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BIOSTATISTICS
This document provides an overview of key concepts in biostatistics. It defines biostatistics as the application of statistical methods in the fields of biology, public health, and medicine. Some key points covered include: - The types of data: qualitative, quantitative, discrete, continuous - Descriptive statistics like mean, median, and mode - Inferential statistics like hypothesis testing and estimating parameters - Important statistical tests like t-tests, ANOVA, and chi-squared tests - Measures of diagnostic accuracy like sensitivity, specificity, and predictive values - The process of determining sample size for studies based on factors like confidence interval, power, and allowable error.
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Introduction slide with presenter information.
Definitions, types of data, variables, and the importance of statistics in medicine and public health.
Primary vs Secondary data, variables, and significance of qualitative and quantitative data.
Descriptive statistics summarizing data and inferential statistics for hypothesis testing.
Point and interval estimates, including confidence intervals, and steps in hypothesis testing.
Null and alternative hypotheses, basic terms related to hypothesis testing.
Discussion on parametric tests, normal distribution, and its properties.
Detailed features and significance of the normal distribution in data analysis.
Explanation of skewed data and the usage of non-parametric statistics.
Understanding p-values in hypothesis testing with an example study.
Case-control study methodologies and explanation of odds ratios and relative risk.
Sensitivity, specificity, and predictive values in the context of diagnostic tests.
Understanding positive and negative predictive values in diagnostic tests.
Reasons for sampling, methods, and types of samples.
Importance of calculating appropriate sample sizes for reliability in studies.
Examples of calculating sample sizes for qualitative and quantitative studies.
Thank you slide to conclude the presentation.
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BIOSTATISTICS
- 1. Murtaza KamalMurtaza Kamal Dec22, 2018Dec 22, 2018 murtaza.vmmc@gmail.commurtaza.vmmc@gmail.com 1
- 2. Definition ofbiostatistics Data and its types: Qualitative/ Quantitative Variable and its types Mean/ median/ mode Normal curve Sn/ Sp/ PV Sample and its types and calculation of sample size Points to be covered… 2
- 3. Science dealing withmethods of data collection, compilation, tabulation and analysis to provide meaningful and valid interpretation 3
- 4. Bio-statisticsBio-statistics Application of statisticalmethods in field of biology, public health and medicine 4
- 5. Quality ofclinical & health planning decision depends on Quality of information on which they are based • Medicine: A science with chance playing very significant role • Statistics help to quantify contribution of chance and helps individual clinician make valid diagnostic, prognostic or therapeutic decisions • Helps programme managers+ policy planners to plan, monitor+ evaluate public health initiatives Remember this… 5
- 6. Datum: Latin "fact" Collectionof processed information Sources of Data: Primary Data : Collected and recorded by investigator/s themselves by observation, interviews or measuring instruments usually systematically and for defined purposes Secondary Data : Collected by somebody else or for other purposes e.g. information derived from hospital Data 6
- 7. • Choice ofstatistical tests to be used depend on kind of variable studied • An attribute, quality, characteristic or property of persons or things being studied that can be quantitatively measured or enumerated • Varies from person to person or from time to time in same person • Ex: Height, weight, age , gender, blood pressure, pulse rate, smoking status Variable 7
- 8. A variablethat is manipulated or applied by investigator or explains outcome Eg: Maternal age, age at marriage, spacing between successive pregnancies, pre-pregnancy weight, weight gain during pregnancy Independent (stimulus/ explanatory) variable 8
- 9. • Resulting responseor behaviour that is observed when exposed to independent variable e. g. Independent Dependent Maternal age Birth weight Birth spacing Birth weight PIH Perinatal mortality Dependent (Outcome/ response) variable 9
- 10.
