Rehabilitation Symposium

POTH 612AQuantitative AnalysisPOTH 612AQuantitative Analysis

Dr. Nancy Mayo

A Framework for Asking QuestionsA Framework for Asking Questions

PopulationPopulation

Exposure (Level 1)Exposure (Level 1)

Comparison Level 2Comparison Level 2

OutcomeOutcome

TimeTime

PECOTPECOT

PECOT FormatPECOT Format

In people with___________________________________________________________In people with___________________________________________________________

Does suboptimal level of factor 1Does suboptimal level of factor 1

____________________________________________________________________________________________________________________________________________________________________________________

In Comparison to optimal level of factor 1_______________________________________________________________________In Comparison to optimal level of factor 1_______________________________________________________________________

Affect (outcomes)__________________________________________________________________________________________Affect (outcomes)__________________________________________________________________________________________

At Time ____________________________________At Time ____________________________________

Types of QuestionsTypes of Questions

About hypothesesAbout hypotheses

Is treatment A better than treatment B?Is treatment A better than treatment B?

Answer: Yes or NoAnswer: Yes or No

About parametersAbout parameters

What is the extent to which treatment A improvesoutcome in comparison to treatment B?What is the extent to which treatment A improvesoutcome in comparison to treatment B?

Answer: A number / value (parameter)Answer: A number / value (parameter)

Research is about relationshipsResearch is about relationships

Links one variable or factor to anotherLinks one variable or factor to another

One is thought or supposed(hypothesized) to be the “cause” of thesecond variableOne is thought or supposed(hypothesized) to be the “cause” of thesecond variable

Example: Risk factors for fallsExample: Risk factors for falls

Your JobYour Job

When reading an article (later doing yourown research)When reading an article (later doing yourown research)

IDENTIFY THESE VARIABLESIDENTIFY THESE VARIABLES

IDENTIFY WHAT SCALE THEY AREMEASURED ONIDENTIFY WHAT SCALE THEY AREMEASURED ON

What tables should I find in anarticleWhat tables should I find in anarticle

Table 1 – basic characteristics sampleTable 1 – basic characteristics sample

Table 2 – outcomes / exposuresTable 2 – outcomes / exposures

Table 3 - answer the main questionTable 3 - answer the main question

–Relationship between exposure and outcome–Relationship between exposure and outcome

Table 4 – interesting subgroupTable 4 – interesting subgroup

Fall yes

Fall no

Foot problem +

480 (24% of thecolumn)

717 (20.1%) ofcolumn

1197

Foot problem -

1517

2856

4373

1997

3573

5570

P of falls for foot probmel + 480 / 1197 = 0.4

Prob of falls for foot problem - 1517 / 4373 = 0.35

Risk of falls / foot problem relative to risk of falls / no foot problem =

0.4 / 0.35 = 1.14

Prevalence and Risk Factors for Falls in anOlder Community-Dwelling PopulationPrevalence and Risk Factors for Falls in anOlder Community-Dwelling Population

What type of study is this?What type of study is this?

Study of prevalenceStudy of prevalence

Study of factorsStudy of factors

What is prevalence?What is prevalence?

–N of people with condition / All people in study–N of people with condition / All people in study

Incidence = N of people who develop the outcome / N ofpeople starting the studyIncidence = N of people who develop the outcome / N ofpeople starting the study

Both require a time frameBoth require a time frame

In Falls study, time frame is 90 days after assessmentIn Falls study, time frame is 90 days after assessment

So they estimated a period prevalenceSo they estimated a period prevalence

MeasurementMeasurement

Outcome: fall (yes or no) in 90 daysfollowing assessmentOutcome: fall (yes or no) in 90 daysfollowing assessment

–Binary–Binary

Exposure: manyExposure: many

– some continuous (age) some categorical– some continuous (age) some categorical

Analysis: Logistic regressionAnalysis: Logistic regression

TABLE 1: WHAT HAVE THEYPRESENTEDTABLE 1: WHAT HAVE THEYPRESENTED

Characteristic

No Falls (n = 3573) n(%) or M ± SE

Falls (n = 1997) n (%)or M ± SE

p Value

Age (years)

