statistics short course - [email protected] statistics short course . llorenç...

ASYRAS 2017 Barcelona 1 Llorenç Badiella & Oliver Valero

STATISTICS SHORT COURSE Servei d’Estadística Aplicada UAB

Llorenç Badiella Oliver Valero Servei d'Estadística Aplicada Universitat Autònoma de Barcelona www.uab.cat/s-estadistica [email protected]

Statistics short course



Contenido

Chapter Section



Contents

1) Evidence:

• Relevance

• Validity

• Reliability

2) Study Design

• Objective and Hypothesis

• Experimental units

• Variables

3) Statistical Methodology – Study Case

• Summary measures

• Baseline comparisons and Bivariate Analyses

• Statistical models



Statistics

1) Evidence



1) Evidence

In order to obtain solid conclusions from an experiment or survey,

3 conditions are needed:.

3) Relevance

1) Reliability

2) Validity 2) Study Design

1) Sample Size

3) Conclusions



1) Evidence

Low Reliability: Imprecise conclusions

3) Relevance

1) Reliability

2) Validity



1) Evidence

Low Reliability: Imprecise conclusions



1) Evidence

3) Relevance

1) Reliability

2) Validity

Low validity: bad experimental design, unrealistic conclusions



1) Evidence

Low validity, bad experimental design: Unrealistic conclusions



1) Evidence

Doubtful Relevance: Conclusions with no value

3) Relevance

1) Reliability

2) Validity



1) Evidence

Doubtful Relevance: Conclusions with no value



2) Study Design Objective

o Descriptive

o Comparative

o Predictive

o Classification

Types of Studies by objective




Types of Studies by objective

Objective: The purpose toward which an endeavor is directed.

o Demonstrate Murphy’s law (Anything that can go wrong will go wrong)

o Explore if Scots (or Catalans) are frugal

o Investigate if a pleasant working environment improves productivity (relaxing

music)

o Predict whether a patient, hospitalized due to a heart attack, will have a second

heart attack (based on demographic, diet and clinical measurements for that

patient).

o Perform a segmentation of customers (products purchased)




Hypothesis: A quantifiable and testable statement involving population traits. Descriptive: Scots are cheap o The majority of scots do not leave large tips at restaurants o Less than 20% of scots leave tips larger than 15% at restaurants

Comparative: Investigate the effect of relaxing music in productivity (in a clothes shop) o Relaxing music compared to Silent environment, improves sales by 10%. Predictive: Predict whether a patient will have a second heart attack o ¿Are the following variables: Gender, age, social status, diet, clinical measurements,

complaints,… related to the observation of a second heart attack?

Classification: Perform a segmentation of the costumers o ¿Do the following variables Gender, age, social status, Loyalty, profitability, … help to define

a set of costumers clusters?



2) Study Design Experimental units

Experimental Units: A unit in a statistical analysis refers to one member of a set of entities being independently studied (patients, subjects, animals, emails, images, pixels, etc.).

The extrapolation of results (prediction) using statistical tools, based on the analysis of a sample of units is only valid for the population where those units come from.

Variables (features, measures, inputs, output) will be evaluated on each experimental unit .



2) Study Design Variables

Types of variables (based on their nature):

Variable Examples

Nominal A, B, C

Binary Y, N

Ordinal None, Mild,

Moderate, High, Severe

Ordinal I, II, III, IV

Discrete (0,1,2,3…)

Continuous R

Time R+

Rate R+

Qu

alit

ativ

e Q

uan

tita

tive

Centre, Region, Treament, Political party

Sex, Cure, Success

Improvement, Satisfaction, Severity

Improvement, Satisfaction, Severity

Nº Events, Nº Products

Age, Revenue, Income

Time to some event occurrence

Success rate



Types of data (based on their role):

2) Study Design Variables

A unique variable capable of providing the most relevant and convincing evidence directly related to the primary objective of the trial. This will usually be an efficacy (or safety) variable.

Primary Response Variable (target variable, primary endpoint)

Secondary Response Variable

Supportive measurements related to the primary objective or measurements of effects related to the secondary objectives.

Explanatory Variables

Those variables, usually individual characteristics used to explain and predict response variables.



We want to measure the student’s opinion about a course they have just received. Questionnaires are provided to students and filled out voluntarily and anonymous.

The results were: Global average satisfaction (0-10): 4.25 (n=31)

It is possible to conclude that students are unsatisfied?

2) Study Design Examples



We want to value the efficacy of a course for a group of unemployed people (n = 504). The registration for the course is voluntary. After 6 months, the efficacy of the course is evaluated measuring the percentage of people still unemployed between those wo assisted and those who didn’t. The results were:

Attended the course (n=120): 23% are still unemployed Did not attend the course (n=384): 64% are still unemployed

(p<0.001)

It is possible to conclude that the course was effective?




An experimental study to evaluate the efficacy of a reinforcement course for students with learning difficulties was carried out. After a certain period of time, an important improvement is detected in students who attended all sessions.