- 11. Nominal: This variablehas mutually exclusive categories and unordered E.g. Blood group: A, B, AB, O, Marital status: Unmarried, Married, Divorced, Widowed Ordinal: This variable has mutually exclusive categories and ordered E.g. Disease severity: Mild, Moderate, Severe, Qualitative data 11
- 12. Quantitative data Discrete: Oftenrepresents counts e.g. Number of children Number of times admitted to hospital in the last 5 years Continuous: Can take any value within a range of values e.g. Height in cm Weight in kg Distance from home to work in km 12
- 13. Importance of datatype Type of data: Critically important in determining which methods of analysis will be appropriate and valid 13
- 14. Descriptive statistics Describes basic features of data in a study Provide summaries about sample Inferential statistics Investigate questions, models, and hypotheses Infer population characteristics based on sample Make judgments about what we observe Types of Statistics 14
- 15. Descriptive Statistics Univariate analysis(one variable at a time) •Qualitative Data: • Proportions or percentages •Quantitative Data: • Central tendencies (Mean, Median, Mode) • Measures of dispersion (Range, Standard deviation, Coefficient of variation, Percentiles, interqurtile range) 15
- 16. Two approaches 1. EstimatingParameters: Process of using sample information to draw conclusions about the value of a population parameter e.g., Proportion, mean, SD, Correlation 2. Testing Hypothesis Inferential Statistics 16
- 17. 1. Point Estimates: Proportion, mean, SD, correlation 2. Interval Estimates: Confidence Intervals: Define an upper limit & lower limit with an associated probability Ends of confidence intervals Confidence limits 95% confidence interval – 95% probability of containing the population mean 99% confidence interval – 99% probability of containing the population mean Wider/ greater range of values must be included for greater confidence Estimating Parameters 17
- 18. To permitgeneralizations from a sample to the population from which it came Steps in Hypothesis Testing 1. State the research question in terms of Statistical hypothesis 2. Decide on appropriate test statistic 3. Select level of significance 4. Determine value the test statistic must attain to be declared significant 5. Perform calculations 6. Draw and State conclusions Hypothesis Testing 18
- 19. Null hypothesis, Ho Statement that no difference or relationship If related then Ho is rejected If unrelated then Ho is retained (not accepted!!) Alternative hypothesis, Ha Disagrees with Ho Step 1: State the research question in terms of Statistical hypothesis 19
- 20. Statistics whoseprimary use is in testing hypotheses are called test statistics Parametric & non-parametric tests Step 2: Decide on appropriate Test Statistic 20
- 21. • Some assumptionsare to be met before a particular test of significance can be applied to a set of data • Sample measurements drawn from normally distributed population of measurements in a random manner • Parametric tests are Student 't' test (paired and unpaired), F test for analysis of variance, correlation and regression analyses Parametric Statistics 21
- 22. Many naturallyoccurring events follow a pattern with: Many observations clustered around the mean Few observations with values away from the mean This bell-shaped curve was named Normal distribution by a mathematician Gauss Normal distribution 22
- 23. Normal distribution The symmetrical clustering of values around a central location Normal curve The bell-shaped curve that results when a normal distribution is graphed Normal distribution 23
- 24. Normal Distribution Developedby Karl F. Gauss (1777-1855) ‘Gaussian distribution’ Called ‘normal’ because many continuous variables in biology and other sciences follow this particular distribution 24
- 25. The Normal Distribution Properties 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 -3 -2.5-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 x f(x)1- Symmetric about mean 25
- 26. The Normal Distribution Properties 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 -3 -2.5-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 x f(x)2- Mean, median and mode coincides Mean = Median = Mode 26
- 27.
- 28. Skewed (or Asymmetric)Data When the left and right-side sides of a frequency distribution do not approximate mirror images, the data are said to be skewed or asymmetrical Curve A Curve B negative skew positive skew Mean>Median>Mode Mean<Median<Mode 28
- 29. • Suitable alternativeparticularly when data is in form of ranks or counts • Chi- squared test: MC employed nonparametric test • Wilcoxan Rank Sum, Mann Whitney U or median test , Kruskal-Wallis 1-way and Friedman 2-way analysis of variance Non-Parametric Statistics or Distribution Free Methods 29
- 30. p value:Related to hypothesis test Probability that the observed result is due to chance alone Calculated after test has been performed Small p-value (typically ≤ 0.05) indicates strong evidence against null hypothesis, so you reject null hypothesis P = 5% is not a rule written on stone More generous (p=0.1) More strict (p =0.01) Step 3: Select the level of significance for the statistical test 30
- 31. Example Study of theeffects of anticonvulsant therapy on serum calcium concentration in the elderly. • group of treated patients • group of untreated patients Outcome variable: serum calcium concentration Independent variable: Anticonvulsant therapy Null Hypothesis: Both the groups (treated and untreated) have same mean serum calcium conc. Test of Significance : . t test 31
- 32. Direction of inquiry Onsetof study Time Exposed Unexposed Cases Controls Exposed Unexposed Case-control study (retrospective) 32
- 33. Cases Controls Total Ate Raw Yes 17 (a) 7(c) 24 Hamburger No 20 (b) 26 (d) 46 Total 37 33 70 Cross Product Ratio 2.3 )7)(20( )26)(17(^ == × × = cb da OR Controls Cases ddsO ddsO ^ ^ = Case-control study: Outbreak of Diarrheal Disease at a Resort Club 33
- 34. Odds ratiois a ratio of two odds Relative risk is a ratio of two probabilities ODDS RATIO & RR 34
- 35.
