Basic Biostatistics

Basic BiostatisticsAssoc. Prof. Dr. Jamalludin Ab Rahman MD MPH

Department of Community Medicine

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Learning outcomesAt the end of this workshop, you should be able to1. Describe about population & sample, causation,

level of measurement, distribution of data2. Summarise categorical & numerical data3. Use appropriate statistical test for bi-variable

analyses using SPSS

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We observe, we believe.What we (can) observe might

not be the truth

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Population vs. Sample

Parameter

Statistics

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Parameter vs. Statistics Parameter

characteristic of the whole population Statistics

characteristic of a sample, presumably measurable.

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Statistics estimate parameters But how ‘representative’ a sample to the population When sample statistics ≠ population statistics =

sampling error A different sample statistics from the same population

may yield different estimates If sampling is repeated many times, the statistics will

approach the actual value of the population parameters

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N = 35Red = 15/35 = 42.8%

N = 6Red = 3/6 = 50%

N = 6Red = 2/6 = 33.3%

N = 6Red = 4/6 = 66.7%

Average % Red = = 50%

50% 42.8%Parameter

Statistics

Statistics Parameter

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Variable & its role A value and whose associated value may be

changed

DependentIndependent

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Causation Relation of events (cause and effect) But correlation (between two events) does not

(always) imply causation Rooster's crow does not cause the sun to rise Switch does not cause the bulb to light

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Time & causation

Time

Exposure Exposure

Exposure

Outcome

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Time & causation (example)

Time

AgeExposure to

silica

Smoking

Lung Cancer

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Causal Model

OutcomeExposure Exposure Exposure

Exposure

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Study design & causality Not all design can prove causality Cross sectional can’t determine causality Must have temporality – exposure precedes

outcome

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Type of data(Level of measurement)

Categorical

Nominal Ordinal

Numerical

Discrete Continuous

e.g. Gender, Race e.g. Cancer staging, Severity of CXR for PTB

e.g. Parity, Gravida

e.g. Hb, RBS, cholesterol.

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Distribution (shape) of data Applicable to numerical value Discrete or Continuous Discrete ~ Binomial, Poisson, Negative Binomial,

Hypergeometry, Multinomial etc. Continuous ~ Normal, t, chi-square, F etc.

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Normal Distribution

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𝑓 (𝑥 ;𝜇 ,𝜎2 )= 1𝜎√2𝜋

𝑒− 1

2( 𝑥−𝜇𝜎

)2

¿

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Characteristics Smooth, symmetrical (around the mean, not

skewed, appropriate height), uni-modal, bell shaped curve

Mean = Median = Mode The total area under the curve

(AUC) = 1 Asymptotic to the x-axis – never touch x-axis

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Test of Normality Anderson–darling Test Corrected Kolmogorov–Smirnov Test (Lilliefors Test) Cramér–von-mises Criterion D'agostino's K-squared Test Jarque–bera Test Pearson's Chi-square Test Shapiro–francia Shapiro–wilk Test

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Use Normality test with caution Small samples almost always pass a normality test.

Normality tests have little power to tell whether or not a small sample of data comes from a Gaussian distribution.

With large samples, minor deviations from normality may be flagged as statistically significant, even though small deviations from a normal distribution won’t affect the results of a t test or ANOVA.

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Why run statistical test?1. Determine presence of difference (or similarity)2. Determine degree of difference3. Determine the direction of changes (outcome)4. Predict changes (outcomes)

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A B C

Is there any difference between A & B?

How big is the difference between A & B?

Which one is taller? A or B?

Is C different from A & B?

Is there any pattern now?

If there is D, can you predict how tall is D?

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Statistical analysis

AnalyticalDescriptive

e.g. Describe socio-demographic characteristics - Age, Sex, Race etc.

e.g. Prevalence of hypertension.

e.g. Compare demographic characteristics between two population – Compare age between male & female

e.g. Distribution of gender by hypertension status

e.g. How demographic characteristics (more than one factors) explain hypertension

Univariable Bivariable MultivariableIV DV IV DV IV DV IV

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Descriptive Statistics Explain one variable at one time Method based on type of measure

CategoricalFrequency (Percentage)

NumericalCentral measures (e.g. mean, median) & Dispersion (e.g. variance, standard deviation, range, min-max, interquartile range)

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Data

CategoricalFrequency (count) &

Percentage

Numerical

Normal Mean (SD)

Not Normal Median (Range/IQR)

How to describe a data

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DifferenceA

B C

Which of the following shows true difference between two populations?

