c+d) www.dnbpediatrics.com
  58. 58.  Incidence among smokers=70/7000=10/1000  Incidence among non smokers=3/3000=1/1000  Total incidence= 73/10000=7.3/1000 www.dnbpediatrics.com
  59. 59. RR=lncidence of disease among exposed/ incidence among non exposed Relative risk of lung cancer=10/1=10 Incidence of lung cancer is 10 times higher in exposed group (smokers) , ie having a Positive relationship with smoking Larger RR ,more the strength of association www.dnbpediatrics.com
  60. 60. Attributable risk  It is the difference in incidence rates of disease between exposed group(EG) and non exposed group(NEG)  Often expressed in percent www.dnbpediatrics.com
  61. 61.  (Incidence of disease rate in EG- Incidence of disease in NEG/incidence rate in EG ) * 100 AR= 10-1/10=90% I.e. 90% lung cancers in smokers was due to their smoking www.dnbpediatrics.com
  62. 62. Population attributable Risk  It is the incidence of the disease in total population - the incidence of disease among those who were not exposed to the suspected causal factor/incidence of disease in total population  PAR=7.3-1/7.3=86.3%, ie 86.3 % disease can be avoided if risk factors like cigarettes were avoided www.dnbpediatrics.com
  63. 63. Mortality rates & Ratios  Crude Death rate  No of deaths (from all cases )per 1000 estimated mid year population(MYP) in one year in a given place  CDR=(No. deaths during the year /MYP)*1000 www.dnbpediatrics.com
  64. 64.  CDR in Panchayath A is 15.2/1000  Panchayath B is 8.2/1000 population Health status of Panchayath B is better than A www.dnbpediatrics.com
  65. 65.  Specific Death rate=(No of diseases due to specific diseases during a calendar year/ MYP)*1,000 Can calculate death rate in separate diseases eg . TB, HIV 2/1000, 1/1000 resp Age groups 5-20yrs, <5yrs - 1/1000, 3/3000 resp. Sex eg. More in males, Specific months,etc www.dnbpediatrics.com
  66. 66. Case fatality rate(ratio)  (Total no of deaths due to a particular disease/Total no of cases due to same disease)*100  Usually described in A/c infectious diseases  Dengue, cholera, food poisoning etc  Represent killing power of the disease www.dnbpediatrics.com
  67. 67. Proportional mortality rate(ratio)  Due to a specific disease=(No of deaths from the specific disease in a year/ Total deaths in an year )*100  Under 5 Mortality rate=(No of deaths under 5 years of age in a given year/Total no of deaths during the same period)*100 www.dnbpediatrics.com
  68. 68. Survival rate  (Total no of patients alive after 5yrs/Total no of patients diagnosed or treated)*100  Method of prognosis of certain disease conditions mainly in cancers  Can be used as a yardstick for assessment of standards of therapy www.dnbpediatrics.com
  69. 69. INCIDENCE  No of new cases occurring in a defined population during a specified period of time  (No of new cases of specific disease during a given time period / Population at risk)*1000  Eg 500 new cases of TB in a population of 30000, Incidence is (500/3000)*1000 ie 16.7/1000/yr expressed as incidence rate www.dnbpediatrics.com
  70. 70. Incidence-uses  Can be expressed as Special incidence rate , Attack rate , Hospital admission rate , case rate etc  Measures the rate at which new cases are occurring in a population  Not influenced by duration  Generally use is restricted to acute conditions www.dnbpediatrics.com
  71. 71. PREVALENCE  Refers specifically to all current cases (old & new) existing at a given point of time, or a period of time in a given population  Referred to as a rate , it is really a a ratio www.dnbpediatrics.com
  72. 72.  Point prevalence=(No of all currant cases (old& new) of a specified disease existing at a given point of time / Estimated population at the same point of time)*100  Period prevalence=(No of existing cases (old& new) of a specified disease during a given period of time / Estimated mid interval population at risk)*100 www.dnbpediatrics.com
  73. 73. jan1 dec 31 case1 3 4  5 case 6 case 7 case 8 www.dnbpediatrics.com
  74. 74.  Incidence - 3,4,5,8  Point prevalence at jan 1- 1,2& 7  Point prevalence at Dec 31- 1,3,5&8  Period prevalence(jan-Dec)- 1,2,3,4,5,7&8 www.dnbpediatrics.com
  75. 75. Relationship b/n Incidence & prevalence  Prevalence=Incidence*Mean duration  P=I*D I=P/D D=P/I  Eg: Incidence=10 cases/1000 population/yr  Mean duration 5 yrs  Prevalence=10*5 =50/1000 population www.dnbpediatrics.com
  76. 76. PREVALENCE-USES  Helps to estimate magnitude of health/disease problems in the community, & identify potential high risk populations  Prevalence rates are especially useful for administrative and planning purposes eg: hospital beds, man power needs,rehabilation facilities etc. www.dnbpediatrics.com
