View
215
Download
0
Category
Tags:
Preview:
Citation preview
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Which statistical method?
How to decide if the correct (initial) statistical test was used
Al M Best, PhDDavid C Sarrett, DMD, MS
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Threats to validity– Bias– Confounding– Chance– Multiplicity
Some solutions– Study design– Randomization– Masking (AKA blinding)– Analysis
Analysis– Descriptive stats– SD vs SE– T-test and ANOVA– Statistical significance vs
Clinical importance– Ordinal data and
nonparametric stats– Correlation– Survival analysis
Did the paper do the right stats?
Recall: Stats 3—Overview
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Which statistical method?How to decide if the correct statistical test was used? Questions are of the form: For ___ response
variable, is there a relationship with ___ predictor variable?
For ___ response variable, is there a difference between the characteristic identified by the ___ predictor variable?
See the “decision matrix” and presentation online.
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Given a Question, which stat method?
Q: Are the predictor variable’s values related to the response variable’s values?– Is the predictor related to the response?
Variables have values– What type of values does the variable
have? Which variable is the predictor, and which
the response?– What is the role of the variable in the
analysis? Look up the stat method in the “decision
matrix”
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Types of data
Qualitative (named categories):– Nominal– Ordinal
Quantitative (numeric):– Continuous, Discrete, Interval– Time to event
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Recall: Data classification
Type of data
Distinguishing Characteristics Examples
Discrete or qualitative
Observations grouped into distinct classes
Nominal Classes without a natural order or rank
Sex, treatment group, presence or absence
Ordinal Classes with a predetermined or natural order
Disease severity, bone density, plaque accumulation, bleeding
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Data classificationType of data
Distinguishing Characteristics Examples
Continuous or quantitative (numeric)
Observation may assume any value on a continuous scale
Interval Numeric value with equal unit differences; arbitrary zero
Temperature, GPA
Time to event
Survival analysis,Censored observations
Restoration survival time,Implant success
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
What is your sex?
A. FemaleB. Male
Femal
eM
ale
0%0%
Sex, the biological makeup of each person (based on his or her genes and chromosomes), is different from gender, which is how society and each particular culture see the roles of men and women. Source: JM Torpy et al “Men and women are different” JAMA 289(4):510 2003.
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
What is your age?
Rank Responses
1
2
3
4
5
6
1 2 3 4 5 6
0% 0% 0%0%0%0%
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Types of data
Qualitative (named categories):– Nominal– Ordinal
Quantitative (numeric):– Continuous, Discrete, Interval– Time to event
Think of the raw data from an individual participant (NOT the summary/descriptive statistic: which is always numeric.NOT the test statistic or p-value: which is always numeric.)
Raw Data Descriptive statistic
Teststatistic & p-value
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Example: Barasch’s “Risk Factors for Osteonecrosis
of the Jaws” “We conducted a case-control study in
dental practices to determine the risk associated with bisphosphonates and to identify other risk factors for ONJ,…”
From the introduction of Barasch, et al. (2011) J Dent Res 90(4), 439-444. pubmed/21317246
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Predictor variable
Recall that the main summary of results appeared as:
– BP use: Yes or No– ONJ group: Case or Control
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Which is the Predictor Variable?
A. BP useB. ONJ group
BP use
ONJ
group
0%0%
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
What’s the question?
“Outcomes” are related to “Predictors” Questions are of the form:
– For ___ response variable, is there a relationship with ___ predictor variable?
– For ___ response variable, is there a difference between the groups identified by the ___ predictor variable?
Look at the predictor variable first.
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Predictor variable:
Decide which row? Quantitative (numeric)
continuous or discrete Qualitative
nominal or ordinal
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Predictor variable:
Decide which row? Quantitative (numeric)
continuous or discrete Qualitative
nominal or ordinal
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
ONJ Group is what type of variable?
A. Quantitative (numeric) continuous or discrete
B. Qualitative, nominal or ordinal
Quan
titat
ive
(num
eric
)...
Qual
itativ
e, n
omin
al or..
.
0%0%
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
What’s the question?
Questions are of the form:– For ___ response variable,
is there a relationship with ___ predictor variable?
– For ___ response variable, is there a difference between the groups identified by the ___ predictor variable?
Now look at the outcome variable next.
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Which is the Response Variable?