I II

IIII II

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P in hypothesis testing The mean glucose from 9 rabbits decreased from 7.3

mmol/L to 7.0 (0.9) mmol/L within 24 hours. Using t-test, taking critical value of P=0.05, is the difference significant?

Ho: No difference i.e. 7.3= 7.0 z = (7.0-7.3)/(0.9/9) = -1 Based on t-table, z at -1, df=9, two-tailed, P is between -

0.4 & -0.3 Therefore, P > 0.05

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One-tailed vs. two-tailed Is there a difference between Hb 14 g% vs. Hb 12

g% in male & female respectively?Ho: HbM – HbF = 0H1: HbM = HbFH2: HbM > HbFH3: HbM < HbM

Note: Should be determined a priori

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One-tailed vs. two-tailed

Two-sided Right-sidedLeft-sided

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Hypothesis testingTruth

Ho True Ho False

Test

Do notreject Ho Correct Type II error

()

Reject Ho

Type I error () Correct

P-value is the probability to make Type I error (based on frequentist inference)

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P & Sample Size

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The truth about P value Currently effectiveness is measured by P value (even by US

FDA) < P means statistically significant, NOT clinical significant P is affected BOTH by effectiveness AND sample size P can be < 0.05 even though the effectiveness is marginal

when sample size is huge Compare Ps between studies only appropriate if the sampling

& sample size is the same Therefore, be careful when interpreting P value

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P < 0.05 Why 5%? Cut-off point proposed by Sir Ronald A. Fisher

1925 to reject or not to reject a hypothesis If P < 0.05 = Probability to make Type I error is

less than 5% If P > 0.05, > 5% of the difference occurred by

chance & not due to the TRUE difference

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Hypothesis Testing using bivariable analysis Try to prove that Exposure causes the Disease

e.g. Smoking causing Lung Cancer Ho: No difference of risk to get Lung Cancer

between smoker and non-smoker

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Lung Cancer No Lung Cancer

Smoking 20 (18.2%) 90 (81.8%)

Not Smoking 5 (4.5%) 105 (95.5%)

The occurrence of lung cancer is significantly higher (18.2%) among smokers compared to non-smokers (4.5%) (2 (df=1)= 10.15, P =0.001, OR = 4.7 (CI95% 1.7 – 13.0))

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Confidence Interval Range of plausible values2 Narrow interval high precision

Wide interval poor precision How narrow is narrow?

And how wide is wide? Base of your clinical judgment

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Interpret Confidence Interval Compare with the null value

i.e. can be 0 for % or 1 for risk Compare with practical significance or the clinical

significance/indifference

Null

Null

A

B

Source: http://www.childrens-mercy.org/stats/journal/confidence.asp

Null

Null

C

D

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http://www.childrens-mercy.org/stats/journal/confidence.asp

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Effect size The measure of effect irrespective of sample size Cohen (1988) classify ES into

Low (<0.3)Medium (0.3-0.7)Large (> 0.7)

Manual calculation or web based calculation

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Statistical Test Univariate ~ One dependent & one independent Multivariate ~ Multiple dependent & multiple

independent variable

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What test to use?Variable 1 Variable 2 Test

Categorical Categorical Chi-square

Categorical (2 pop) Numerical (Normal) Independent sample t-test

Categorical (2 pop) Numerical (Not Normal) Mann-Whitney U test

Categorical (> 2 pop) Numerical (Normal) One-way ANOVA

Categorical (> 2 pop) Numerical (Not Normal) Kruskal-Wallis test

Numerical (Normal) Numerical (Normal) Pearson Correlation Coefficient Test

Numerical (Normal/ Not Normal)

Numerical (Not Normal) Spearman Correlation Coefficient Test

Numerical (Normal) Numerical (Normal) – Paired

Paired t-test

Numerical (Not Normal) Numerical (Not Normal) – Paired

Wilcoxon Signed Rank Test

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Univariate Analyses Compare means

