applications of statistics in research bandit thinkhamrop, ph.d.(statistics) department of...
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Applications of Applications of Statistics in ResearchStatistics in Research
Bandit Thinkhamrop, Ph.D.(Statistics)Bandit Thinkhamrop, Ph.D.(Statistics)Department of Biostatistics and DemographyDepartment of Biostatistics and Demography
Faculty of Public HealthFaculty of Public HealthKhon Kaen UniversityKhon Kaen University
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Steps of Statistical ApplicationsSteps of Statistical Applications(Practical guides for beginners)(Practical guides for beginners)
Begin at the conclusion Begin at the conclusion Identify the primary research questionIdentify the primary research questionIdentify the primary study outcomeIdentify the primary study outcomeIdentify type of the study outcomeIdentify type of the study outcomeIdentify type of the study designIdentify type of the study designGenerate a mock data setGenerate a mock data setIdentify type of the main statistical goalIdentify type of the main statistical goalList choices of the statistical methodsList choices of the statistical methodsSelect the most appropriate statistical methodSelect the most appropriate statistical methodPerform the data analysis using a softwarePerform the data analysis using a softwareReport and interpret the results from the outputsReport and interpret the results from the outputs
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Begin at the conclusion Begin at the conclusion Identify the primary research questionIdentify the primary research questionIdentify the primary study outcomeIdentify the primary study outcomeIdentify type of the study outcomeIdentify type of the study outcomeIdentify type of the study designIdentify type of the study designGenerate a mock data setGenerate a mock data setIdentify type of the main statistical goalIdentify type of the main statistical goalList choices of the statistical methodsList choices of the statistical methodsSelect the most appropriate statistical methodSelect the most appropriate statistical methodPerform the data analysis using a softwarePerform the data analysis using a softwareReport and interpret the results from the outputsReport and interpret the results from the outputs
Steps of Statistical ApplicationsSteps of Statistical Applications(Practical guides for beginners)(Practical guides for beginners)
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Begin at the conclusionBegin at the conclusion
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Begin at the conclusion Begin at the conclusion Identify the primary research questionIdentify the primary research questionIdentify the primary study outcomeIdentify the primary study outcomeIdentify type of the study outcomeIdentify type of the study outcomeIdentify type of the study designIdentify type of the study designGenerate a mock data setGenerate a mock data setIdentify type of the main statistical goalIdentify type of the main statistical goalList choices of the statistical methodsList choices of the statistical methodsSelect the most appropriate statistical methodSelect the most appropriate statistical methodPerform the data analysis using a softwarePerform the data analysis using a softwareReport and interpret the results from the outputsReport and interpret the results from the outputs
Steps of Statistical ApplicationsSteps of Statistical Applications(Practical guides for beginners)(Practical guides for beginners)
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Identify the primary research Identify the primary research questionquestion
Where to find the research question?Where to find the research question?– Title of the studyTitle of the study– The objective(s)The objective(s)– The conclusion(s)The conclusion(s)
If more than one, find the primary aim.If more than one, find the primary aim.