  77. 77. Statistical significance  P value (hypothesis)  95% CI (Interval) www.dnbpediatrics.com
  78. 78. P value & its interpretation “it is the probability of type 1 error”  The chance that, a difference or association is concluded , when actually there is none. www.dnbpediatrics.com
  79. 79.  Study of prevalence of obesity in male & female child in a classroom. 50 students of 25 boys- 10 obese of 25 girls - 16 obese p value : 0.02 www.dnbpediatrics.com
  80. 80. Null hypothesis: “no difference in obesity among boys & girls in the classroom” www.dnbpediatrics.com
  81. 81. study ,Bubble vs conventional CPAP for prevention of extubation Failure( EF) in preterm very low birth weight infants. EF bCPAP =4(16) cCPAP =9(16) p value-0.14 www.dnbpediatrics.com
  82. 82. Null hypothesis: “ no difference in EF among preterm babies treated with bCPAP &cCPAP.” www.dnbpediatrics.com
  83. 83. 95% CI 95%CI= Mean ‡1.96SD(2SD) = Mean ‡ 2SE 1) 100 children attending pediatric OP. mean wt=15kg SD=2 95%CI =? www.dnbpediatrics.com
  84. 84. Interpretation of 95%CI  If a test is repeated 100times , 95 times the mean value comes between this value.  If CI of 2 variables overlap, the chance of significant difference is very less. www.dnbpediatrics.com
  85. 85. Measures Of Risk  case control study- Odds ratio  Cohort study -RR,AR www.dnbpediatrics.com
  86. 86. Chi-Squared (2) Test  Chi-Squared (2) Formula  Not applicable in small samples  If fewer than 5 observations per cell, use Fisher’s exact test www.dnbpediatrics.com
  87. 87. BREAK www.dnbpediatrics.com
  88. 88. Correlation  Assesses the linear relationship between two variables  Example: height and weight  Strength of the association is described by a correlation coefficient- r  r = 0 - .2 low, probably meaningless  r = .2 - .4 low, possible importance  r = .4 - .6 moderate correlation  r = .6 - .8 high correlation  r = .8 - 1 very high correlation  Can be positive or negative  Pearson’s, Spearman correlation coefficient  Tells nothing about causation www.dnbpediatrics.com
  89. 89. Correlation Source: Harris and Taylor. Medical Statistics Made Easy www.dnbpediatrics.com
  90. 90. Correlation Perfect Correlation Source: Altman. Practical Statistics for Medical Research www.dnbpediatrics.com
  91. 91. Regression  Based on fitting a line to data  Provides a regression coefficient, which is the slope of the line  Y = ax + b  Use to predict a dependent variable’s value based on the value of an independent variable.  Very helpful- In analysis of height and weight, for a known height, one can predict weight.  Much more useful than correlation  Allows prediction of values of Y rather than just whether there is a relationship between two variable. www.dnbpediatrics.com
  92. 92. Regression  Types of regression  Linear- uses continuous data to predict continuous data outcome  Logistic- uses continuous data to predict probability of a dichotomous outcome  Poisson regression- time between rare events.  Cox proportional hazards regression- survival analysis. www.dnbpediatrics.com
  93. 93. Multiple Regression Models  Determining the association between two variables while controlling for the values of others.  Example: Uterine Fibroids  Both age and race impact the incidence of fibroids.  Multiple regression allows one to test the impact of age on the incidence while controlling for race (and all other factors) www.dnbpediatrics.com
  94. 94. Multiple Regression Models  In published papers, the multivariable models are more powerful than univariable models and take precedence.  Therefore we discount the univariable model as it does not control for confounding variables.  Eg: Coronary disease is potentially affected by age, HTN, smoking status, gender and many other factors.  If assessing whether height is a factor:  If it is significant on univariable analysis, but not on multivariable analysis, these other factors confounded the analysis. www.dnbpediatrics.com
  95. 95. Survivial Analysis  Evaluation of time to an event (death, recurrence, recover).  Provides means of handling censored data  Patients who do not reach the event by the end of the study or who are lost to follow-up  Most common type is Kaplan-Meier analysis  Curves presented as stepwise change from baseline  There are no fixed intervals of follow-up- survival proportion recalculated after each event. www.dnbpediatrics.com
  96. 96. Survival Analysis Source: Altman. Practical Statistics for Medical Researchwww.dnbpediatrics.com
  97. 97. Kaplan-Meier Curve Source: Wikipedia www.dnbpediatrics.com
  98. 98. Kaplan-Meier Analysis  Provides a graphical means of comparing the outcomes of two groups that vary by intervention or other factor.  Survival rates can be measured directly from curve.  Difference between curves can be tested for statistical significance. www.dnbpediatrics.com
