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Introduction to Biostatistics in medical research

Biostatics and parametric and nonparametric test -its use in reserach

Health & Medicine◦
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Basics in Bio-statistics
2 Basics & Distribution of Data Contents • Introduction • Application and uses • Limitations • Branches • Data • Types • Scales • Collection • Presentation DOMAIN 1
3 Basics & Distribution of Data Introduction – Statistics defined as the science of Collection, organisation, presentation, analysis and interpretation of numerical data.” Concise definition by Croxton and Cowden DOMAIN 1
4 Introduction • Health statistics • Medical statistics • Vital statistics Basics & Distribution of Data DOMAIN 1
5 Application and Uses of Biostatistics Association between causative factors and effects by comparison with statistical tests of significance Evaluation of preventive and therapeutic strategies Utilization of services Prediction of events Basics & Distribution of Data DOMAIN 1
6 Application and Uses of Biostatistics Physiology and anatomy • To find difference between means and proportions between 2 groups of populations or at 2 different places or in different periods Pharmacology • To find the action of a drug • To compare action of 2 different drugs or 2 successive dosages of the Basics & Distribution of Data DOMAIN 1
7 Application and Uses of Biostatistics To compare the efficacy of a particular drug, operation or line of treatment To find an association between 2 attributes To find signs and symptoms of a disease To test usefulness of In epidemiological studies Evaluation of measures Basics & Distribution of Data DOMAIN 1
8 Limitations of statistics in health science  How representative is your sample?  How well the statistics is suited to the study of qualitative phenomena?  Statistics does not study individuals  Statistical Laws are not exact Basics & Distribution of Data DOMAIN 1
Branches of Statistics 9 Basics & Distribution of Data DOMAIN 1
10 Types of Data Basics & Distribution of Data Wayne W Daniel. Basic Concepts and Methodology for the Health Sciences, 9th Edition. DOMAIN 1
11 08/05/2025 11 Nominal scale Ordinal scale Interval scale Ratio Scale Scales of Data/ Measurements Basics & Distribution of Data DOMAIN 1
12 Collection & Presentation of data • Introduction • Collection of data primary data Secondary data • Methods of collection of data • Presentation of data Qualitative data Quantitative data • Summary • Conclusion • References FAQs: Collection and presentation of data; Presentation of quantitative data Basics & Distribution of Data DOMAIN 1
Methods of data collection Secondary Sources Primary Sources Documents oGovt publications oEarlier research oCensus oPersonal records oClient histories oService records Observation Participant Non-participant Interviewing Structured Unstructured Questionnaire Mailed Collective Basics & Distribution of Data Wayne W Daniel. Basic Concepts and Methodology for the Health Sciences, 9th Edition. Wiley India. New Delhi; 2011. DOMAIN 1 13
14 Presentation of Data Qualitative/ discrete / counted data Bar diagram Pie/sector diagram Pictogram Map diagram / spot diagram Quantitative/ continuous / measured data Histogram Frequency polygon Frequency curve Line chart/ graph Cumulative frequency diagram Scatter / dot diagram Basics & Distribution of Data DOMAIN 1
Qualitative Data • Bar Charts/ Diagram – Simple – Compound - To compare between two or more sets of related groups. – Proportional - To compare proportion of components present in 2 or more groups. • Pie Chart - Class frequency/total observation x 360 • Pictogram / Spot Diagrams 15 Presentation of data Basics & Distribution of Data DOMAIN 1
Quantitative Data Histogram Frequency Polygon Frequency Curve Line Graph 16 Basics & Distribution of Data Presentation of data DOMAIN 1
17 Tables Objectives Nature of enquiry Coverage Reference table Summary table Original or primary Derived or derivative table Simple table Complex table Presentation of data Basics & Distribution of Data DOMAIN 1
18 Characteristics of table • 1st step ….. Before analysis/interpretation • Rules for frequency distribution table – Each table should contain title and no-Table1,Table2…. – Headings …rows & columns clear n concise – Units of measurements specified – Source of data mentioned – Additional Information - end note Presentation of data Basics & Distribution of Data DOMAIN 1