Try to make the question “quantifiable”Try to make the question “quantifiable”
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Begin at the conclusion Begin at the conclusion Identify the primary research questionIdentify the primary research questionIdentify the primary study outcomeIdentify the primary study outcomeIdentify type of the study outcomeIdentify type of the study outcomeIdentify type of the study designIdentify type of the study designGenerate a mock data setGenerate a mock data setIdentify type of the main statistical goalIdentify type of the main statistical goalList choices of the statistical methodsList choices of the statistical methodsSelect the most appropriate statistical methodSelect the most appropriate statistical methodPerform the data analysis using a softwarePerform the data analysis using a softwareReport and interpret the results from the outputsReport and interpret the results from the outputs
Steps of Statistical ApplicationsSteps of Statistical Applications(Practical guides for beginners)(Practical guides for beginners)
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Identify the primary study Identify the primary study outcomeoutcome
It is the “primary” dependence variableIt is the “primary” dependence variableIt is the main finding that was used as the basis It is the main finding that was used as the basis for the conclusion of the studyfor the conclusion of the studyIt is the target of the statistical inference It is the target of the statistical inference It is the basis for sample size calculationIt is the basis for sample size calculationIt resided in the :It resided in the :– TitleTitle– Research questionResearch question– ObjectiveObjective– Sample size calculationSample size calculation– Main finding in the RESULTS section of the reportMain finding in the RESULTS section of the report– ConclusionConclusion
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Begin at the conclusion Begin at the conclusion Identify the primary research questionIdentify the primary research questionIdentify the primary study outcomeIdentify the primary study outcomeIdentify type of the study outcomeIdentify type of the study outcomeIdentify type of the study designIdentify type of the study designGenerate a mock data setGenerate a mock data setIdentify type of the main statistical goalIdentify type of the main statistical goalList choices of the statistical methodsList choices of the statistical methodsSelect the most appropriate statistical methodSelect the most appropriate statistical methodPerform the data analysis using a softwarePerform the data analysis using a softwareReport and interpret the results from the outputsReport and interpret the results from the outputs
Steps of Statistical ApplicationsSteps of Statistical Applications(Practical guides for beginners)(Practical guides for beginners)
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Type of the study outcome: Key for Type of the study outcome: Key for selecting appropriate statistical methodsselecting appropriate statistical methods
Study outcomeStudy outcome– Dependent variable or response variableDependent variable or response variable– Focus on primary study outcome if there are Focus on primary study outcome if there are
moremore
Type of the study outcomeType of the study outcome– ContinuousContinuous– Categorical (dichotomous, polytomous, ordinal)Categorical (dichotomous, polytomous, ordinal)– Numerical (Poisson) countNumerical (Poisson) count– Even-free durationEven-free duration
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Continuous outcomeContinuous outcome
Primary target of estimation: Primary target of estimation: – Mean (SD) Mean (SD) – Median (Min:Max)Median (Min:Max)– Correlation coefficient: r and ICC Correlation coefficient: r and ICC
Modeling:Modeling:– Linear regressionLinear regression
The model coefficient = Mean differenceThe model coefficient = Mean difference– Quantile regressionQuantile regression
The model coefficient = Median differenceThe model coefficient = Median differenceExample: Example: – Outcome = Weight, BP, score of ?, level of ?, etc.Outcome = Weight, BP, score of ?, level of ?, etc.– RQ: Factors affecting birth weightRQ: Factors affecting birth weight
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Categorical outcomeCategorical outcome
Primary target of estimation : Primary target of estimation : – Proportion or Risk Proportion or Risk
Modeling:Modeling:– Logistic regressionLogistic regression
The model coefficient = Odds ratioThe model coefficient = Odds ratio (OR)(OR)
Example: Example: – Outcome = Disease (y/n), Dead(y/n), Outcome = Disease (y/n), Dead(y/n),
cured(y/n), etc.cured(y/n), etc.– RQ: Factors affecting low birth weight RQ: Factors affecting low birth weight
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Numerical (Poisson) count outcomeNumerical (Poisson) count outcome
Primary target of estimation : Primary target of estimation : – Incidence rate (e.g., rate per person time) Incidence rate (e.g., rate per person time)
Modeling:Modeling:– Poisson regressionPoisson regression
The model coefficient = Incidence rate ratio (IRR)The model coefficient = Incidence rate ratio (IRR)
Example: Example: – Outcome = Total number of fallsOutcome = Total number of falls
Total time at risk of fallingTotal time at risk of falling– RQ: Factors affecting elderly fallRQ: Factors affecting elderly fall
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Event-free duration outcomeEvent-free duration outcome
Primary target of estimation : Primary target of estimation : – Median survival time Median survival time
Modeling:Modeling:– Cox regressionCox regression
The model coefficient = Hazard ratio (HR)The model coefficient = Hazard ratio (HR)
Example: Example: – Outcome = Overall survival, disease-free Outcome = Overall survival, disease-free
survival, progression-free survival, etc.survival, progression-free survival, etc.– RQ: Factors affecting survivalRQ: Factors affecting survival
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The outcome determine statisticsThe outcome determine statistics
Continuous
MeanMedian
Categorical
Proportion(PrevalenceOrRisk)
Count
Rate per “space”
Survival
Median survivalRisk of events at T(t)
Linear Reg. Logistic Reg. Poisson Reg. Cox Reg.