- 36. THREE KEY MEASURESOF VALIDITY 1. SENSITIVITY 2. SPECIFICITY 3. PREDICTIVE VALUE 36
- 37. True Disease Status Screening/ Diagnostic Test PositiveNegative Total Positive True Positives (TP) False Positives (FP) TP+FP Negative False Negatives (FN) True Negatives (TN) FN+TN Total TP+FN FP+TN TP+FP+FN+TN Outcomes of a Screening/ Diagnostic Test 37
- 38. 38 What is usedas a “gold standard” 1. Most definitive diagnostic procedure e.g. microscopic examination of a tissue specimen 2. Best available laboratory test e.g. polymerase chain reaction (PCR) for HIV virus 3. Comprehensive clinical evaluation e.g. clinical assessment of arthritis
- 39. 39 True positive True negative False positive False negative Sensitivity = True positives Allcases a + c b + d = a a + c Specificity = True negatives All non-cases = d b + d a + b c + d True Disease Status Cases Non-cases Positive Negative Screening Test Results a d b c
- 40. 40 True Disease Status CasesNon-cases Positive Negative Screening Test Results a d 1,000 b c 60 Sensitivity = True positives All cases 200 20,000 = 140 200 Specificity = True negatives All non-cases = 19,000 20,000 1,14 0 19,060 140 19,000 = = 70% 95%
- 41. 41 Interpreting test results: predictivevalue Probability (proportion) of those tested who are correctly classified PPV = Cases identified /all positive tests NPV = Non-cases identified /all negative tests
- 42. Positive predictivevalue: Probability that subjects with a positive screening test truly have disease Negative predictive value: Probability that subjects with a negative screening test truly don't have disease 42
- 43. 43 True positive True negative False positive False negative PPV = True positives Allpositives a + c b + d = a a + b NPV = True negatives All negatives = d c + d a + b c + d True Disease Status Cases Non-cases Positive Negative Screening Test Results a d b c
- 44. 44 True Disease StatusCases Non-cases Positive Negative Screening Test Results a d 1,000 b c 60 PPV= True positives All positives 200 20,000 = 140 1,140 NPV = True negatives All negatives = 19,000 19,060 1,14 0 19,060 140 19,000 = = 12.3% 99.7%
- 45. 45 Positive predictive value, Sensitivity,specificity, and prevalence Prevalence (%) PV+ (%) Se (%) Sp (%) 0.1 1.4 70 95 1.0 12.3 70 95 5.0 42.4 70 95 50.0 93.3 70 95
- 46.
- 47. Study populationare large: Not possible to meet all population members (Not feasible practically and costly) Ideally: Study everyone so that we can generalize a finding to study population Cannot study everyone due to limited time and resources If we cannot study everyone then we sample the population, but in manner so that we can generalize the findings Why Sampling? 47
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- 51. Sample Size Determination •To carry out any scientific study, MC asked question: What should be minimum sample size? • If sample is too small Fails to detect true difference •An exceedingly large sample size •Wastage of time and money •Will report tiniest relation/difference as significant • Sample size should be calculated at planning stage Neither too small nor too large 51
- 52. Need to knowfollowing: Estimated prevalence/ SD Confidence interval (95% CI) Power: Ability to find significance when two groups are really different (80%) Allowable error or precision (5-10%) Sample size calculation 52
- 53.