A. BP useB. ONJ group
BP use
ONJ
group
0%0%
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Response variable:
Decide which column? Quantitative (numeric)
continuous or discrete Qualitative
nominal or ordinal Time to event
Quantitative (numeric),
continuous or discrete Qual
itative,
Nominal or
Ordinal
Time to
event
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
BP use is what type of variable?
A. Quantitative (numeric) continuous or discrete
B. Qualitative, nominal or ordinal
C. Time to event
Quan
titat
ive
(num
eric
)...
Qual
itativ
e, n
omin
al o...
Time
to e
vent
0% 0%0%
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
For BP use as a response and ONJ group as a predictor, what statistical test should be
used?A. Linear regression,
correlationB. Logistic regressionC. Proportional hazardsD. Two group t-testE. ANOVAF. Chi-squareG. Kaplan-Meier survival
analysisH. Paired t-testI. Repeated measures
ANOVAJ. McNemar’s chi-square
Linea
r regre
ssion, c
orrela
tion
Logistic
regre
ssion
Proporti
onal h
azard
s
Two g
roup t-
test
ANOVA
Chi-squa
re
Kaplan-M
eier
surv
ival
analy
sis
Paired t-
test
Repeated
meas
ures A
NOVA
McNem
ar’s c
hi-squar
e
0% 0% 0% 0% 0%0%0%0%0%0%
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Nominal predictor (independent groups),Nominal response:
Q: is there an association between two nominal variables?
Q: is the % on one variable different across the groups of the other variable?
Chi-square test of association
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Doll R, Peto R. Mortality in relation to smoking: 20 years’ observations on male British doctors. Br Med
J 1976;2:1525-1536.In 1951 the British Medical Association forwarded to all British doctors a questionnaire about their smoking habits, and 34,440 men replied. With few exceptions, all men who replied in 1951 have been followed for 20 years. The certified causes of all 10,072 deaths and subsequent changes in smoking habits were recorded. The ratio of the death rate among cigarette smokers to that among lifelong non-smokers of comparable age was, for men under 70 years, about 2:1, while for men over 70 years it was about 1.5:1. These ratios suggest that between a half and a third of all cigarette smokers will die because of their smoking, if the excess death rates are actually caused by smoking. To investigate whether this is the case, the relation of many different causes of death to age and tobacco consumption were examined, as were the effects of giving up smoking. Smoking caused death chiefly by heart disease among middle-aged men (and, with a less extreme relative risk, among old men), lung cancer, chronic obstructive lung disease, and various vascular diseases. The distinctive features of this study were the completeness of follow-up, the accuracy of death certification, and the fact that the study population as a whole reduced its cigarette consumption substantially during the period of observation. As a result lung cancer grew relatively less common as the study progressed, but other cancers did not, thus illustrating in an unusual way the causal nature of the association between smoking and lung cancer.
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
What’s the question?
Questions are of the form:– For ___ response variable,
is there a relationship with ___ predictor variable?
– For ___ response variable, is there a difference between the groups identified by the ___ predictor variable?
The predictor variable and type: The response variable and type:
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
For mortality as a response and smoking as a predictor, what statistical test should be
used?A. Linear regression,
correlationB. Logistic regressionC. Proportional hazardsD. Two group t-testE. ANOVAF. Chi-squareG. Kaplan-Meier survival
analysisH. Paired t-testI. Repeated measures
ANOVAJ. McNemar’s chi-square
Linea
r regre
ssion, c
orrela
tion
Logistic
regre
ssion
Proporti
onal h
azard
s
Two g
roup t-
test
ANOVA
Chi-squa
re
Kaplan-M
eier
surv
ival
analy
sis
Paired t-
test
Repeated
meas
ures A
NOVA
McNem
ar’s c
hi-squar
e
0% 0% 0% 0% 0%0%0%0%0%0%
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Messerli FH Chocolate consumption, cognitive function, and Nobel laureates. N Engl J Med. 2012
367(16):1562-4. Purpose: To determine if there was a relationship between a country’ level of chocolate consumption and its population’s cognitive function.
Method: Determine the number of Nobel laureates per 10 million persons from Wikipedia. Determine per capita yearly chocolate consumption from Chocosuisse, Theobroma-cacao, and Caobisco.
Results: There was a close, significant linear correlation (r=0.791, P<0.0001) between chocolate consumption per capita and the number of Nobel laureates per 10 million persons in a total of 23 countries.
Conclusions: Chocolate consumption enhances cognitive function, which is a sine qua non for winning the Nobel Prize, and it closely correlates with the number of Nobel laureates in each country.