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Statistics quantify errors for judgmentsStatistics quantify errors for judgmentsParameter estimation
[95%CI]
Hypothesis testing[P-value]
Parameter estimation[95%CI]
Hypothesis testing[P-value]
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Statistics quantify errors for judgmentsStatistics quantify errors for judgments
7
Parameter estimation[95%CI]
Hypothesis testing[P-value]
Parameter estimation[95%CI]
Hypothesis testing[P-value]
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Begin at the conclusion Begin at the conclusion Identify the primary research questionIdentify the primary research questionIdentify the primary study outcomeIdentify the primary study outcomeIdentify type of the study outcomeIdentify type of the study outcomeIdentify type of the study designIdentify type of the study designGenerate a mock data setGenerate a mock data setIdentify type of the main statistical goalIdentify type of the main statistical goalList choices of the statistical methodsList choices of the statistical methodsSelect the most appropriate statistical methodSelect the most appropriate statistical methodPerform the data analysis using a softwarePerform the data analysis using a softwareReport and interpret the results from the outputsReport and interpret the results from the outputs
Steps of Statistical ApplicationsSteps of Statistical Applications(Practical guides for beginners)(Practical guides for beginners)
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Types of Research
Qualitative Quantitative
Observational Experimental
Descriptive Analytical
Cross-sectional Case-control Cohort
Quasi-experimental Randomized-controlled
Clinical trialField trial
Community intervention trial
Parallel or Cross-over or factorialFixed length or group sequential
With or without baseline
Systematic reviewMeta-analysis
Cross-sectional descriptivePrevalence survey
Poll
PhenomenologyGrounded TheoryEthnographyDescription
Prevalence case-controlNested case-controlCase-cohort case-control
Prospective cohortRetrospective cohortAmbi-spective cohort
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Caution about biasesCaution about biases
Selection bias
Information bias
Confounding bias
Research Design-Prevent them-Minimize them
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Caution about biasesCaution about biases
Selection bias (SB)
Information bias (IB)
Confounding bias (CB)
If data available:SB & IB can be assessedCB can be adjusted using multivariable analysis
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Begin at the conclusion Begin at the conclusion Identify the primary research questionIdentify the primary research questionIdentify the primary study outcomeIdentify the primary study outcomeIdentify type of the study outcomeIdentify type of the study outcomeIdentify type of the study designIdentify type of the study designGenerate a mock data setGenerate a mock data setIdentify type of the main statistical goalIdentify type of the main statistical goalList choices of the statistical methodsList choices of the statistical methodsSelect the most appropriate statistical methodSelect the most appropriate statistical methodPerform the data analysis using a softwarePerform the data analysis using a softwareReport and interpret the results from the outputsReport and interpret the results from the outputs
Steps of Statistical ApplicationsSteps of Statistical Applications(Practical guides for beginners)(Practical guides for beginners)
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Generate a mock data setGenerate a mock data set
General format of the data layoutGeneral format of the data layout
id y x1 x2 X3
11
22
33
44
55
……
nn
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Generate a mock data setGenerate a mock data set
Continuous outcome exampleContinuous outcome example
id y x1 x2 X3
11 22 11 2121 2222
22 22 00 1212 1919
33 00 11 44 2020
44 22 00 8989 2121
55 1414 11 00 1818
……
nn 66 00 4545 2121
Mean (SD)
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Generate a mock data setGenerate a mock data set
Continuous outcome exampleContinuous outcome example
id y x1 x2 X3
11 11 11 2121 2222
22 11 00 1212 1919
33 00 11 44 2020
44 00 00 8989 2121
55 00 11 00 1818
……
nn 00 00 4545 2121
n, percentage
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Begin at the conclusion Begin at the conclusion Identify the primary research questionIdentify the primary research questionIdentify the primary study outcomeIdentify the primary study outcomeIdentify type of the study outcomeIdentify type of the study outcomeIdentify type of the study designIdentify type of the study designGenerate a mock data setGenerate a mock data setIdentify type of the main statistical goalIdentify type of the main statistical goalList choices of the statistical methodsList choices of the statistical methodsSelect the most appropriate statistical methodSelect the most appropriate statistical methodPerform the data analysis using a softwarePerform the data analysis using a softwareReport and interpret the results from the outputsReport and interpret the results from the outputs