- 54. Sample Size forQualitative outcome variable P = Estimated prevalence (percentage) Q =1-P L = Allowable Error 2 4 L PQ n = 54
- 55. Definition P =Estimated prevalence (percentage) From pilot study, published papers, experience Q =1-P L = Allowable Error L and Q and P are in same unit 55
- 56. L; Allowable Error Suppose, the survey wants to estimate the true prevalence of a disease in population The estimate we get from the survey will be within +/- L% of the true prevalence - L +L 56
- 57. Example A surveyis to estimate prevalence of influenza virus infection in school kids Suppose the available evidence suggests that approximately 20% (P=20) of the children will have antibodies to the virus Assume the investigator wants to estimate the prevalence within 6% of the true value (6% is called allowable error; L) 57
- 58. Example The requiredsample size is n = (4 x 20 x 80) / (6 x 6) = 177.78 Thus approximately 180 kids would be needed for the survey 2 4 L PQ n = Note: population size not involved in the formula 58
- 59. Sample Size forEstimation of the Mean (Quantitative outcome variable) S = Standard Deviation of the parameter L = Allowable Error S and L are in the same unit The average we find in the survey will be within +/- L of the true 2 24 L S n = - L +L 59
- 60. Example Suppose aninvestigator has some evidence suggesting that the standard deviation of rat weight is about 455 g He wishes to provide an estimate within 80 g of the true average (80 g is the allowable error; L) 60
- 61. Example The requiredsample size is n = 4 x (455)2 / (80)2 = 129.39 Thus approximately 130 rats would be needed. 2 24 L S n = 61
- 62.
Editor's Notes
- #15 Descriptive Statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data. With descriptive statistics you are simply describing what is, what the data shows. Inferential Statistics investigate questions, models and hypotheses. In many cases, the conclusions from inferential statistics extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population thinks. Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what&apos;s going on in our data.
- #17 Researchers focus on probabilities (often called p values) that fall lower end of continum. The reason for this is partly intuitive and partly historic.
- #18 Researchers focus on probabilities (often called p values) that fall lower end of continum. The reason for this is partly intuitive and partly historic.
- #19 Given a underlying theatrical structure, a representative sample, an appropriate research design, researcher. can test hypothesis. We test to see whether data support the hypothesis. Alterative hypothesis is called research hypothesis
- #20 Given a underlying theatrical structure, a representative sample, an appropriate research design, researcher. can test hypothesis. We test to see whether data support the hypothesis. Alterative hypothesis is called research hypothesis
- #21 Given a underlying theatrical structure, a representative sample, an appropriate research design, researcher. can test hypothesis. We test to see whether data support the hypothesis. Alterative hypothesis is called research hypothesis
- #39 As noted, calculation of sensitivity and specificity, and therefore calculation of predictive value, requires a way to determine authoritatively who has and does not have the condition of interest. This “gold standard” is typically the most definitive diagnostic procedure (for example, the definitive diagnosis of cancer is generally based on microscopic examination of a tissue specimen), the best available laboratory test (for example, a polymerase chain reaction (PCR) test for the actual virus, as opposed to a test for antibody to the virus), or a comprehensive clinical evaluation, where there is no definitive laboratory test. For example, the best diagnosis for arthritis might be obtained through an examination.
- #40 Data for estimating sensitivity and specificity are typically displayed in a 2 x 2 table that classifies people according to their disease status and test results. The above table has the True disease status along one dimension, with a column for cases and a column for non-cases, and the Test results on the other dimension, with a row for people who tested positive and a row for people who tested negative. In the top left-hand corner – the “a” cell – are the people who have the disease and whose test came up positive. They are “true positives”, cases who were correctly classified. In the lower right-hand corner – the “d” cell – are the people who do not have the disease and whose test came up negative. They are “true negatives”, non-cases who were correctly classified. The other two cells, b and c, contain people who were misclassified. Non-cases who nevertheless received a positive test are often called “false positives”, and cases who received a negative test are often called “false negatives”, but these terms are not always employed with these meanings. If cell “c” is in the lower left-hand corner of the table, then the left-hand column – the cases – has a total of (a + c) people, and we we can write the formula for sensitivity as a / (a+c): the number of cases correctly classified divided by the total number of cases. Similarly, the formula for specificity is d / (b+d): the number of correctly classified non-cases divided by the total number of non-cases.