Independent sample t-test (Unpaired t-test) ~ Two unrelated means

Paired t-test ~ Two related meansOne-way ANOVA ~ More than 2 means

2 Test ~ Between categorical variables Non-parametric tests (Kruskall-Wallis, Man-Whitney

U tests) ~ If data is not normally distributed

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Writing plan for statistical analysis #1

May 1, 2023Basic Biostatistics

Data were analyzed using the complex sample function of SPSS (version 13.0). Sampling errors were estimated using the primary sampling units and strata provided in the data set. Sampling weights were used to adjust for nonresponse bias and the oversampling of blacks, Mexican Americans, and the elderly in NHANES. The prevalence of hypertension, as well as the awareness, treatment, and control rates, were age adjusted by direct standardization to the US 2000 standard population.10 To analyze differences over time, the 2003–2004 data were compared with the 1999–2000 data. Estimates with a coefficient of variation >0.3 were considered unreliable. A 2-tailed P value <0.05 was considered statistically significant. (Ong et al. 2009)

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Writing plan for statistical analysis #2

May 1, 2023Basic Biostatistics

To assess the effect of the selection process on the characteristics of the cases, we compared cases included in the final analysis to the rest of the cases. Since controls included in the present analysis were different from the rest of the diabetes free participants by design, no similar comparisons were performed for that group. To compare baseline characteristics of cases and controls appropriate univariate statistics were used. Similar binary logistic and multiple linear regression models were built with incident diabetes or HbA1c as respective outcomes and additive block entry of adiponectin and potential confounders. For linear regression CRP and triglycerides were log transformed. Since HbA1c could be modified by drug treatment, we ran a sensitivity analysis excluding all participants on antidiabetic medication. A p-value of <0.05 was considered significant. Analyses were performed with SPSS 14.0 for Windows.

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Reporting analysis (example)

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Summary1. Identify & define variables2. Type – independent vs. dependent3. Level of measurements – nominal, ordinal or

continuous4. Check distribution – Normal vs. Not Normal5. Decide what to do - descriptive vs. analytical

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Chapter 2Introduction to SPSSIBM SPSS Statistics v21 for WindowsJamalludin Ab Rahman MD MPHDepartment of Community MedicineKulliyyah of Medicine

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IBM SPSS Statistics

IBM Corporation Software Group Route 100 Somers, NY 10589Produced in the United States of AmericaMay 2012

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Basic Biostatistics 50

SPSS Layout

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LayoutMain menu

Toolbar

Variables

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Data editor

Rows = variablesRows = each data

Define & describe your variables here

Enter your data here

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Viewer

The output of analyses will be displayed here.

Output is separated from

data

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Syntax

We can compile all the steps of the analyses here. Extend the programming

function in SPSS. Ability to perform complex steps e.g.

“looping”

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Creating Dataset

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Before even you start SPSS! You must identify & define relevant variables Define means

1. Name – preferably short single name, begins with alphabet, no special character, no space

2. Type of data – e.g. Numeric, Date, String3. Width & Decimal Places (if numeric)4. Label – description for the Name (will be displayed in Viewer)

5. Values – labels for value e.g. 1=Male, 2=Female6. Missing – define missing value e.g. 999 for N/A

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Define your variables

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Variable Types

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Variable Type

Decide the suitable

variable type

For numeric, determine Width

& Decimal. Decimal < Width

For String, no option for

Decimal Place

New option for Numerics with leading zeros

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Value Labels

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Missing ValueThis question is

Not Applicable to male

e.g. Assign 999 to represent N/A value

& this won’t be included in any

analysis

Chapter 3Descriptive StatisticsIBM SPSS Statistics v21 for WindowsJamalludin Ab Rahman MD MPHDepartment of Community MedicineKulliyyah of Medicine

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Exercise data Hypothetical Study to describe factors related to HbA1c &

Homocystein (HCY) N=301 13 variables

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Retrieve file information

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healthstatus001

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Task 11. Describe socio-demographic characteristics of

the respondent (age, gender & race)2. Describe the explanatory variables

1. Exercise2. smoking status3. BMI status &4. BP status

3. Describe HbA1c (taking cut-off for Poor HbA1c ≥ 6.5%) & HCY

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Describe numerical data

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Explore

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Results Check for Normality.Is Age data distributed Normally?

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Is this Normaldistribution?

