Applications of Statistics in Research

Applications of Statistics in Research Bandit Thinkhamrop, Ph.D.(Statistics) Department of Biostatistics and Demography Faculty of Public Health Khon Kaen University

Steps of Statistical Applications(Practical guides for beginners) • Begin at the conclusion • Identify the primary research question • Identify the primary study outcome • Identify type of the study outcome • Identify type of the study design • Generate a mock data set • Identify type of the main statistical goal • List choices of the statistical methods • Select the most appropriate statistical method • Perform the data analysis using a software • Report and interpret the results from the outputs

Begin at the conclusion

Identify the primary research question • Where to find the research question? • Title of the study • The objective(s) • The conclusion(s) • If more than one, find the primary aim. • Try to make the question “quantifiable”

Identify the primary study outcome • It is the “primary” dependence variable • It is the main finding that was used as the basis for the conclusion of the study • It is the target of the statistical inference • It is the basis for sample size calculation • It resided in the : • Title • Research question • Objective • Sample size calculation • Main finding in the RESULTS section of the report • Conclusion

Type of the study outcome: Key for selecting appropriate statistical methods • Study outcome • Dependent variable or response variable • Focus on primary study outcome if there are more • Type of the study outcome • Continuous • Categorical (dichotomous, polytomous, ordinal) • Numerical (Poisson) count • Even-free duration

Continuous outcome • Primary target of estimation: • Mean (SD) • Median (Min:Max) • Correlation coefficient: r and ICC • Modeling: • Linear regression The model coefficient = Mean difference • Quantile regression The model coefficient = Median difference • Example: • Outcome = Weight, BP, score of ?, level of ?, etc. • RQ: Factors affecting birth weight

Categorical outcome • Primary target of estimation : • Proportion or Risk • Modeling: • Logistic regression The model coefficient = Odds ratio(OR) • Example: • Outcome = Disease (y/n), Dead(y/n), cured(y/n), etc. • RQ: Factors affecting low birth weight

Numerical (Poisson) count outcome • Primary target of estimation : • Incidence rate (e.g., rate per person time) • Modeling: • Poisson regression The model coefficient = Incidence rate ratio (IRR) • Example: • Outcome = Total number of falls Total time at risk of falling • RQ: Factors affecting elderly fall

Event-free duration outcome • Primary target of estimation : • Median survival time • Modeling: • Cox regression The model coefficient = Hazard ratio (HR) • Example: • Outcome = Overall survival, disease-free survival, progression-free survival, etc. • RQ: Factors affecting survival

Continuous Categorical Count Survival Mean Median Proportion (Prevalence Or Risk) Rate per “space” Median survival Risk of events at T(t) Linear Reg. Logistic Reg. Poisson Reg. Cox Reg. The outcome determine statistics

Parameter estimation [95%CI] Hypothesis testing [P-value] Statistics quantify errors for judgments

Parameter estimation [95%CI] Hypothesis testing [P-value] Statistics quantify errors for judgments 7

Quantitative Qualitative Phenomenology Grounded Theory Ethnography Description Observational Experimental Randomized-controlled Quasi-experimental Analytical Descriptive Clinical trial Field trial Community intervention trial Cross-sectional descriptive Prevalence survey Poll Parallel or Cross-over or factorial Fixed length or group sequential With or without baseline Cross-sectional Case-control Cohort Prevalence case-control Nested case-control Case-cohort case-control Prospective cohort Retrospective cohort Ambi-spective cohort Systematic review Meta-analysis Types of Research

Selection bias Information bias Confounding bias • Research Design • Prevent them • Minimize them Caution about biases

If data available: SB & IB can be assessed CB can be adjusted using multivariable analysis Caution about biases Selection bias (SB) Information bias (IB) Confounding bias (CB)

Generate a mock data set • General format of the data layout

Mean (SD) Generate a mock data set • Continuous outcome example

n, percentage Generate a mock data set • Continuous outcome example

Common types of the statistical goals • Single measurements (no comparison) • Difference (compared by subtraction) • Ratio (compared by division) • Prediction (diagnostic test or predictive model) • Correlation (examine a joint distribution) • Agreement (examine concordance or similarity between pairs of observations)

Dependency of the study outcome required special statistical methods to handle it • Example of dependency or correlated data: • Before-after or Pre-post design • Measuring paired organs i.e., ears, eyes, arms, etc. • Longitudinal data, repeated measurement • Clustered data, many observation unit within a cluster • Choices of approaches: • Ignore it => use ordinary analysis as independency - not save • Simplify it => use summary measure then analyze the data as it is independent – not efficient • Handle it => Mixed model, multilevel modeling, GEE - recommended

Continuous Categorical Count Survival Dependency of the study outcome required special statistical methods to handle it Mean Median Proportion (Prevalence Or Risk) Rate per “space” Median survival Risk of events at T(t) Linear Reg. Logistic Reg. Poisson Reg. Cox Reg. Mixed model, multilevel model, GEE

Continuous Categorical Count Survival Answer the research question based on lower or upper limit of the CI Back to the conclusion Appropriate statistical methods Mean Median Proportion (Prevalence or Risk) Rate per “space” Median survival Risk of events at T(t) Magnitude of effect 95% CI P-value

Always report the magnitude of effect and its confidence interval • Absolute effects: • Mean, Mean difference • Proportion or prevalence, Rate or risk, Rate or Risk difference • Median survival time • Relative effects: • Relative risk, Rate ratio, Hazard ratio • Odds ratio • Other magnitude of effects: • Correlation coefficient(r), Intra-class correlation (ICC) • Kappa • Diagnostic performance • Etc.

2+2+0+2+14 = 20 2+2+0+2+14 = 20 = 4 5 5 0 2 2 2 14 Variance = SD2 X X X Standard deviation = SD Touch the variability (uncertainty) to understand statistical inference

Measure of central tendency X X X Measure of variation Touch the variability (uncertainty) to understand statistical inference

Degree of freedom Standard deviation (SD) = The average distant between each data item to their mean

Same mean BUT different variation Heterogeneous data Skew distribution Heterogeneous data Symmetry distribution Homogeneous data Symmetry distribution

Facts about Variation • Because of variability, repeated samples will NOT obtain the same statistic such as mean or proportion: • Statistics varies from study to study because of the role of chance • Hard to believe that the statistic is the parameter • Thus we need statistical inference to estimate the parameter based on the statistics obtained from a study • Data varied widely = heterogeneous data • Heterogeneous data requires large sample size to achieve a conclusive finding

The Histogram

The Frequency Curve

Area Under The Frequency Curve

Right Skew X1 X2 X3 X1 XX Xn Symmetry Left Skew Normally distributed  Central Limit Theorem

X1 X2 X3 X1 XX Xn Distribution of the raw data Distribution of thesampling mean Central Limit Theorem 

X1 XX Xn Distribution of thesampling mean  Large sample (Theoretical) Normal Distribution Central Limit Theorem Distribution of the raw data

X1 XX Xn X Many , , SE X XX  Large sample Standard deviation of the sampling mean Standard error (SE) Estimated by Standardized for whatever n, Mean = 0, Standard deviation = 1 SE = SD n  Central Limit Theorem Many X, , SD

(Theoretical) Normal Distribution

99.73% of AUC Mean ± 3SD

95.45% of AUC Mean ± 2SD

Applications of Statistics in Research