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Introduction to Bio-Statistics

Introduction to Bio-Statistics. Dr. N Srinivasa Murthy, PhD, FAMS, FSMS. Professor and Research Director, DRP, GEF(M) and Professor and Research Coordinator, MS Ramaiah Medical College and Hospitals, Bangalore-560054 nsmurthymsrmc@gmail.com. Lessons to be learnt.

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Introduction to Bio-Statistics

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  1. Introduction to Bio-Statistics Dr. N Srinivasa Murthy, PhD, FAMS, FSMS. Professor and Research Director, DRP, GEF(M) and Professor and Research Coordinator, MS Ramaiah Medical College and Hospitals, Bangalore-560054 nsmurthymsrmc@gmail.com

  2. Lessons to be learnt • To understand importance of Bio-Statistics in Bio-medical studies • Steps in the design of bio-medical research studies. • Sample size estimation • Presentation and interpretation of data • Books for reference

  3. ….. Biological Sciences Statistical Science

  4. What is Statistics? • Lay man: Impression about numerical facts. : Scientific worker ?

  5. Science of Statistics deals with: Scientific manner : • Methodology of collection, compilation, analysis and meaningful interpretation of numerical facts. • Analysis of variability present in the observations (variation is a rule rather than an exception) • Subjecting the factual descriptions to objective tests to validate their reliability • Understanding the contribution through model building-risk factor models, prognostic factors, etc.,

  6. Ex. Numerical facts • Pulse rate, • Haemoglobin percentage • Birth weight of a new born child. • Creatinine levels, WBC, RBC, • Odds ratio, relative risk, Attributable risk, • Five year survival rate, • Disease prediction models • Risk scores for classifying persons likely to develop CVD, Br. Cancer, etc. , etc.

  7. Birth weight of new born child-Affected • Gestation week • Nutritional status of a mother • Parity, No. ANCs attended, • Co-morbidities etc., etc., Affected to a large extent-Biological, Social, environmental, genetic factors, How to segregate and assess the importance? Analytical statistical Procedures, Cause and effect

  8. Statistical methods helps in biomedical studies - to take care of • Control of Bias • Evaluating the role of chance factor • Evaluating the role of confounding

  9. CONTROL OF BIAS • Careful study design • Appropriate Choice of study of population • Appropriate methods of data analysis • Appropriately defining sources of exposure and disease information • Meticulous conduct of study.

  10. How to measure the chance factor? Evaluating the role of chance factor • Scientific assessment of random variability is predominantly done by tests of statistical significance. • p-value • Deals with the question of whether an observed difference between the sample estimates is due to chance or a real effect

  11. Control of confounding- • Multivariate statistical analysis

  12. Basic steps in formulation of research protocol • i. Definition of a research problem • ii. Formulation of objectives & hypothesis • iii. Methodology of research & study design • Iv. Selection of variables • v. Designing tools for data collection • vi. Def. study population, sample, controls, inclusion & exclusion criterion, adequate sample size and time coverage • vii. Analytical methods of data collection • viii. Various sources of error & rectification

  13. Bio-medical research Experimental Observational Provide rates. Defining population is important Provide association between variables. Defining population is not important Intervention Prophylactic Therapeutic effectiveness of treatment effectiveness of vaccinee Effectiveness interventions Prevalence or incidence Cause and effect Ethical principles Cross-sectional study: observed at one point in time Case-control study Backward in time Longitudinal study: observed over a period of time Cohort study Forward in time Sequential Non-sequential FIG.. Types of research studies

  14. Sample size estimation • One of the most frequently asked questions at the time of planning of any research study is: • how large a sample do I need ? • for a specific research study.

  15. Sample size consideration • Constraints - on small numbers studied. • Sample size must be decided based on statistical methods. • Adequate statistical power should be present.

  16. Example • Treatment efficacy once a week versus once every 3 weeks cisplatin chemo-radiation for locally advanced head and neck cancer: • Loco-regional control (LRC) once a week at the end of 2 year =58.5%, • (LRC) once every 3 weeks at the end of 2 year :=73.5%. • Experimental research, to utilise for patient care &publish • To compare the efficacy and safety

  17. NEED- Why Sample size calculation • The main idea behind the sample size calculations is: • to have a high chance (Prob.) of detecting a statistically significant, a worthwhile effect if it exits, _ Power of the study False negative conclusion (beta error) 10-20% • and thus to be reasonably sure that no such benefit exists if it is not found in the trial. False positive conclusion (Alpha error) <=5%

  18. Types of statistical Errors

  19. The greater the power of the study, the more sure we can be but greater power requires a larger sample. • It is common to require a power of between 80% and 90%. A power of 90% means that the investiga­tor has a 10% chance of accepting the null hypoth­esis, that there is no difference, when there is really a difference of a specified size between the rates of the two treatments.

  20. Sample SIZE -Too small? • If the number of observations is too few, the investigator may not have enough to test the hypothesis • A study with a sample that is too small will be unable to detect clinically relevant treatment differences.