Steps of Statistical ApplicationsSteps of Statistical Applications(Practical guides for beginners)(Practical guides for beginners)
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Common types of the statistical goalsCommon types of the statistical goals
Single measurements (no comparison)Single measurements (no comparison)
Difference (compared by subtraction)Difference (compared by subtraction)
Ratio (compared by division)Ratio (compared by division)
Prediction (diagnostic test or predictive Prediction (diagnostic test or predictive model)model)
Correlation (examine a joint distribution) Correlation (examine a joint distribution)
Agreement (examine concordance or Agreement (examine concordance or similarity between pairs of observations)similarity between pairs of observations)
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Begin at the conclusion Begin at the conclusion Identify the primary research questionIdentify the primary research questionIdentify the primary study outcomeIdentify the primary study outcomeIdentify type of the study outcomeIdentify type of the study outcomeIdentify type of the study designIdentify type of the study designGenerate a mock data setGenerate a mock data setIdentify type of the main statistical goalIdentify type of the main statistical goalList choices of the statistical methodsList choices of the statistical methodsSelect the most appropriate statistical methodSelect the most appropriate statistical methodPerform the data analysis using a softwarePerform the data analysis using a softwareReport and interpret the results from the outputsReport and interpret the results from the outputs
Steps of Statistical ApplicationsSteps of Statistical Applications(Practical guides for beginners)(Practical guides for beginners)
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Dependency of the study outcome required Dependency of the study outcome required special statistical methods to handle itspecial statistical methods to handle it
Example of dependency or correlated data: Example of dependency or correlated data: – Before-after or Pre-post designBefore-after or Pre-post design– Measuring paired organs i.e., ears, eyes, arms, etc.Measuring paired organs i.e., ears, eyes, arms, etc.– Longitudinal data, repeated measurementLongitudinal data, repeated measurement– Clustered data, many observation unit within a cluster Clustered data, many observation unit within a cluster
Choices of approaches:Choices of approaches:– Ignore it => use ordinary analysis as independency - Ignore it => use ordinary analysis as independency -
not savenot save– Simplify it => use summary measure then analyze the Simplify it => use summary measure then analyze the
data as it is independent – not efficientdata as it is independent – not efficient– Handle it => Mixed model, multilevel modeling, GEE - Handle it => Mixed model, multilevel modeling, GEE -
recommendedrecommended
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Dependency of the study outcome required Dependency of the study outcome required special statistical methods to handle itspecial statistical methods to handle it
Continuous Categorical Count Survival
MeanMedian
Proportion(PrevalenceOrRisk)
Rate per “space”
Median survivalRisk of events at T(t)
Linear Reg. Logistic Reg. Poisson Reg. Cox Reg.
Mixed model, multilevel model, GEE
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Answer the research questionbased on lower or upper limit of the CI
Back to the conclusionBack to the conclusion
Continuous Categorical Count Survival
Magnitude of effect95% CIP-value
Magnitude of effect95% CIP-value
MeanMedian
Proportion(Prevalence or Risk)
Rate per “space”
Median survivalRisk of events at T(t)
Appropriate statistical methods
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Always report the magnitude of Always report the magnitude of effect and its confidence intervaleffect and its confidence interval
Absolute effects: Absolute effects: – Mean, Mean differenceMean, Mean difference– Proportion or prevalence, Rate or risk, Rate or Risk differenceProportion or prevalence, Rate or risk, Rate or Risk difference– Median survival timeMedian survival time
Relative effects:Relative effects:– Relative risk, Rate ratio, Hazard ratioRelative risk, Rate ratio, Hazard ratio– Odds ratioOdds ratio
Other magnitude of effects: Other magnitude of effects: – Correlation coefficientCorrelation coefficient (r), Intra-class correlation (ICC)(r), Intra-class correlation (ICC)– KappaKappa– Diagnostic performanceDiagnostic performance– Etc.Etc.