19 Tabular representation in statistics I. Frequency distribution table • Grouped frequency • Relative frequency • Cumulative frequency II. Contingency Table III. Cross Tabulation Presentation of data Basics & Distribution of Data DOMAIN 1
20 Descriptive Statistics Contents • Measures of central tendency • Measures of frequency • Measures of dispersion or variation • Measures of position DOMAIN 2
21 Central Tendency Mean Median Mode Weighted mean Harmonic mean Geometric mean Descriptive Statistics DOMAIN 2 Unimodal Bi Modal
22 Mean (Arithmetic Mean) 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14 Mean = 5 Mean = 6 Descriptive Statistics DOMAIN 2 Harmonic mean - (either too big or too small) Weighted mean: When each observation carries different levels of importance. Geometric Mean - Exponential data
23 Median • Robust measure of central tendency • Not affected by extreme values • In an ordered array, the median is the “middle” number – If n or N is odd, the median is the middle number – If n or N is even, the median is the average of the two middle numbers 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14 Median = 5 Median = 5 Descriptive Statistics DOMAIN 2
24 Mode • The term mode originates with Karl Pearson in 1895. • Not affected by extreme values • Used for either numerical or categorical data • There may be no mode • There may be several modes 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mode = 9 0 1 2 3 4 5 6 No Mode Descriptive Statistics DOMAIN 2
25 Measures of Variation Variance/ Dispersion Variance Standard Deviation Population Variance Sample Variance Population Standard Deviation Sample Standard Deviation Range Interquartile Range Descriptive Statistics DOMAIN 2
26 MEASURES OF FREQUENCY FREQUENCY Count Proportion Ratio Rate Risk Descriptive Statistics DOMAIN 2
27 MEASURES OF POSITION POSITION Percentile , Deciles, Quartiles Hinges Five number summary Box and Whiskers Plot Outliers Descriptive Statistics DOMAIN 2
28 Normal Distribution Curve • Bell shaped Gaussian distribution • Mean = median = mode • Symmetrical about the mean. • Area Under the curve is 1 ( 100%) • Uni- modal (only 1 mode). • For each value of X, here is a corresponding value of Y • Theoretically, no matter how far in either direction the curve extends, it never meets the x axis, but it gets increasingly closer to the x axis. Descriptive Statistics DOMAIN 2
29 Significance of Normal Curve . Empirical Rule : most of the data falls under mean + 2 SD. Data following the normal curve – parametric analysis Descriptive Statistics DOMAIN 2
30 Skewness • Skewness is a measure of the asymmetry of the probability distribution about its mean. Descriptive Statistics DOMAIN 2
31 Kurtosis Kurtosis is a descriptor of the shape of a probability distribution. Descriptive Statistics DOMAIN 2
32
33 Hypothesis Testing DOMAIN 3
34 Hypothesis Testing Contents • Rationale • Errors • Steps & Process • Tests of Significance • Parametric • Non-parametric • Individual tests • Bivariate • Multivariate DOMAIN 3
35 Introduction & Rationale of Hypothesis Testing • It is considered as one of the principal instrument in the research • A statistical procedure by which one can conclude if the observed results from the sample is due to chance or not. • In social science, it enables us to make probability statement and generalization to the population. DOMAIN 3
38 Steps in Statistical Hypothesis Testing NEYMAN-PEARSON HYPOTHESIS TESTING MODEL Step 1: State the hypotheses. Step 2: Set the criteria for a decision. Step 3: Compute the test statistic. Step 4: Make a decision. DOMAIN 3
39 Non Critical Region Critical Region Critical Region Critical Value Critical Value Two-Tailed CV=-1.65 CV=1.65 α=0.10 α/2=0.05 α/2=0.05 Process of Statistical Hypothesis Testing • Step 1: State the Null Hypothesis H0:μ1=μ2= =μ ⋯ k, for k levels of an experimental treatment. • Step 2: State the Alternative Hypothesis • Step 3: Set α • Step 4: Collect Data • Step 5: Calculate a test statistic • Step 6: Construct Acceptance / Rejection regions DOMAIN 3
40 • Step 7: Based on steps 5 and 6, draw a conclusion about H0 If the calculated value < table value accept the null hypothesis If the calculated value > table value reject the null hypothesis So the decision rule is as follows: If the p-value obtained is less than α, then Reject H0 and accept HA. Process of Statistical Hypothesis Testing DOMAIN 3