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
What’s the question?
Questions are of the form:– For ___ response variable,
is there a relationship with ___ predictor variable?
– For ___ response variable, is there a difference between the groups identified by the ___ predictor variable?
The predictor variable and type: The response variable and type:
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
For Nobel laureates as a response and chocolate as a predictor, what stat. test
should be used?A. Linear regression,
correlationB. Logistic regressionC. Proportional hazardsD. Two group t-testE. ANOVAF. Chi-squareG. Kaplan-Meier survival
analysisH. Paired t-testI. Repeated measures
ANOVAJ. McNemar’s chi-square Lin
ear r
egressi
on, corre
latio
n
Logistic
regre
ssion
Proporti
onal h
azard
s
Two g
roup t-
test
ANOVA
Chi-squa
re
Kaplan-M
eier
surv
ival
analy
sis
Paired t-
test
Repeated
meas
ures A
NOVA
McNem
ar’s c
hi-squar
e
0% 0% 0% 0% 0%0%0%0%0%0%
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Continuous predictor,Continuous response:
Q: is there a correlation between two numeric variables?
Answer with: Correlation,Simple linear regression
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
“… significant linear correlation between chocolate consumption per capita and the number of Nobel laureates per 10 million persons …” Messerli FH. Chocolate consumption, cognitive function, and Nobel laureates. N Engl J Med. 2012 Oct 18;367(16):1562-4. PubMed:23050509
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Can you switch the outcome and the predictor?
If both variables are continuous, correlation is used and it doesn’t matter which variable is in which role.
If both variables are nominal, chi-square is used and it doesn’t matter which variable is in which role.
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Warraich R, et al. Evaluation of postoperative discomfort following third molar surgery using submucosal
dexamethasone. Oral Surg Oral Med Oral Pathol Oral Radiol 2013;116:16-22.Background. Surgical removal of impacted lower third molar
is still the most frequent procedure done by Oral and Maxillofacial surgeons and is often associated with pain, swelling and trismus. These postoperative sequelae can cause distress to the patient as a result of tissue trauma and affect the patient’s quality of life after surgery. Use of antiseptic mouthwashes, drains, muscle relaxants, cryotherapy, antibiotics, corticosteroids and physiotherapy seems to decrease postoperative discomfort. Among them corticosteroids are well-known adjuncts to surgery for suppressing tissue mediators of inflammation, thereby reducing transudation of fluids and lessening edema. The rationale of this study is to determine the effectiveness of submucosal injection of dexamethasone in reducing postoperative discomfort after third molar surgery.
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Warraich, 2013 … continued
Patients and Methods. 100 patients requiring surgical removal of third molar under local anesthesia were randomly divided into 2 groups, group I receiving 4 mg dexamethasone as submucosal injection and the control group II received no steroid administration. Facial swelling was quantified by anatomical facial landmarks. Furthermore, pain and patient satisfaction, as well as neurological score and the degree of mouth opening were observed from each patient.
Results. Patients receiving dexamethasone showed significant reduction in pain, swelling, trismus, a tendency to less neurological complaints and improved quality of life compared with the control group.
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
What type of study is this?
A. Randomized control trial
B. Case-control study
C. Qualitative study
D. Prospective cohort study
Randomiz
ed c
ontrol t
rial
Case-c
ontrol s
tudy
Qual
itativ
e st
udy
Prosp
ectiv
e co
hort st
udy
0% 0%0%0%
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
The “IC” in PICO for this study is:
A. Pain, no painB. Swelling, less
swellingC. Dexamethasone
, noneD. Removal of 3rd
molar, no removal Pai
n, no p
ain
Swel
ling, l
ess
swelli
ng
Dexam
ethas
one, n
one
Remova
l of 3
rd m
olar,.
..
0% 0%0%0%
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
The “O” in PICO for this study is:
A. Reduced pain, facial swelling, and trismus
B. Less neurological complaints
C. Improved quality of life
D. All of the aboveReduce
d pai
n, fac
ial s
...
Less n
euro
logic
al c
om...
Impro
ved q
uality
of l
ife
All of t
he above
0% 0%0%0%
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
What’s the question?
Questions are of the form:– For ___ response variable,
is there a relationship with ___ predictor variable?
– For ___ response variable, is there a difference between the groups identified by the ___ predictor variable?
The predictor variable and type: – Group (dexamethasone vs control) —
nominal The response variable and type:
– “degree of mouth opening” Trismus — ???