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Touch the Touch the variabilityvariability (uncertainty) (uncertainty) to understand statistical inferenceto understand statistical inference
id A (x- ) (x- ) 2
11 22 -2-2 44
22 22 -2-2 44
33 00 -4-4 1616
44 22 -2-2 44
55 1414 1010 100100
Sum (Sum ()) 2020 00 128128
Mean( )Mean( ) 44 00 32.032.0
SDSD 5.665.66
MedianMedian 22
X
X X2+2+0+2+14 = 202+2+0+2+14 = 20
2+2+0+2+14 = 20 = 4 5 52+2+0+2+14 = 20 = 4 5 5
0 2 2 2 140 2 2 2 14
Variance = SD2Variance = SD2
Standard deviation = SDStandard deviation = SD
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Touch the Touch the variabilityvariability (uncertainty) (uncertainty) to understand statistical inferenceto understand statistical inference
id A (x- ) (x- ) 2
11 22 -2-2 44
22 22 -2-2 44
33 00 -4-4 1616
44 22 -2-2 44
55 1414 1010 100100
Sum (Sum ()) 2020 00 128128
Mean( )Mean( ) 44 00 32.032.0
SDSD 5.665.66
MedianMedian 22
X
X X
Measure of variation
Measure of variation
Measure of central tendency
Measure of central tendency
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1
2
n
XXSD
1
2
n
XXSD
Degree of freedom
Standard deviation (SD) = The average distant between each data item to their mean
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Same mean BUT different variationSame mean BUT different variation
id A
11 22
22 22
33 00
44 22
55 1414
Sum (Sum ()) 2020
MeanMean 44
SDSD 5.665.66
MedianMedian 22
id C
11 44
22 33
33 55
44 44
55 44
Sum (Sum ()) 2020
MeanMean 44
SDSD 0.710.71
MedianMedian 44
Heterogeneous dataSkew distribution
Heterogeneous dataSymmetry distribution
id B
11 00
22 44
33 1212
44 44
55 00
Sum (Sum ()) 2020
MeanMean 44
SDSD 4.904.90
MedianMedian 44
Homogeneous dataSymmetry distribution
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Facts about VariationFacts about Variation
Because of variability, repeated samples will Because of variability, repeated samples will NOT obtain the same statistic such as mean or NOT obtain the same statistic such as mean or proportion:proportion:– Statistics varies from study to study because of the Statistics varies from study to study because of the
role of chancerole of chance– Hard to believe that the statistic is the parameter Hard to believe that the statistic is the parameter – Thus we need statistical inference to estimate the Thus we need statistical inference to estimate the
parameter based on the statistics obtained from a parameter based on the statistics obtained from a studystudy
Data varied widely = heterogeneous dataData varied widely = heterogeneous dataHeterogeneous data requires large sample size Heterogeneous data requires large sample size to achieve a conclusive findingto achieve a conclusive finding
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The HistogramThe Histogramid A
11 22
22 22
33 00
44 22
55 1414
id B
11 44
22 33
33 55
44 44
55 44
00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414
00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414
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The Frequency CurveThe Frequency Curveid A
11 22
22 22
33 00
44 22
55 1414
id B
11 44
22 33
33 55
44 44
55 44
00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414
00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414
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Area Under The Frequency CurveArea Under The Frequency Curveid A
11 22
22 22
33 00
44 22
55 1414
id B
11 44
22 33
33 55
44 44
55 44
00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414
00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414
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Central Limit TheoremCentral Limit Theorem
Right Skew
X1
Symmetry
X2
Left Skew
X3
Normally distributedX1 XX Xn
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Distribution of Distribution of thethe sampling meansampling mean
Distribution of Distribution of the raw datathe raw data
Central Limit TheoremCentral Limit Theorem
X1
X2
X3
X1 XX Xn
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Central Limit TheoremCentral Limit TheoremDistribution of Distribution of
the raw datathe raw data
X1 XX Xn
Distribution of Distribution of
thethe sampling meansampling mean
(Theoretical) Normal Distribution
Large sampleLarge sample
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Central Limit TheoremCentral Limit TheoremMany X, , SDMany X, , SD
Standardized for whatever n, Mean = 0, Standard deviation = 1
Large sampleLarge sample