- #41 If a population has a total of 200 cases, and the test correctly identifies 140 of them as cases, then a = 140, a+c = 200, and the sensitivity is: a / (a+c) = 140 / 200 = 70% If there are 20,000 people without the disease, and the test correctly classifies 19,000 of them as non-cases, then d = 19,000, b+d = 20,000, and the specificity is: d / (b+d) = 19,000 / 20,000 = 95%. As is often the case for a rare disease, even with what seems like a high specificity (95%), the number of false positives can easily exceed the number of true positives. This observation brings us to the concept of predictive value.
- #42 Sensitivity and specificity tell us what happens to cases and non-cases, respectively. However, appropriate interpretation of the results of a test – both screening tests and diagnostic tests – makes use of another concept that is very important for both the epidemiologic and the clinical perspectives, predictive value. Predictive value is also a probability of correct classification, but here the starting point, the denominator for the probability, is the way people have been classified by the test. There are two types of predictive value – predictive value of a positive test and predictive value of a negative test. Predictive value tells us the probability that the test was correct. This is obviously a key question for the clinician (and the patient), since we generally do not know whether someone is a case or not, but we do know whether the person tests positive or negative. In clinical epidemiology, the prevalence of a disease is referred to as the “prior probability” or “pretest probability”, since it is our initial estimate of the probability that the condition is present. Predictive values are referred to as posterior or posttest probabilities, since they provide estimates of probability that take into account the result of the screening or diagnostic test. The relation of the posttest and pretest probabilities indicates the informativeness of the test.
- #44 The table for examining predictive value is the same as that for sensitivity and specificity. Instead of using the total numbers of cases and non-cases, though, predictive value involves the total number of people with a positive test and the total number with a negative test. Positive predictive value, abbreviated PPV or PV+, is the proportion of all people with positive tests who truly have the condition – a / (a+b) in the above table. Negative predictive value (NPV or NP-) is the proportion of all people with negative tests who truly do not have the condition – d / (c+d) in the above table.
- #45 Using the same numbers as in our example for calculating sensitivity and specificity, we find that the predictive value of a positive test (PPV) is only 140 / 1,140 = 12.3%. The predictive value of a negative test (NPV) is 19,000 / 19,060 = 99.7%. Although the NPV is very high, that is not such an impressive result in this population, since the prevalence of the condition is only 200 / 20,200, which is not quite 1%. That means that if we select a person at random from the population, there is a 1% probability that the person will be a case (the pretest probability). The probability that a person who tests positive actually is a case is 12.3% (the posterior probability), so the test raises the probability substantially. On the other hand, the probability that a person randomly selected from the population does not actually have the condition is already 99%, so the additional information that a person tested negative cannot shift that estimate significantly. However, the PPV of 12.3% poses a dilemma. Of the 1,140 people who tested positive, the vast majority – 87.7% – are falsely positive. They do not have the disease. Thus, for every person whose disease is detected and who may therefore be helped, 7 people who do not have the disease and will therefore not derive any benefit will undergo a diagnostic workup that may be costly, uncomfortable, and possibly harmful. This tradeoff is the dilemma in population screening for a rare disease.
- #46 The above table illustrates the relation among positive predictive value (PPV), sensitivity, specificity, and prevalence of the condition. Note that sensitivity and specificity are being regarded as properties of the test, unaffected – in principle – by the rarity of the condition. In contrast, prevalence is a property of the population in which the test being screened, and PPV shows the result of applying a test with given sensitivity and specificity to a population with a given prevalence. For sensitivity held constant at 70% and specificity held constant at 95%, PPV is only 1.4% for a disease with a prevalence of 1 in 1,000, but rises to over 40% when the prevalence is 5%. This table illustrates the difference between using a test for screening and for diagnosis. Using the test in the general population, where the disease is rare (say, less than 1%), will result in a positive predictive value below 15% – the large majority of people who test positive will not have the condition. In contrast, people with symptoms are much more likely to have the condition. If the prevalence among them is above 5%, then the proportion of false positive tests is greatly reduced. The challenge in population screening is to try to target a population at sufficiently high risk that the number of false positives is acceptable and yet a sufficient proportion of the cases are included. A point often not mentioned in introductory presentations is that while sensitivity and specificity are in principle fixed properties of the test, in practice a test is not a fixed entity. Various factors can affect the sensitivity and specificity of a test when it is actually implemented, since there are often human factors involved in interpreting test results, equipment may require frequent calibration, etc.
- #48 Suggestions to the facilitator Ask participants why and when sampling is required and explain.