76.4 ± 0.21

78.7 ± 0.24

<.001

Gender (female)

2088 (58.4)

1192 (58.9)

.19

Cognitive Performance

2.15 ± 0.03

2.17 ± 0.04

.72

ADL impairment

4.54 ± 0.05

4.81 ± 0.05

<.001

Foot problems

717 (20.1)

480 (24.0)

<.001

Gait problems

1893 (53.0)

1454 (72.8)

<.001

Fear of falling

1525 (42.7)

1152 (57.7)

<.001

Visual impairment

1595 (44.6)

964 (48.3)

.005

Wandering

98 (2.7)

148 (7.4)

<.001

Alzheimer's disease

136 (3.8)

78 (3.9)

.45

CHF

562 (17.3)

342 (18.7)

.12

Depression

1960 (54.9)

1370 (68.6)

<.001

Diabetes mellitus

623 (19.2)

379 (20.7)

.09

Parkinsonism

228 (6.4)

158 (7.9)

.04

Peripheral artery

597 (18.4)

352 (19.3)

.24

Urinary incontinence

1087 (30.4)

657 (32.9)

.03

Environmental hazards

1486 (41.6)

1097 (54.9)

<.001

N and % of people with fallsaccording to risk factor stausN and % of people with fallsaccording to risk factor staus

Risk Factor +

Risk Factor -

RR (95% CI)

Foot problems

480 (40)

1517 (35%

1.14

Gait problems

Age, probability that faller and non fallersdiffered by ageAge, probability that faller and non fallersdiffered by age

Falls = ageFalls = age

Age = falls (yes or no)Age = falls (yes or no)

Does age depend on fallsDoes age depend on falls

Does exposure depend on outcomeDoes exposure depend on outcome

E│OE│O

What is the age range?

What is the standard error?

Standard Normal DistributionStandard Normal Distribution

Showing the proportion of the population thatlies within 1, 2 and 3 SD (Wikipedia)

MeasuresMeasures

Theoretical range: 0 to 36

ADLADL

Table 1Table 1

Proportion of Fallers (non-fallers) who werewomenProportion of Fallers (non-fallers) who werewomen

–2088 women / 3573 fallers (women and men)–2088 women / 3573 fallers (women and men)

This is the prevalence of exposure givingoutcome (PE | Fall)This is the prevalence of exposure givingoutcome (PE | Fall)

Is this what you want to know?Is this what you want to know?

Is this the question? NOIs this the question? NO

The question relates to the probability of havinga fall, given exposure (PFALL | E )The question relates to the probability of havinga fall, given exposure (PFALL | E )

Lets make a tableLets make a table

PE | Fall+ = 1454 / 1997 = 72.8%PE | Fall- = 1893 / 3573 = 53.0%

But, what we really want is …..

PFALL | E+ = 1454 / 3347 = 43.4%

PFALL | E- = 543 / 2223 = 24.4%

Risk ratio or Relative risk = 1.78

Risk of Fall | E+ 0.434

Risk of Fall | E- 0.244

Exposure

Fall NO

Fall YES

Total

Gait problems NO

1680

543

2223

Gait problems YES

1893

1454

3347

3573

1997

5570

Lets Look at Table 2Lets Look at Table 2

Presented are the odds ratiosPresented are the odds ratios

–(approximately equivalent to risk ratio when the outcome is rare<15% prevalence)–(approximately equivalent to risk ratio when the outcome is rare<15% prevalence)

Parameter arising from statistical programs for logisticregressionParameter arising from statistical programs for logisticregression

Gait problems OR 2.13Gait problems OR 2.13

Our friend the 95% CI: 1.81–2.51Our friend the 95% CI: 1.81–2.51

RR was 1.78 close to the adjusted OR of 2.13RR was 1.78 close to the adjusted OR of 2.13

Adjustment was for age, sex and significant variables inTable 2Adjustment was for age, sex and significant variables inTable 2