X1 XX Xn
Many , , SEMany , , SEX XX
X
Standard deviation of the sampling mean Standard error (SE)Estimated by
SE = SD n
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(Theoretical) Normal (Theoretical) Normal DistributionDistribution
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(Theoretical) Normal (Theoretical) Normal DistributionDistribution
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Mean ± 3SD
99.73% of AUC
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Mean ± 2SD
95.45% of AUC
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Mean ± 1SD
68.26% of AUC
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n = 25X = 52SD = 5
Sample
PopulationParameter estimation
[95%CI]
Hypothesis testing[P-value]
Parameter estimation[95%CI]
Hypothesis testing[P-value]
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n
SDSE
n
SDSE
25
5SE25
5SE 5 = 1
5
Z = 2.58Z = 1.96Z = 1.64
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n = 25X = 52SD = 5SE = 1
Sample
PopulationParameter estimationParameter estimation
[95%CI] : 52-1.96(1) to 52+1.96(1) 50.04 to 53.96We are 95% confidence that the population mean would lie between 50.04 and 53.96
[95%CI] : 52-1.96(1) to 52+1.96(1) 50.04 to 53.96We are 95% confidence that the population mean would lie between 50.04 and 53.96
Z = 2.58Z = 1.96Z = 1.64
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n = 25X = 52SD = 5SE = 1
Sample
Hypothesis testing
Hypothesis testing
Population
Z = 55 – 52 1
3H0 : = 55HA : 55
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Hypothesis testing
H0 : = 55HA : 55If the true mean in the population is 55, chance to obtain a sample mean of 52 or more extreme is 0.0027.
Hypothesis testing
H0 : = 55HA : 55If the true mean in the population is 55, chance to obtain a sample mean of 52 or more extreme is 0.0027.
Z = 55 – 52 1
3 P-value = 1-0.9973 = 0.0027
5552
-3SE +3SE
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Report and interpret p-value appropriatelyReport and interpret p-value appropriately
Example of over reliance on p-value: Example of over reliance on p-value: – Real results: n=5900; ORReal results: n=5900; ORDrug A vs Drug BDrug A vs Drug B = 1.02 = 1.02
(P<0.001) (P<0.001) – Inappropriate: Quote p-value as < 0.05 or put * Inappropriate: Quote p-value as < 0.05 or put *
or **** (star) to indicate significant resultsor **** (star) to indicate significant results– Wrong: Drug A is highly significantly better Wrong: Drug A is highly significantly better
than Drug B (P<0.001) than Drug B (P<0.001) – What if 95%CI: 1.001 to 1.300?What if 95%CI: 1.001 to 1.300?– This is no clinical meaningful at all….!This is no clinical meaningful at all….!
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Report and interpret p-value appropriatelyReport and interpret p-value appropriately
Example of over reliance on p-value: Example of over reliance on p-value: – Real results: n=30; ORReal results: n=30; ORDrug A vs Drug BDrug A vs Drug B = 9.2 (P=0.715) = 9.2 (P=0.715) – Inappropriate: Quote p-value as > 0.05Inappropriate: Quote p-value as > 0.05– Wrong: There is no statistical significant difference Wrong: There is no statistical significant difference
of the treatment effect (P<0.05). Thus Drug A is as of the treatment effect (P<0.05). Thus Drug A is as effective as Drug B effective as Drug B
– What if 95%CI: 0.99 to 28.97?What if 95%CI: 0.99 to 28.97?– This is study indicated a low power, NOT suggested This is study indicated a low power, NOT suggested
an equivalence…!an equivalence…!– Correct: There was no sufficient information to Correct: There was no sufficient information to
concluded that . . . => inconclusive findingsconcluded that . . . => inconclusive findings
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P-value is the magnitude of chance P-value is the magnitude of chance NOT magnitude of effectNOT magnitude of effect
P-value < 0.05 = Significant findingsP-value < 0.05 = Significant findings
Small chance of being wrong in rejecting the null Small chance of being wrong in rejecting the null hypothesishypothesis
If in fact there is no [If in fact there is no [effecteffect], it is unlikely to get the ], it is unlikely to get the [[effecteffect] = [] = [magnitude of effectmagnitude of effect] or more extreme] or more extreme
Significance DOES NOT MEAN importanceSignificance DOES NOT MEAN importance