  99. 99. Cox Regression Model  Proportional Hazards Survival Model.  Used to investigate relationship between an event (death, recurrence) occurring over time and possible explanatory factors.  Reported result: Hazard ratio (HR).  Ratio of the hazard in one group divided the hazard in another.  Interpreted same as risk ratios and odds ratios  HR 1 = no effect  HR > 1 increased risk  HR < 1 decreased risk www.dnbpediatrics.com
  100. 100. Cox Regression Model  Common use in long-term studies where various factors might predispose to an event.  Example: after uterine embolization, which factors (age, race, uterine size, etc) might make recurrence more likely. www.dnbpediatrics.com
  101. 101. True disease state vs. Test result not rejected rejected No disease (D = 0)  specificity X Type I error (False +)  Disease (D = 1) X Type II error (False -)   Power 1 - ; sensitivity Disease Test www.dnbpediatrics.com
  102. 102. Specific Example Test Result Pts with disease Pts without the disease www.dnbpediatrics.com
  103. 103. Test Result Call these patients “negative” Call these patients “positive” Threshold www.dnbpediatrics.com
  104. 104. Test Result Call these patients “negative” Call these patients “positive” without the disease with the disease True Positives Some definitions ... www.dnbpediatrics.com
  105. 105. Test Result Call these patients “negative” Call these patients “positive” without the disease with the disease False Positives www.dnbpediatrics.com
  106. 106. Test Result Call these patients “negative” Call these patients “positive” without the disease with the disease True negatives www.dnbpediatrics.com
  107. 107. Test Result Call these patients “negative” Call these patients “positive” without the disease with the disease False negatives www.dnbpediatrics.com
  108. 108. Test Result without the disease with the disease ‘‘-’’ ‘‘+’’ Moving the Threshold: right www.dnbpediatrics.com
  109. 109. Test Result without the disease with the disease ‘‘-’’ ‘‘+’’ Moving the Threshold: left www.dnbpediatrics.com
  110. 110. TruePositiveRate (sensitivity) 0% 100% False Positive Rate (1-specificity) 0% 100% ROC curve www.dnbpediatrics.com
  111. 111. TruePositiveRate 0 % 100% False Positive Rate 0 % 100% TruePositiveRate 0 % 100% False Positive Rate 0 % 100% A good test: A poor test: ROC curve comparison www.dnbpediatrics.com
  112. 112. Best Test: Worst test: TruePositiveRate 0 % 100% False Positive Rate 0 % 100 % TruePositive Rate 0 % 100% False Positive Rate 0 % 100 % The distributions don’t overlap at all The distributions overlap completely ROC curve extremes www.dnbpediatrics.com
  113. 113. Best Test: Worst test: TruePositiveRate 0 % 100% False Positive Rate 0 % 100 % TruePositive Rate 0 % 100% False Positive Rate 0 % 100 % The distributions don’t overlap at all The distributions overlap completely ROC curve extremes www.dnbpediatrics.com
  114. 114. FOREST PLOT 114www.dnbpediatrics.com
  115. 115.  An example forest plot of five odds ratios (squares) with the summary measure (centre line of diamond) and associated confidence intervals (lateral tips of diamond), and solid vertical line of no effect. Names of (fictional) studies are shown on the left, odds ratios and confidence intervals on the right. 115www.dnbpediatrics.com
  116. 116.  A forest plot (or blobbogram[1]) is a graphical display designed to illustrate the relative strength of treatment effects in multiple quantitative scientific studies addressing the same question. It was developed for use in medical research as a means of graphically representing a meta-analysis of the results of randomized controlled trials. 116www.dnbpediatrics.com
  117. 117. 117www.dnbpediatrics.com
  118. 118.  i. Probably a small study, with a wide CI, crossing the line of no effect (OR = 1). Unable to say if the intervention works  ii. Probably a small study, wide CI , but does not cross OR = 1; suggests intervention works but weak evidence  iii. Larger study, narrow CI: but crosses OR = 1; no evidence that intervention works www.dnbpediatrics.com
  119. 119.  iv. Large study, narrow confidence intervals: entirely to left of OR = 1; suggests intervention works  v. Small study, wide confidence intervals, suggests intervention is detrimental  vi. Meta-analysis of all identified studies: suggests intervention works. www.dnbpediatrics.com
  120. 120. PICOT  Used to test evidence based research  Population  Intervension or issue  Comparison with another intervention  Outcome  Time frame www.dnbpediatrics.com

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