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Dr. Murtaza Kamal MRCPCH,MD,DNB,DrNB Ped Cardiology, profile picture
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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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Murtaza KamalMurtaza Kamal Dec 22, 2018Dec 22, 2018 murtaza.vmmc@gmail.commurtaza.vmmc@gmail.com 1
  Definition of biostatistics  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
Science dealing with methods of data collection, compilation, tabulation and analysis to provide meaningful and valid interpretation 3
Bio-statisticsBio-statistics Application of statistical methods in field of biology, public health and medicine 4
 Quality of clinical & 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
Datum: Latin "fact" Collection of 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
• Choice of statistical 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
 A variable that 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
• Resulting response or 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
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Nominal: This variable has 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
Quantitative data Discrete: Often represents 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
Importance of data type Type of data: Critically important in determining which methods of analysis will be appropriate and valid 13
 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
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
Two approaches 1. Estimating Parameters: 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
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
 To permit generalizations 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
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
 Statistics whose primary use is in testing hypotheses are called test statistics  Parametric & non-parametric tests Step 2: Decide on appropriate Test Statistic 20
• Some assumptions are 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
 Many naturally occurring 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
 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
Normal Distribution  Developed by Karl F. Gauss (1777-1855) ‘Gaussian distribution’  Called ‘normal’ because many continuous variables in biology and other sciences follow this particular distribution 24
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
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 The Normal Distribution Properties 3- Area property
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
• Suitable alternative particularly 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
 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
Example Study of the effects 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
Direction of inquiry Onset of study Time Exposed Unexposed Cases Controls Exposed Unexposed Case-control study (retrospective) 32
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
  Odds ratio is a ratio of two odds  Relative risk is a ratio of two probabilities ODDS RATIO & RR 34
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THREE KEY MEASURES OF VALIDITY 1. SENSITIVITY 2. SPECIFICITY 3. PREDICTIVE VALUE 36
True Disease Status Screening/ Diagnostic Test Positive Negative 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 What is used as 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 True positive True negative False positive False negative Sensitivity = True positives All cases 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 True Disease Status Cases Non-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 Interpreting test results: predictive value Probability (proportion) of those tested who are correctly classified PPV = Cases identified /all positive tests NPV = Non-cases identified /all negative tests
  Positive predictive value: 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 True positive True negative False positive False negative PPV = True positives All positives 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 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 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
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 Study population are 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
Sampling Process Defining the population Developing a sampling Frame Determining Sample Size Specifying Sample Method SELECTING THE SAMPLE 48
TYPES OF SAMPLES 49
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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
Need to know following:  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
Single Group Studies 53
Sample Size for Qualitative outcome variable  P = Estimated prevalence (percentage)  Q =1-P  L = Allowable Error 2 4 L PQ n = 54
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
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
Example  A survey is 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
Example  The required sample 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
Sample Size for Estimation 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
Example  Suppose an investigator 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
Example  The required sample size is n = 4 x (455)2 / (80)2 = 129.39  Thus approximately 130 rats would be needed. 2 24 L S n = 61
 THANKS… 62