Any extra-large studies can give a very small P-Any extra-large studies can give a very small P-value even if the [value even if the [magnitude of effectmagnitude of effect] is very ] is very smallsmall
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P-value is the magnitude of chance P-value is the magnitude of chance NOT magnitude of effectNOT magnitude of effect
P-value > 0.05 = Non-significant findingsP-value > 0.05 = Non-significant findingsHigh chance of being wrong in rejecting the null High chance of being wrong in rejecting the null hypothesishypothesisIf in fact there is no [If in fact there is no [effecteffect], the [], the [effecteffect] = ] = [[magnitude of effectmagnitude of effect] or more extreme can be ] or more extreme can be occurred chance.occurred chance.Non-significance DOES NOT MEAN no Non-significance DOES NOT MEAN no difference, equal, or no associationdifference, equal, or no associationAny small studies can give a very large P-value Any small studies can give a very large P-value even if the [even if the [magnitude of effectmagnitude of effect] is very large] is very large
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P-value P-value vs.vs. 95%CI 95%CI (1)(1)
A study compared cure rate between Drug A and Drug B
Setting:Drug A = Alternative treatmentDrug B = Conventional treatment
Results:Drug A: n1 = 50, Pa = 80%Drug B: n2 = 50, Pb = 50%
Pa-Pb = 30% (95%CI: 26% to 34%; P=0.001)
An example of a study with dichotomous outcome
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P-value P-value vs.vs. 95%CI 95%CI (2)(2)
Pa-Pb = 30% (95%CI: 26% to 34%; P< 0.05)
Pa > Pb
Pb > Pa
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P-value P-value vs.vs. 95%CI 95%CI (3)(3)Adapted from: Armitage, P. and Berry, G. Statistical methods in medical research. 3rd edition. Blackwell Scientific Publications, Oxford. 1994. page 99
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Tips #6 Tips #6 (b)(b) P-value P-value vs.vs. 95%CI 95%CI (4)(4)
Adapted from: Armitage, P. and Berry, G. Statistical methods in medical research. 3rd edition. Blackwell Scientific Publications, Oxford. 1994. page 99
There were statistically significant different between the two groups.
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Tips #6 Tips #6 (b)(b) P-value P-value vs.vs. 95%CI 95%CI (5)(5)
Adapted from: Armitage, P. and Berry, G. Statistical methods in medical research. 3rd edition. Blackwell Scientific Publications, Oxford. 1994. page 99
There were no statistically significant different between the two groups.
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P-value P-value vs.vs. 95%CI 95%CI (4)(4)
Save tips:Save tips:– Always report 95%CI with p-value, NOT report Always report 95%CI with p-value, NOT report
solely p-valuesolely p-value– Always interpret based on the lower or upper Always interpret based on the lower or upper
limit of the confidence interval, p-value can be limit of the confidence interval, p-value can be an optional an optional
– Never interpret p-value > 0.05 as an indication Never interpret p-value > 0.05 as an indication of no difference or no association, only the CI of no difference or no association, only the CI can provide this message.can provide this message.
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Begin at the conclusion Begin at the conclusion Identify the primary research questionIdentify the primary research questionIdentify the primary study outcomeIdentify the primary study outcomeIdentify type of the study outcomeIdentify type of the study outcomeIdentify type of the study designIdentify type of the study designGenerate a mock data setGenerate a mock data setIdentify type of the main statistical goalIdentify type of the main statistical goalList choices of the statistical methodsList choices of the statistical methodsSelect the most appropriate statistical methodSelect the most appropriate statistical methodPerform the data analysis using a softwarePerform the data analysis using a softwareReport and interpret the results from the outputsReport and interpret the results from the outputs
Steps of Statistical ApplicationsSteps of Statistical Applications(Practical guides for beginners)(Practical guides for beginners)
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The outcome determine statisticsThe outcome determine statistics
Continuous Categorical Count Survival
MeanMedian
Proportion(PrevalenceOrRisk)
Rate per “space”
Median survivalRisk of events at T(t)
Linear Reg. Logistic Reg. Poisson Reg. Cox Reg.