Tests of significance Parametric test Non Parametric test z-test , t- test, ANOVA Mann-Whitney U test, Wilcoxon signed rank test, Kruskal-Wallis ANOVA test Fried man test Tests of Significance Chi- Square test Correlation RegressionAnalysis DOMAIN 3
42 Parameters Parametric tests Non Parametric Tests Distribution of Data Normally Distributed Non Normal Distribution Sample selection Randomized Non Randomized Type of Data Quantitative Qualitative Measurement Scales Ratio ; Interval Nominal ; Ordinal Tests of Significance DOMAIN 3
45 Parametric Tests Parametric statistics is a branch of statistics which assumes that sample data comes from a population that follows: • A normal distribution • Fixed set of parameters • Randomly selected • Quantitative in nature Tests of Significance DOMAIN 3
46 Parametric tests Bivariate Z test t test Tests of correlation Multivariate ANOVA Regression analysis Tests of Significance DOMAIN 3
47 Parametric tests Bivariate Z test t test Tests of correlati on Multivariate ANOVA Regressio n analysis Tests of Significance DOMAIN 3 Bivariate Weight 2 Groups-Gender Gp1- Boys Gp 2-Girls
48 Parametric tests Bivariate Z test t test Tests of correlati on Multivariate ANOVA Regressio n analysis Tests of Significance DOMAIN 3 Multivariate
50 Student’s t test The t distributions were introduced by William Sealy Gosset (1876-1937) in 1908. The t-test is one type of inferential statistics used to determine whether there is a significant difference between the means of two groups and to know if those differences could have happened by chance. Tests of Significance DOMAIN 3
51 Student’s t test Criteria for applying t test • The sample or samples must be randomly selected. • The data must be quantitative. • It can be used when sample size less than 30. • when the data is normally distributed. Tests of Significance DOMAIN 3
52 Classification of t Test t test Single sample t- test Independent / Un-paired t test Unequal variances Equal variances Paired t test Tests of Significance DOMAIN 3
53 t test Single sample t-test Independent / Un- paired t test Unequal variances Equal variances Paired t test DOMAIN 3 Single sample t- test 120/80
54 t test Single sample t-test Independent / Un- paired t test Unequal variances Equal variances Paired t test DOMAIN 3 Independent t test
55 t test Single sample t-test Independent / Un- paired t test Paired t test DOMAIN 3 Paired t test DMFT 1 year DMFT
56 Formula for t test: Where, X = sample mean Mu = hypothesised mean S= standard deviation N= sample size t = Student t value with n-1 degrees of freedom Tests of Significance DOMAIN 3
57 • Paired t Test (Paired Samples t Test / Dependent Samples t Test) ( Before-and-after observations on the same subjects ) – The dependent variable must be continuous (interval/ratio). – The observations are independent of one another. – The dependent variable should be approximately normally distributed. – The dependent variable should not contain any outliers. Tests of Significance DOMAIN 3
58 Chi square test • First used by Karl Pearson • Simplest & most widely used non-parametric test in statistical work. • The test of difference between the observed frequencies and the expected frequencies. • Written as χ2 . • USED FOR Categorical data Tests of Significance DOMAIN 3
59 Tests of Significance DOMAIN 3 Yes No No Yes Smoking
60 LUNG CANCER-YES LUNG CANCER-NO Total SMOKING-Yes A B SMOKING-No C D Total
61 Procedure of Chi-Square test 1. State null and alternate hypothesis. 2. Construct contingency table. 3. Note the frequencies observed (O) 4. Determine the expected number (E) Expected number (E) is obtained by : Row total x Column total Grand total Tests of Significance DOMAIN 3
62 YES NO Total Yes No Total E1 E2 E3 E4 χ2 = ∑ ( Oi – Ei )2 Ei
63 5. Calculate test statistics by χ2 = ∑ ( O – E )2 E 6. Calculated value of χ2 is compared with table value of χ2 for given degrees of freedom. 7. Reject H0 if calculated value is more than critical value. 8. Interpret, and make decision. 9. Draw conclusion Tests of Significance DOMAIN 3
64 3 unique functions of χ2 test 1. Test of association: (smoking & cancer, treatment & outcome of disease, vaccination & immunity) 2. Test of proportions: (compare frequencies of diabetics & non-diabetics in groups weighing 40-50kg, 50-60kg, 60-70kg & >70kg.) 3. The chi-square for goodness of fit: (determine if actual numbers are similar to the expected/theoretical numbers) Tests of Significance DOMAIN 3
