POTH 612A Quantitative Analysis Dr. Nancy Mayo. © Nancy E. Mayo A Framework for Asking Questions Population Exposure (Level 1) Comparison Level 2 OutcomeTimePECOT

POTH 612APOTH 612AQuantitative Analysis Quantitative Analysis

Dr. Nancy Mayo

© Nancy E. Mayo© Nancy E. Mayo

A Framework for Asking QuestionsA Framework for Asking Questions

PopulationPopulation

Exposure (Level 1)Exposure (Level 1)

Comparison Level 2Comparison Level 2

OutcomeOutcome

TimeTime

PECOT PECOT


PECOT FormatPECOT FormatIn people with In people with ______________________________________________________________________________________________________________________Does suboptimal level of factor 1 Does 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 hypothesesIs treatment A better than treatment B?Is treatment A better than treatment B?

Answer: Yes or NoAnswer: Yes or No

About parameters About parameters What is the extent to which treatment A improves What is the extent to which treatment A improves outcome in comparison to treatment B?outcome 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 One is thought or supposed (hypothesized) to be the “cause” of the (hypothesized) to be the “cause” of the second variablesecond variable

Example: Risk factors for fallsExample: Risk factors for falls

Your JobYour Job

When reading an article (later doing your When reading an article (later doing your own research)own research)

IDENTIFY THESE VARIABLESIDENTIFY THESE VARIABLES

IDENTIFY WHAT SCALE THEY ARE IDENTIFY WHAT SCALE THEY ARE MEASURED ONMEASURED ON

What tables should I find in an What tables should I find in an articlearticle

Table 1 – basic characteristics sample Table 1 – basic characteristics sample

Table 2 – outcomes / exposures Table 2 – outcomes / exposures

Table 3 - answer the main question Table 3 - answer the main question – Relationship between exposure and outcomeRelationship between exposure and outcome

Table 4 – interesting subgroup Table 4 – interesting subgroup

Fall yes Fall no

Foot problem + 480 (24% of the column)

717 (20.1%) of column

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 an Prevalence and Risk Factors for Falls in an Older Community-Dwelling PopulationOlder 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 studyN of people with condition / All people in study

Incidence = N of people who develop the outcome / N of Incidence = N of people who develop the outcome / N of people starting the studypeople 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 prevalence So they estimated a period prevalence

MeasurementMeasurement

Outcome: fall (yes or no) in 90 days Outcome: fall (yes or no) in 90 days following assessmentfollowing assessment– BinaryBinary

Exposure: many Exposure: many – some continuous (age) some categorical some continuous (age) some categorical

Analysis: Logistic regression Analysis: Logistic regression

TABLE 1: WHAT HAVE THEY TABLE 1: WHAT HAVE THEY PRESENTED PRESENTED

CharacteristicNo Falls (n = 3573) n

(%) or M ± SEFalls (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 falls N and % of people with falls according to risk factor stausaccording to risk factor staus

Risk Factor + Risk Factor - RR (95% CI)

Foot problems 480 (40) 1517 (35% 1.14

Gait problems

Xx

Xx

Xx

Xx

x

Age, probability that faller and non fallers Age, probability that faller and non fallers differed by agediffered 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 DistributionShowing the proportion of the population that

lies within 1, 2 and 3 SD (Wikipedia)

http://upload.wikimedia.org/wikipedia/commons/8/8c/Standard_deviation_diagram.svg

MeasuresMeasures

Theoretical range: 0 to 36

ADLADL

Table 1Table 1

Proportion of Fallers (non-fallers) who were Proportion of Fallers (non-fallers) who were womenwomen– 2088 women / 3573 fallers (women and men)2088 women / 3573 fallers (women and men)

This is the prevalence of exposure giving outcome This is the prevalence of exposure giving outcome (P(PE E | Fall)| 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 having a The question relates to the probability of having a fall, given exposure (Pfall, given exposure (PFALLFALL | E | 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 = 1.78Risk of Fall | E+ 0.434Risk 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 (approximately equivalent to risk ratio when the outcome is rare

<15% prevalence) <15% prevalence)

Parameter arising from statistical programs for logistic Parameter arising from statistical programs for logistic regression regression

Gait problems OR 2.13 Gait 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 in Adjustment was for age, sex and significant variables in Table 2Table 2

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

AdjustmentAdjustment

Adjustment mathematically makes the two Adjustment mathematically makes the two groups equal on the adjustment variables groups equal on the adjustment variables to find the independent effect of the to find the independent effect of the variable under studyvariable under study

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

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

0.7 0.8 0.9 1 2 3 4

95% CI that include 1.0 indicate no effect

95% CI that exclude 1.0 indicate an effect

Ratio could be 1 = no effect

Increased risk of fallDecreased risk of fall

What else can we learn from What else can we learn from this paper?this 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










Wandering

No Yes

Gait NO 1 1.34

Gait Yes 2.25 ?




Environmental Hazards

No Yes

Depression - 1 2.03

Depression+ 2.08 ?




Environmental Hazards

No Yes

Wandering - 1 1.67

Wandering + 2.49 ?

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

Descriptive stats Descriptive stats – Understand distribution by looking at SDUnderstand distribution by looking at SD

Correlation Correlation – Strength of linear relationshipStrength of linear relationship– % variance explained r% variance explained r22

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

Chi to NormalChi to Normal

As the number of df increases the As the number of df increases the distribution approaches a normal distribution approaches a normal distributiondistribution

Some of the computer programs for Some of the computer programs for comparing 2 proportions use the normal comparing 2 proportions use the normal distribution (F distribution) rather than Chi. distribution (F distribution) rather than Chi.

As df increase closer to normalAs df increase closer to normal1 2 4 normal

K by k tableK by k table

1 2 3 4 5 6 7 8 Total

A

B

C

D

E

F

G

H

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 strong Does not tell you where it is or how strong it isit is

Need to calculate relative risks or odds Need to calculate relative risks or odds ratiosratios

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://math.hws.edu/javamath/ryan/ChiSquare.html

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 paper Look a paper

Kuspinar et al. Kuspinar et al.

Predicting Exercise Capacity Through Predicting Exercise Capacity Through Submaximal Fitness Tests in Persons Submaximal Fitness Tests in Persons With Multiple Sclerosis With Multiple Sclerosis

Documents

POTH 612A Quantitative Analysis Dr. Nancy Mayo. © Nancy E. Mayo A Framework for Asking Questions Population Exposure (Level 1) Comparison Level 2 OutcomeTimePECOT