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- 1. Statistical Methods in Clinical Research Dr Ranjith P DNB Resident ACME Pariyaram , Kerala
- 2. Overview Data types Summarizing data using descriptive statistics Standard error Confidence Intervals
- 3. Overview P values Alpha and Beta errors Statistics for comparing 2 or more groups with continuous data Non-parametric tests
- 4. Overview Regression and Correlation Risk Ratios and Odds Ratios Survival Analysis Cox Regression
- 5. Forest plot PICOT overview
- 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.
- 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
- 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
- 9. Descriptive Statistics Characterize data set Graphical presentation Histograms Frequency distribution Box and whiskers plot Numeric description Mean, median, SD, interquartile range
- 10. Histogram Continuous Data No segmentation of data into groups
- 11. Frequency Distribution Segmentation of data into groups Discrete or continuous data
- 12. Box and Whiskers Plots
- 13. Box and Whisker Plots Popular in Epidemiologic Studies Useful for presenting comparative data graphically
- 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
- 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.
- 16. Eg mean Height of 6 adolescent children 146 ,142,150,148,156,140 Ans ? 882/6 =147
- 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.
- 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
- 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 .
- 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.
- 21. Mean deviation(standard deviation ) Mean deviation(SD) = £I X- I / nẌ n is the no of observations is the mean ,Ẍ X each observation Square mean deviation= variance= £I X- I² / nẌ Root mean square deviation =√£I X- I² / nẌ
- 22. 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
- 23. 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
- 24. 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
- 25. 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.
- 26. 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.
- 27. Mean +/- 1 sd = 68.27% value Mean +/- 2 sd = 95.49% value Mean +/- 3 sd = 99.7% value Mean +/- 4 sd = 99.9% value
- 28. 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.
- 29. Confidence Intervals Commonly reported in studies to provide an estimate of the precision of the mean.
- 30. 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
- 31. 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.
- 32. 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 α error. Typically 0.05 is used
- 33. Errors Type II error Claiming there is no difference between two samples when in fact there is. Also called a β error. The probability of not making a Type II error is 1 - β, which is called the power of the test. Hidden error because can’t be detected without a proper power analysis
- 34. Errors Null Hypothesis H0 Alternative Hypothesis H1 Null Hypothesis H0 No Error Type I α Alternative Hypothesis H1 Type II β No Error Test result Truth
- 35. 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.
- 36. 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.
- 37. 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.
- 38. Statistical Tests Parametric tests Continuous data normally distributed Non-parametric tests Continuous data not normally distributed Categorical or Ordinal data
- 39. 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
- 40. 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
- 41. 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.
- 42. Non-parametric Tests Testing proportions (Pearson’s) Chi-Squared (χ2) 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
- 43. 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?
- 44. (Pearson’s) Chi-Squared (χ2) 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
- 45. 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
- 46. 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.
- 47. 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
- 48. 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.
- 49. 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.
- 50. ODDS RATIO In case control study – measure of the strength of the association between risk factor and out come
- 51. 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)
- 52. 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
- 53. RELATIVE RISK Measure of risk in a cohort study RR=lncidence of disease among exposed / incidence among non exposed
- 54. 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)
- 55. Incidence among smokers=70/7000=10/1000 Incidence among non smokers=3/3000=1/1000 Total incidence= 73/10000=7.3/1000
- 56. 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
- 57. Attributable risk It is the difference in incidence rates of disease between exposed group(EG) and non exposed group(NEG) Often expressed in percent
- 58. (Incidence of disease rate in EG- Incidence of disease in NEG/incidence rate in EG ) * 100 . AR= 10-1/10=90% Ie 90% lung cancers in smokers was due to their smoking
- 59. 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
- 60. 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
- 61. CDR in Panchayath A is 15.2/1000 Panchayath B is 8.2/1000 population Health status of Panchayath B is better than A
- 62. 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
- 63. 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
- 64. 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
- 65. 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
- 66. 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
- 67. 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
- 68. 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
- 69. 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
- 70. 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
- 71. 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
- 72. 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.
- 73. Statistical significance P value (hypothesis) 95% CI (Interval)
- 74. 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.
- 75. 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
- 76. Null hypothesis: “no difference in obesity among boys & girls in the classroom”
- 77. 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
- 78. Null hypothesis: “ no difference in EF among preterm babies treated with bCPAP &cCPAP.”
- 79. 95% CI 95%CI= Mean ‡1.96SD(2SD) = Mean ‡ 2SE 1) 100 children attending pediatric OP. mean wt=15kg SD=2 95%CI =?
- 80. 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.
- 81. Measures Of Risk case control study- Odds ratio Cohort study -RR,AR
- 82. Chi-Squared (χ2) Test Chi-Squared (χ2) Formula Not applicable in small samples If fewer than 5 observations per cell, use Fisher’s exact test
- 83. BREAK
- 84. 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
- 85. Correlation Source: Harris and Taylor. Medical Statistics Made Easy
- 86. Correlation Perfect Correlation Source: Altman. Practical Statistics for Medical Research
- 87. 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.
- 88. 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.
- 89. 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)
- 90. 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.
- 91. 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.
- 92. Survival Analysis Source: Altman. Practical Statistics for Medical Research
- 93. Kaplan-Meier Curve Source: Wikipedia
- 94. 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.
- 95. 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
- 96. 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.
- 97. True disease state vs. Test result not rejected rejected No disease (D = 0) specificity X Type I error (False +) α Disease (D = 1) X Type II error (False -) β Power 1 - β; sensitivity Disease Test
- 98. Specific Example Test Result Pts withPts with diseasedisease Pts withoutPts without the diseasethe disease
- 99. Test Result Call these patients “negative” Call these patients “positive” Threshold
- 100. Test Result Call these patients “negative” Call these patients “positive” without the disease with the disease True Positives Some definitions ...
- 101. Test Result Call these patients “negative” Call these patients “positive” without the disease with the disease False Positives
- 102. Test Result Call these patients “negative” Call these patients “positive” without the disease with the disease True negatives
- 103. Test Result Call these patients “negative” Call these patients “positive” without the disease with the disease False negatives
- 104. Test Result without the disease with the disease ‘‘‘‘-’’-’’ ‘‘‘‘+’’+’’ Moving the Threshold: right
- 105. Test Result without the disease with the disease ‘‘‘‘-’’-’’ ‘‘‘‘+’’+’’ Moving the Threshold: left
- 106. TruePositiveRate (sensitivity) 0% 100% False Positive Rate (1-specificity) 0% 100% ROC curve
- 107. 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
- 108. 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
- 109. 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
- 110. FOREST PLOT 114
- 111. 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 115
- 112. 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. 116
- 113. 117
- 114. 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
- 115. 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.
- 116. PICOT Used to test evidence based research Population Intervension or issue Comparison with another intervention Outcome Time frame

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