Download Lecture 11d - Statistics II

POTH 612A
Quantitative Analysis
Dr. Nancy Mayo
A Framework for Asking Questions
Population
Exposure (Level 1)
Comparison Level 2
Outcome
Time
PECOT
© Nancy E. Mayo
PECOT Format
In people with
_____________________________________________
______________
Does suboptimal level of factor 1
_____________________________________________
_____________________________________________
In Comparison to optimal level of factor 1
_____________________________________________
__________________________
Affect (outcomes)
_____________________________________________
_____________________________________________
At Time ____________________________________
© Nancy E. Mayo
Types of Questions
About hypotheses
Is treatment A better than treatment B?
Answer: Yes or No
About parameters
What is the extent to which treatment A improves
outcome in comparison to treatment B?
Answer: A number / value (parameter)
© Nancy E. Mayo
Research is about relationships
Links one variable or factor to another
One is thought or supposed
(hypothesized) to be the “cause” of the
second variable
Example: Risk factors for falls
Your Job
When reading an article (later doing your
own research)
IDENTIFY THESE VARIABLES
IDENTIFY WHAT SCALE THEY ARE
MEASURED ON
What tables should I find in an
article
Table 1 – basic characteristics sample
Table 2 – outcomes / exposures
Table 3 - answer the main question
– Relationship between exposure and outcome
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
Older Community-Dwelling Population
What type of study is this?
Study of prevalence
Study of factors
What is prevalence?
– N of people with condition / All people in study
Incidence = N of people who develop the outcome / N of
people starting the study
Both require a time frame
In Falls study, time frame is 90 days after assessment
So they estimated a period prevalence
Measurement
Outcome: fall (yes or no) in 90 days
following assessment
– Binary
Exposure: many
– some continuous (age) some categorical
Analysis: Logistic regression
TABLE 1: WHAT HAVE THEY
PRESENTED
No Falls (n = 3573) n
Characteristic
(%) or M ± SE
Age (years)
76.4 ± 0.21
Gender (female)
2088 (58.4)
Cognitive Performance 2.15 ± 0.03
Falls (n = 1997) n (%)
or M ± SE
p Value
78.7 ± 0.24
<.001
1192 (58.9)
.19
2.17 ± 0.04
.72
ADL impairment
4.54 ± 0.05
4.81 ± 0.05
<.001
Foot problems
Gait problems
Fear of falling
Visual impairment
Wandering
717 (20.1)
1893 (53.0)
1525 (42.7)
1595 (44.6)
98 (2.7)
480 (24.0)
1454 (72.8)
1152 (57.7)
964 (48.3)
148 (7.4)
<.001
<.001
<.001
.005
<.001
Alzheimer's disease
CHF
Depression
Diabetes mellitus
Parkinsonism
Peripheral artery
Urinary incontinence
Environmental hazards
136 (3.8)
562 (17.3)
1960 (54.9)
623 (19.2)
228 (6.4)
597 (18.4)
1087 (30.4)
1486 (41.6)
78 (3.9)
342 (18.7)
1370 (68.6)
379 (20.7)
158 (7.9)
352 (19.3)
657 (32.9)
1097 (54.9)
.45
.12
<.001
.09
.04
.24
.03
<.001
N and % of people with falls
according to risk factor staus
Foot problems
Gait problems
Xx
Xx
Xx
Xx
x
Risk Factor +
Risk Factor -
RR (95% CI)
480 (40)
1517 (35%
1.14
Age, probability that faller and non fallers
differed by age
Falls = age
Age = falls (yes or no)
Does age depend on falls
Does exposure depend on outcome
E│O
What is the age range?
What is the standard error?
Standard Normal Distribution
Showing the proportion of the population that
lies within 1, 2 and 3 SD (Wikipedia)
Measures
Theoretical range: 0 to 36
ADL
Table 1
Proportion of Fallers (non-fallers) who were
women
– 2088 women / 3573 fallers (women and men)
This is the prevalence of exposure giving
outcome (PE | Fall)
Is this what you want to know?
Is this the question? NO
The question relates to the probability of having
a fall, given exposure (PFALL | E )
Lets make a table
Exposure
Fall NO
Fall YES
Total
Gait problems NO
1680
543
2223
Gait problems YES
1893
1454
3347
3573
1997
5570
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
Lets Look at Table 2
Presented are the odds ratios
– (approximately equivalent to risk ratio when the outcome is rare
<15% prevalence)
Parameter arising from statistical programs for logistic
regression
Gait problems OR 2.13
Our friend the 95% CI: 1.81–2.51
RR was 1.78 close to the adjusted OR of 2.13
Adjustment was for age, sex and significant variables in
Table 2
OR > RR when outcome is prevalent
Adjustment
Adjustment mathematically makes the two
groups equal on the adjustment variables
to find the independent effect of the
variable under study
Eg. People are given average age
95% CI for Risk Factors for Falls
95% CI that
include 1.0
indicate no
effect
0.7
0.8
0.9
Decreased risk of fall
95% CI that
exclude 1.0
indicate an
effect
1
2
3
4
Increased risk of fall
Ratio could be 1 = no effect
What else can we learn from
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:M722M726
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:M722M726
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:M722M726
The Gerontological Society of America
Odds ratios and 95% confidence intervals of significant risk factor interactions for falling.
Wandering
No
Yes
Gait NO
1
1.34
Gait Yes
2.25
?
Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722M726
The Gerontological Society of America
Odds ratios and 95% confidence intervals of significant risk factor interactions for falling.
Environmental Hazards
No
Yes
Depression - 1
2.03
Depression+
?
2.08
Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722M726
The Gerontological Society of America
Odds ratios and 95% confidence intervals of significant risk factor interactions for falling.
Environmental Hazards
Wandering -
No
Yes
1
1.67
Wandering + 2.49
?
Cesari M et al. J Gerontol A Biol Sci Med Sci 2002;57:M722M726
The Gerontological Society of America
What have we learned so far?
Descriptive stats
– Understand distribution by looking at SD
Correlation
– Strength of linear relationship
– % variance explained r2
Statistics for Inference
– On means (t-test)
– On proportions (chi-square)
Inference on Proportions
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 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 Normal
As the number of df increases the
distribution approaches a normal
distribution
Some of the computer programs for
comparing 2 proportions use the normal
distribution (F distribution) rather than Chi.
As df increase closer to normal
1
2
4
normal
K by k table
1
A
B
C
D
E
F
G
H
Total
2
3
4
5
6
7
8
Total
Beyond Chi-square
Tells you that there is an association
Does not tell you where it is or how strong
it is
Need to calculate relative risks or odds
ratios
Useful Websites
http://faculty.vassar.edu/lowry/VassarStats.html
http://people.ku.edu/~preacher/chisq/chisq.htm
http://math.hws.edu/javamath/ryan/ChiSquare.ht
ml
http://math.hws.edu/javamath/
On to Regression
Last class we will look at regression
Look a paper
Kuspinar et al.
Predicting Exercise Capacity Through
Submaximal Fitness Tests in Persons
With Multiple Sclerosis