67 Multivariate Analysis Introduction • Multivariate analysis consists of a collection of methods that can be used when several measurements are made on each individual or object in one or more samples. Application • To equalize research groups • To build causal models from observational studies • To create clinical indices Tests of Significance DOMAIN 3
68 Classification ANOVA • One Way ANOVA • Two way ANOVA • MANOVA • ANCOVA • MANCOVA Regression Analysis • Linear Regression • Complex linear regression • Logistic Regression Others • Functional Analysis • Discriminant analysis • Structural Equation Model • Path Analysis • ……. Tests of Significance DOMAIN 3
69 ANOVA ( Analysis of Variance)  Statistical technique specially designed to test whether the means of more than 2 quantitative populations are equal.  Developed by Sir Ronald A. Fisher in 1920’s.  ANOVA test tells us whether we have an overall difference between our groups but it does not tell us which specific groups differed.  So we have to go for post hoc analysis. Tests of Significance DOMAIN 3
70 ANOVA One way ANOVA Three way ANOVA Effect of SES on BMI Two way ANOVA Effect of age & SES on BMI Effect of age, SES, Diet on BMI ANOVA with repeated measures - comparing >=3 group means where the participants are same in each group. E.g. Group of subjects is measured more than twice, generally over time, such as patients weighed at baseline and every month after a weight loss program
Post Hoc Analysis 74 Tests of Significance DOMAIN 3 • Most commomnly used post hoc tests 1. Least Significant Difference 2. Bonferroni approach 3. Scheffe’s method 4. Tukey’s procedure • Other post hoc tests 1. Tukey Kramer 2. Dunnett 3. Dunn 4. Holm
75 REGRESSION • The Regression Analysis is a technique of studying the dependence of one variable (called dependant variable), on one or more variables (called independent variable), with a view to estimate or predict the average value of the dependent variables in terms of the known or fixed values of the independent variables. Tests of Significance DOMAIN 3
76 Why Regression ?? • To find the significant relationships between dependent variable and independent variable. • To determine the strength of impact of multiple independent variables on a dependent variable. • To compare the effects of variables measured on different scales Tests of Significance DOMAIN 3
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79 Types of Regression • Linear regression : One outcome variable ( Continuous) Predictor Variable(Continuous, Discrete) i. Simple Linear regression ii. Multiple Linear regression • Logistic regression : One Outcome Variable - Dichotomous Multiple Predictor variables – ( Continuous, discrete, interval, Ratio) • Polynomial regression • Stepwise regression • Ridge regression Tests of Significance DOMAIN 3
Summary Level of Measurement Sample Characteristics Correlation 1 Sample 2 Sample K Sample (i.e., >2) Independe nt Dependent Independent Dependent Friedman’s ANOVA Parametric (Interval & Ratio) z test or t test t test between groups t test within groups 1 way ANOVA between groups 2 way ANOVA (within or repeated measure) Pearson’s Rank or Ordinal Mann Whitney U Wilcoxon Signed Ranks Kruskal Wallis H Spearman’ s rho Tests of Significance DOMAIN 3
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82 Sample Size Estimation Contents • Introduction • Rationale • Importance • Approaches • Factors affecting the sample size • Power of the study • Methods of sample size estimation • Conclusion DOMAIN 4
83 • Introduction Sample size estimation helps us to meticulously arrive at a number, which is feasible & optimum to achieve the desired effect. Sample Size Estimation DOMAIN 4
84 • Rationale Sample Size Estimation Define the problem Define the exposure/ observation Meticulously sort out Inclusion / Exclusion criteria Take care of possible variables Study Design – Best possible methodology Adequate sample size DOMAIN 4
85 Importance – Expected magnitude of scientific significance, to be also statistically significant – Economic reasons – Undersized/ Oversized samples – Critical Issue - Experiments involving humans , animal trial . Sample Size Estimation DOMAIN 4
86 Sample Size Estimation By statistical Analysis approach Confidence interval approach Cost Basis approach Conventional approach Approaches DOMAIN 4