  21. Requirements for estimation of Size of the sample • Approximate idea of the estimate of the parameter under observation. • Variability of this parameter from unit to unit in the population. • Desired accuracy of the estimate of the parameter • Prob. level within which the desired precision of estimates • Availability of the experimental material, resources and other practical considerations

  22. Presentation and interpretation of data

  23. Basic methods of Presentation & analysis of data • Presenting through tables • Graphical presentation • Measures of central tendency • Measures of dispersion • Probability and standard distributions-Normal distribution • Sampling methods, • Sampling variation and tests of significance • Correlation and regression, Multivariate methods, etc.

  24. Tabulation of data • Descriptive Statistics: • Central tendency and dispersion • Probability distributions: • Normal Distribution • Sampling Variation Analytical Statistics: • Tests of significance • Comparison of Means • Comparison of Proportions

  25. How to summarize my results through descriptive tables • Raw data as recoded in a proforma/records will not be of any much help in understanding their meaning. • A preliminary and convenient way of presentation of data is to arrange them in the form of tables.

  26. A study was carried out to test the hypothesis that intramuscular and iron therapies during pregnancy are equally effective in improving various iron variables. • The objective was (i) to compare the efficacy of 3 intramuscular doses (250mg each) of iron dextran with that of 100 consecutive days of 100 mg Fe given orally in treating pregnancy anemia. • (ii) the study also attempted to asses the safety and complications of the 2 treatments. • Am J ClinNutr 2004, 116-22, A Prospective , partially Randomized study…..pregnant women. Sharma JB,….Murthy NS.

  27. Sample of pregnant mothers Hb measurements

  28. Distribution of hemoglobin concentration in the 2 groups before and after treatment

  29. Birth outcomes in the 2 groups

  30. Statistical Methods Estimation Testing of Hypothesis Point Estimation Interval Estimation Parametric Non-parametric

  31. Point and interval estimates

  32. Measures of Central Tendency For Quantitative data: Mean which is mostly arithmetic average Even though there are other averages Median which is the central value of observations when they are arranged in ascending or descending order, Used when there are extreme values of observations Mode is the value of the variable most commonly occurring in the data

  33. For Qualitative, categorical, nominal data: Proportions or percentages Odds ratios Relative risk

  34. Common measures of Dispersion Range to indicate the Minimum & Maximum values of data Percentile to indicate the value of the variable covering certain percent of observations If we say 75th Percentile, it is the value of the variable which covers first 75 % of the observations

  35. Standard deviation ( S.D.) Best measure of variability of observations Calculated as the square root of Variance, which is the average of squared differences of each observation from the mean S.D. is used in almost all other statistical calculations

  36. Blood index values at recruitment and at term in the 2 groups

  37. Co-efficient of Variation ( C.V.) Used to compare the variability between different groups measured in different units Calculated as C.V. = (Standard Deviation x 100 ) / Mean

  38. Interval Estimates Confidence interval Confidence intervals gives a range for the statistical parameter,indicating that the true value of the parameter is contained in the range with a certain confidence 95% confidence interval of mean gives a range which indicates the true value of the mean is within the range with 95% confidence

  39. SAMPLING VARIATION Variation in Sample estimates, even if the samples drawn are from the same population -Chance factor - Random Variability

  40. Question???? The clotting time (seconds) of a sample of 25 individuals are as follows: 20, 21, 31, 42, 32, 10, 22, 23 26 19, 18, 21, 38, 27, 24, 27, 44, 59, 62,45, 37, 44, 54, 29, 50

  41. Thus we observe variation in sample estimates even if samples are from the same population This variation in sample estimates is known as Sampling variation Measure of this Sampling variation is known as Standard Error Standard Error can be estimated from standard deviation obtained by a single sample

  42. Whenever observations are made on two or more samples it is necessary to understand whether the differences observed between the sample estimates are due to sampling variation or not Procedure adopted for this purpose is known as Tests of significance

  43. First we assume that the difference observed is because of sampling variation • For this we formulate a hypothesis known as Null Hypothesis • Null hypothesis is stated as the difference between the sample estimates is due to sampling variation

  44. Certain tests are applied to prove or disprove this null hypothesis • These tests provide an estimate of the probability of sampling variation causing the difference between the sample estimates i.e. Accepting the null hypothesis • P value-Probability level of accepting a null hypothesis is known as Level of significance

  45. How to measure the chance factor?

  46. Scientific assessment of random variability is predominantly done by tests of statistical significance. • p-value • Deals with the question of whether an observed difference between the sample estimates is due to chance or a real effect

  47. Tests of Significance provide an estimate of the Probability, P, Which helps us to conclude whether differences observed between the samples are attributable to sampling variation or otherwise If this Probability is P < 0.05, then we conclude that the difference between sample estimates notdue to random variability

  48. General procedure for testing of a hypothesis • Set up a null hypothesis suitable to the problem either in qualitative or quantitative terms. • Define the alternate hypothesis, if necessary • Calculate the suitable test statistics, t, 2, F etc using the relevant formula. • Determine the degrees of freedom for the test statistics. • Find out the probability level, P, from relevant tables corresponding to the calculated value of the test statistics and its degrees of freedom. • Generally, reject the null hypothesis, if P is less than or equal to 0.05

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