However, only 40% of the students completed the course. The reason is that the course implied a huge ammount of workload.

What would be the conclusions of the study?




2) Study Design Design (Comparative Studies)

Randomized Controlled Study with Parallel Arms

Included Subjects

Random Allocation

Control Treatment

Experimental Treatment

Response Variable

Response Variable



Cross-Over 2x2 - Randomized Controlled Study

Included Subjects

Random Allocation

Control Treatment Period 1

Experimental Treatment Period 1

Experimental Treatment Period 2

Control Treatment Period 2

Response Variable

Response Variable




Observational Study - Cohorts

Subjects Included Risk Factor

Unexposed Cohort

Exposed Cohort

Response Variable

Response Variable




Subjects Included

Response Variable

Risk Factor

Risk Factor

Unexposed

Exposed

Unexposed

Exposed Negative (Controls)

Positive (Cases)

Observational Study : Cases and Controls (Binary Response Variables)




STATISTICS

Statistical techniques

o Descriptive

o Univariate

o Bivariate

o Multivariate

Statistical methods

o Validation

o Summarization and visualization

o Bivariate Baseline Analysis: Group vs Explanatory

o Bivariate Analysis: Response vs Explanatory

o (Multivariate ) Primary analysis

o (Multivariate ) Secondary analysis

3) Statistical methodology



STATISTICS

Validation

Ensure the validity of the data

o Missing values

o Data entry errors

o Outliers

o Inconsistencies between variables


Summarization and visualization

o Description of the target population

o Description of experimental groups

o Description of main results



STATISTICS

Bivariate Baseline Analysis: Group vs Explanatory

o Ensure the comparability between experimental groups

o Identify potential confounders (Colinearity analysis)


(Multivariate ) Primary analysis

o Confirm primary experimental hypothesis

Bivariate Analysis: Response vs Explanatory

o Identify explanatory variables related to the response variable



STATISTICS

(Multivariate ) Secondary analysis

o Analyse secondary response variables or objectives

o Consideration of alternative models for the primary analysis in case of non-compliance with the premises of the technique.

o Explore specific subgroups of the target population, evaluate the influence of outliers, analyse interactions between explanatory variables, etc.




3) Statistical methodology: Study Case



Data Base

3) Statistical methodology: Study Case



Quantitative variables:

3.1) Summary Statistics Summary measures




Quantitative variables:



Results:




Qualitative variables:




Results:




Comparison of a Quantitative Variable between Independent Groups

3.2) Baseline Analysis

Note: in presence of repeated measurements on the same individuals, Mixed Models should be considered.



Comparison of a Quantitative Variable between Independent Groups


Note: in presence of repeated measurements on the same individuals, Mixed Models should be considered.



Results:




Comparison of a Qualitative Variable between Independent Groups




Results:




Results:


Variable Group Effect p-value Test

Type of school (Science)

CLIL 70.1% 0.437 Chi Square

Control 65.7%

Sex (Boy) CLIL 55.5%

0.036 Chi Square Control 42.9%

Extra (Yes) CLIL 56.2%

0.840 Chi Square Control 55.0%

Reading pre CLIL 15.8 (7.4)

0.038 Wilcoxon Control 14.4 (7.8)

Listening pre CLIL 3.0 (1.5)


Proficiency CLIL 3.4 (1.4)




Comparison of two Quantitative Variables: • Pearson Correlation (r): Degree of linear association [-1,1] • Slope: Y = a + b X Note: in absence of Normality, Spearman Correlation should be used.

3.3) Bivariate analysis



Results:

3.3) Bivariate analysis

Variable Category Effect p-value Test

Group CLIL 10.2 (7.0)


Type of school Arts & crafts 10.8 (8.3)

0.757 Wilcoxon Science 10.9 (6.7)

Sex Boy 11.0 (7.0)

0.941 Wilcoxon Girl 10.7 (7.6)

Extra Yes 10.5 (7.1)

0.617 Wilcoxon No 11.1 (7.4)

Reading pre -0.292 <0.001 Spearman Listening pre -0.11 0.069 Spearman Proficiency -0.23 <0.001 Spearman

Proficiency High 7.4 (6.0)

<0.001 Kruskal-Wallis Medium 11.7 (6.7) Low 12.0 (7.8)



Y = a + b1 X1 + … + bkXk + e

• Quantitative response variable • All important explanatory variables are considered • Independent observations • Homogeneity of residual variance • Residuals Normally distributed

3.4) Statistical Models (I)



Results:




Check for Multicollinearity: • Correlations • Variance Inflation Factor (VIF) lower than 3




Model validation:




Interactions:

3.4) Statistical Models (II)



If model premises are not satisfied or the response has another distribution different from Normal: o Transformation

o Logistic regression (binary outcome)

o Poisson regression (counts)

If observations are not independent :

o Mixed models / Generalized mixed models

3.4) Other Statistical Models



Thank You www.uab.es/s-estadistica

statistics short course - [email protected] statistics short course . llorenç...

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