OR > RR when outcome is prevalentOR > RR when outcome is prevalent

AdjustmentAdjustment

Adjustment mathematically makes the twogroups equal on the adjustment variablesto find the independent effect of thevariable under studyAdjustment mathematically makes the twogroups equal on the adjustment variablesto find the independent effect of thevariable under study

Eg. People are given average ageEg. People are given average age

95% CI for Risk Factors for Falls95% CI for Risk Factors for Falls

0.7 0.8 0.9 1 2 3 4

95% CI thatinclude 1.0indicate noeffect

95% CI thatexclude 1.0indicate aneffect

Ratio could be 1 = no effect

Increased risk of fall

Decreased risk of fall

What else can we learn fromthis paper?What else can we learn fromthis paper?

Odds ratios and 95% confidence intervals of significant risk factor interactions for falling.

Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722-M726

The Gerontological Society of America

Odds ratios and 95% confidence intervals of significant risk factor interactions for falling.

Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722-M726

The Gerontological Society of America

Odds ratios and 95% confidence intervals of significant risk factor interactions for falling.

Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722-M726

The Gerontological Society of America

Odds ratios and 95% confidence intervals of significant risk factor interactions for falling.

Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722-M726

The Gerontological Society of America

Wandering

Yes

Gait NO

1.34

Gait Yes

2.25

Odds ratios and 95% confidence intervals of significant risk factor interactions for falling.

Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722-M726

The Gerontological Society of America

Environmental Hazards

Yes

Depression -

2.03

Depression+

2.08

Odds ratios and 95% confidence intervals of significant risk factor interactions for falling.

Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722-M726

The Gerontological Society of America

Environmental Hazards

Yes

Wandering -

1.67

Wandering +

2.49

What have we learned so far?What have we learned so far?

Descriptive statsDescriptive stats

–Understand distribution by looking at SD–Understand distribution by looking at SD

CorrelationCorrelation

–Strength of linear relationship–Strength of linear relationship

–% variance explained r2–% variance explained r2

Statistics for InferenceStatistics for Inference

–On means (t-test)–On means (t-test)

–On proportions (chi-square)–On proportions (chi-square)

Inference on ProportionsInference on Proportions

Chi square test (1 df)Chi square test (1 df)

Exposure

Fall NO

Fall YES

Total

Gait problems NO

1680

543

2223

Gait problems YES

1893

1454

3347

3573

1997

5570

Df = n rows * n columns so with a 2X2 table there is 1 df

Given we would always know how many people were exposedand how many had the outcome (the margins) all we need to knowis 1 of the cells and the rest are derived from that (1 df)

Chi to NormalChi to Normal

As the number of df increases thedistribution approaches a normaldistributionAs the number of df increases thedistribution approaches a normaldistribution

Some of the computer programs forcomparing 2 proportions use the normaldistribution (F distribution) rather than Chi.Some of the computer programs forcomparing 2 proportions use the normaldistribution (F distribution) rather than Chi.

As df increase closer to normalAs df increase closer to normal

1 2 4 normal

K by k tableK by k table

Total

Beyond Chi-squareBeyond Chi-square

Tells you that there is an associationTells you that there is an association

Does not tell you where it is or how strongit isDoes not tell you where it is or how strongit is

Need to calculate relative risks or oddsratiosNeed to calculate relative risks or oddsratios

Useful WebsitesUseful Websites

http://faculty.vassar.edu/lowry/VassarStats.htmlhttp://faculty.vassar.edu/lowry/VassarStats.html

http://people.ku.edu/~preacher/chisq/chisq.htm http://people.ku.edu/~preacher/chisq/chisq.htm

http://math.hws.edu/javamath/ryan/ChiSquare.ht ml http://math.hws.edu/javamath/ryan/ChiSquare.ht ml

http://math.hws.edu/javamath/http://math.hws.edu/javamath/

On to RegressionOn to Regression

Last class we will look at regressionLast class we will look at regression

Look a paperLook a paper

Kuspinar et al.Kuspinar et al.

Predicting Exercise Capacity ThroughSubmaximal Fitness Tests in PersonsWith Multiple SclerosisPredicting Exercise Capacity ThroughSubmaximal Fitness Tests in PersonsWith Multiple Sclerosis