87 Factors affecting sample size calculation Study design , Variables Outcome Minimum Detectable difference Power Other paramaters Sample Size Estimation DOMAIN 4
88 • Study design , Variables Sample Size Estimation Factors Study Designs Sample size Descriptive study Designs : Experimental : More samples Lesser Pre & post studies ½ the number than those studies with the control group Cross-Over designs 1/4th number required compared to a control group Non-randomised 20% > than randomised designs Studies with one tailed 20% < than two tailed Additional 10-20 % subjects are required to allow adjustment to other factors. DOMAIN 4
89 • Outcome – 3 possible categories of outcome i. Binary ii. Mutually exclusive categories iii. Continuous response Sample Size Estimation Factors DOMAIN 4
90 • Minimum detectable difference Effect Size Expected difference/ relationship between two independent variables. If available , it may be useful to use the effect size found from prior studies. If not - Literature review, logical assertion and conjecture. Sample Size Estimation Factors DOMAIN 4
91 • Power of the study – Statistical power means the probability of finding a real effect (of the size that you think is clinically important) – Ideally study should have high power – High chances of detecting the difference if present – The ideal power > 80% Sample Size Estimation Factors DOMAIN 4
92 Power of the study In research – 2 objectives 1. Before data collection 2. After data analysis – when the data is non-significant Sample Size Estimation Factors DOMAIN 4
93 The relationships among power : Sample Size Estimation Factors Parameters Power of the study Variation in the Outcome ( SD) Significance Level Difference ( effect) to be detected One tailed vs. two tailed tests Power is greater in one –tailed than two tailed. DOMAIN 4
94 • Withdrawal, missing data and losses to follow-up – Willingness – Invalid response, technical problems, attrition. • Cohort studies – N = N/1-q, where q is the proportion of attrition and is generally 10% Sample Size Estimation Factors DOMAIN 4
95 • Methods of sample size estimation – BASED ON • Type of study – Observational; Analysis – Survey type – one sample mean , proportion – Between two means , association – Using correlation coefficient, Odds Ratio…. • Parameters – Type of statistical tests to be used. – Alpha value, Power (1- beta value), effect size, mean difference value. Sample Size Estimation DOMAIN 4
96 Example: Sample size estimation for proportion in survey type of studies P - Prevalence of the event E ( Precision)- Margin of error – 10 % of prevalence Z - Level of significance for two tailed hypothesis i.e 95% C I , 5 % - Level of significance – 1.96. Sample Size Estimation DOMAIN 4
97 FACTOR MAGNITUDE REQUIRED SAMPLE SIZE P VALUE OR ALPHA- LEVEL Small Large Large Small POWER Small Small Large Large EFFECT Small Large Large Small ALTERNATIVE HYPOTHESIS One - tailed Small Two – tailed Large Sample Size Estimation DOMAIN 4
98 Conclusions:  Major step in the design of a research study.  Appropriate sized sample = generalize the results.  Inadequately sized studies often result in investigator’s Unrealistic assumptions. Suresh K P, Chandrashekhar S. Sample size estimation and power analysis for clinical research studies J Hum Reprod Sci 2012: 5:7-13. DOMAIN 4 Sample Size Estimation
99 • Other Domains - Short Notes – Agreement & Diagnostic Tests – Vital Statistics – Bimodality – Errors – Odds Ratio – Variables in Research
100 Contents – Diagnostic tests and agreement • INTRODUCTION • SCREENING AND DIAGNOSTIC TESTS DIAGNOSTIC TESTS: – OBJECTIVES – USES – PARAMETERS – WHAT IS A GOLD STANDARD? – EVALUATION OF A DIAGNOSTIC TEST – CUT- OFF POINT - AGREEMENT: - FACTORS AFFECTING AGREEMENT - METHODS OF ANALYSIS OF AGREEMENT: - OVERALL PERCENT AGREEMENT - KAPPA TEST RATIO - WEIGHTED KAPPA
101 References 1. Methods in biostatistics for medical students and research workers by BK Mahajan, 9th edition. 2. Biostatistics for oral health care by Jay S. Kim, Ronald J. Dailey 3. Research methodology methods and techniques by C.R. Kothari, 4th edition. 4. Introductory statistics by Prem S. Mann, 7th edition. 5. Medical Statistics at a Glance by Aviva Petrie, 3rd edition.
102 “He who accepts statistics indiscriminately, will often be duped unnecessarily. But he who distrusts statistics, indiscriminately will often
103 . Thank You. ….