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Dependency of the study outcome required Dependency of the study outcome required special statistical methods to handle itspecial statistical methods to handle it
Continuous Categorical Count Survival
MeanMedian
Proportion(PrevalenceOrRisk)
Rate per “space”
Median survivalRisk of events at T(t)
Linear Reg. Logistic Reg. Poisson Reg. Cox Reg.
Mixed model, multilevel model, GEE
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Back to the conclusionBack to the conclusion
Continuous Categorical Count Survival
Magnitude of effect95% CIP-value
Magnitude of effect95% CIP-value
MeanMedian
Proportion(Prevalence or Risk)
Rate per “space”
Median survivalRisk of events at T(t)
Answer the research questionbased on lower or upper limit of the CI
Appropriate statistical methods
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Begin at the conclusion Begin at the conclusion Identify the primary research questionIdentify the primary research questionIdentify the primary study outcomeIdentify the primary study outcomeIdentify type of the study outcomeIdentify type of the study outcomeIdentify type of the study designIdentify type of the study designGenerate a mock data setGenerate a mock data setIdentify type of the main statistical goalIdentify type of the main statistical goalList choices of the statistical methodsList choices of the statistical methodsSelect the most appropriate statistical methodSelect the most appropriate statistical methodPerform the data analysis using a softwarePerform the data analysis using a softwareReport and interpret the results from the outputsReport and interpret the results from the outputs
Steps of Statistical ApplicationsSteps of Statistical Applications(Practical guides for beginners)(Practical guides for beginners)
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Perform the data analysis using Perform the data analysis using a softwarea software
Use the data being generated as if it would Use the data being generated as if it would be after completion of the researchbe after completion of the researchAnalyze according to the analysis planAnalyze according to the analysis planTry to understand the computer output and Try to understand the computer output and to find if the research question has been to find if the research question has been answered:answered:– What is the magnitude of effect and its 95% What is the magnitude of effect and its 95%
confidence interval?confidence interval?– Was the results due to the role of chance?Was the results due to the role of chance?
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Begin at the conclusion Begin at the conclusion Identify the primary research questionIdentify the primary research questionIdentify the primary study outcomeIdentify the primary study outcomeIdentify type of the study outcomeIdentify type of the study outcomeIdentify type of the study designIdentify type of the study designGenerate a mock data setGenerate a mock data setIdentify type of the main statistical goalIdentify type of the main statistical goalList choices of the statistical methodsList choices of the statistical methodsSelect the most appropriate statistical methodSelect the most appropriate statistical methodPerform the data analysis using a softwarePerform the data analysis using a softwareReport and interpret the results from the outputsReport and interpret the results from the outputs
Steps of Statistical ApplicationsSteps of Statistical Applications(Practical guides for beginners)(Practical guides for beginners)
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Writing Results SectionsOutline Sections: Study algorithm Characteristics of the study sample Results of an exploratory analysis to support ways to
answer the RQ Results to answer the RQ Results of an exploratory analysis to know more
about the answer of the RQFollow formats required by the research sponsor or the target journalBest done with SAP – Statistical Analysis Plan Narrated tables or figures with key messages and avoid repetitionsDo not include explanations in Results section
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Report results with purposeReport results with purpose
Refer to the corresponding table or figures early at the beginning of the descriptions
Report sufficient data to allow evaluation of the calculation while Report sufficient data to allow evaluation of the calculation while avoid redundancyavoid redundancy
Document steps of data analysis from which the results were Document steps of data analysis from which the results were transcribedtranscribed
Provide statistical inference for the main findings that are the basis Provide statistical inference for the main findings that are the basis for the conclusionsfor the conclusions
Always report the confidence intervals, p-value can be an optional Always report the confidence intervals, p-value can be an optional – not the main target– not the main target
Tips for Writing Results SectionTips for Writing Results Section
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Q & AQ & AThank you