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Describe ageNormal The subjects distributed between 23-67 years old

with the average of 34 (SD=8) years.If not Normal The subjects distributed between 23-67 years old

with the median of 33 (IQR=11) years

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Describe categorical data

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Frequency

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Results

Basic Biostatistics

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TRANSFORM

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Compute

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weight / ((height / 100) ** 2)

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Visual binning

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Normal < 23Overweight 23 to < 27.5Obese >= 27.5

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Chapter 4Bivariable analysesIBM SPSS Statistics v21 for WindowsJamalludin Ab Rahman MD MPHDepartment of Community MedicineKulliyyah of Medicine

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To check association of two variables?

HbA1cAge

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The steps1. Determine which is dependant & which is

independent2. Determine level of measurements3. Determine Normality of the numerical

measurement4. Determine the suitable statistical test

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What are the tests?Variable 1 Variable 2 Test

Categorical Categorical Chi-square

Categorical (2 pop) Numerical (Normal) Independent sample t-test

Categorical (2 pop) Numerical (Not Normal) Mann-Whitney U test

Categorical (> 2 pop) Numerical (Normal) One-way ANOVA

Categorical (> 2 pop) Numerical (Not Normal) Kruskal-Wallis test

Numerical (Normal) Numerical (Normal) Pearson Correlation Coefficient Test

Numerical (Normal/ Not Normal)

Numerical (Not Normal) Spearman Correlation Coefficient Test

Numerical (Normal) Numerical (Normal) – Paired Paired t-test

Numerical (Not Normal) Numerical (Not Normal) – Paired

Friedman test

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Tasks 21. Determine association between socio-demographic

characteristics & all the risk factors with HbA1c2. Determine association between socio-demographic

characteristics & all the risk factors with HCY

Note: It would be good if you could construct dummy table for the answers even before the analyses started

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HCY normal range

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Independent sample t-TestComparing Two Means

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Age vs. BP

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Results

Levene’s test check equality between variances. Ho: There is no difference of variances. So if P is significant, we reject Ho, and therefore equal variances assumed.

The original t-test (Student’s t-test) assumes equal variances for equal sample sizes. However if the variances are equal, it is robust for different sizes.

Welch's correction

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Table – Distribution of age by blood pressure status

N Mean SD Statistics df P

Normal BP 156 33.9 7.9 t=0.431 299 0.667

High BP 145 34.4 8.9

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Chi-squared TestDifference of Two Proportions

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Gender vs. BP

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Results

Describe this table first. What is your impression? 49% women vs. 47% men with high BP

Some books may suggest the use of Continuity Correction at ALL time, but recent simulations showed that CC (or Yate’s correction) is OVERCONSERVATIVE. Hence, use Pearson 2 when < 20% of cells have expected count < 5

When 20% of cells have EC < 5, use Fisher’s Exact Test

This is given because we code the variables using numbers. Can be used to measure P-trend

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One-way ANOVAComparing More than Two Means

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Race vs. HbA1c

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ResultsDescribe these results first. What is your impression? HbA1c between races? 6.4 (SD 2.1) vs. 6.7 (SD 2.2) vs. 6.5 (SD 2.2)

The F test shows that there is no single significant difference between any two groups

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Results – BMI status vs. HbA1c

The F test shows that at least there is ONE pair with significant different. Either N vs. OW, N vs. OB or OW vs. OB

We need to run Post-hoc test to determine which of the PAIR is significant.

To decide which Post-hoc test to choose, we have to test for equality of variances i.e. Homogeneity of variances (Levene’s test)

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Results – Post hoc

The significant difference is only for Normal vs. Obese (P=0.002)

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ReportThere is a significant association between BMI Status and HbA1c (F(2,298)=13.129, P<0.001). Post-hoc test showed that Obese subjects have significantly higher HbA1c compared to Normal and Overweight subjects (P=0.001 and P < 0.001 respectively).

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Mann-whitney UNon Parametric Tests

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Gender vs. HCY

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ResultsThis ranks table is not to be cited in the research paper. Instead, describe their MEDIAN

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KRUSKALL WALLISNon-Parametric TESTS

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Race vs. HCY

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Results

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Correlation TestRELATIONSHIP OF TWO NUMERICAL DATA

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Age vs. HbA1c

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Results

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Age vs. HCY

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Education

Basic Biostatistics