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Warraich, 2013 … Figure 5
Refer to the figure, which is a graphical representation of their measurement of trismus (reduced mouth opening) in patients who either did or did not receive 4mg dexamethasone at the time of third molar removal.Fig 5. “Pre-operative mouth opening values did not differ significantly in both groups. On the 2nd postoperative day a significant reduction of mouth opening could be revealed in both groups. The reduction of mouth opening was significantly lower in the dexamethasone group compared to the conventional group.”
Fig 5. “Pre-operative mouth opening values did not differ significantly in both groups. On the 2nd postoperative
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
For the claim “Pre-operative mouth opening
values did not differ significantly in both groups.”, what’s the question? Questions are of the form:– For ___ response variable,
is there a difference between the groups identified by the ___ predictor variable?
The predictor variable and type: – Group (dexamethasone vs control) —
nominal The response variable and type:
– “mouth opening (trismus) in mm — continuous
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
For trismas as a response and drug as a predictor, what stat. test should be used?
A. Linear regression, correlation
B. Logistic regressionC. Proportional hazardsD. Two group t-testE. ANOVAF. Chi-squareG. Kaplan-Meier survival
analysisH. Paired t-testI. Repeated measures
ANOVAJ. McNemar’s chi-square Lin
ear r
egressi
on, corre
latio
n
Logistic
regre
ssion
Proporti
onal h
azard
s
Two g
roup t-
test
ANOVA
Chi-squa
re
Kaplan-M
eier
surv
ival
analy
sis
Paired t-
test
Repeated
meas
ures A
NOVA
McNem
ar’s c
hi-squar
e
0% 0% 0% 0% 0%0%0%0%0%0%
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Nominal predictor (independent groups),Continuous response:
Q: is there a mean difference between the groups?
For two groups: a t-test
For more than two groups: Analysis of Variance– Followed by a
multiple comparison procedure.
“groups” of independent subjects
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Warraich, 2013 … Figure 5
Refer to the figure, which is a graphical representation of the measurement of trismus (reduced mouth opening) in patients who either did or did not receive 4mg dexamethasone at the time of third molar removal.Fig 5. “Pre-operative mouth opening values did not differ significantly in both groups. On the 2nd postoperative day a significant reduction of mouth opening could be revealed in both groups. The reduction of mouth opening was significantly lower in the dexamethasone group compared to the conventional group.”
… “a significant reduction of mouth opening could be revealed in” the dexamethasone group.Think “reduction”=“change”
Post-op − Pre-op → Change
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
For the claim “Mouth opening changed in the dexamethasone group.”,
what’s the question? Questions are of the form:
– For ___ response variable, is there a difference between the groups occasions identified by the ___ predictor variable?
The predictor variable and type: – Postoperative day (Pre-op vs Day 2) —
nominal The response variable and type:
– mouth opening (trismus) in mm— continuous
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
For trismas as a response and time as a predictor, what stat. test should be used?
A. Linear regression, correlation
B. Logistic regressionC. Proportional hazardsD. Two group t-testE. ANOVAF. Chi-squareG. Kaplan-Meier survival
analysisH. Paired t-testI. Repeated measures
ANOVAJ. McNemar’s chi-square Lin
ear r
egressi
on, corre
latio
n
Logistic
regre
ssion
Proporti
onal h
azard
s
Two g
roup t-
test
ANOVA
Chi-squa
re
Kaplan-M
eier
surv
ival
analy
sis
Paired t-
test
Repeated
meas
ures A
NOVA
McNem
ar’s c
hi-squar
e
0% 0% 0% 0% 0%0%0%0%0%0%
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Nominal predictor (paired occasions or measures),Continuous response: Q: is there a
mean change across time?
Q: is there a difference between two paired measures?
Two: paired t-test More than two:
repeated-measuresANOVA
Compare measurements, not “groups” of people
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Continuous predictor,Nominal response:
Q: Does probability of the response change across the numeric predictor?
A: Logistic regression(which yields a chi-square statistic)
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Logistic regression
Janus C, Sbeih I, Best AM. The role of volume of multi-surface restorations in posterior teeth: Treatment options. General Dentistry. 2011;59:486-491
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Nominal predictor (paired occasions or measures),Nominal response: Q: Are paired
nominal outcomes different?
McNemar’s chi-square
Dental example: a split-mouth design
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Time to an event: A response occurs (event) at a time point
Q: Is the survival time different between groups?
Kaplan-Meier survival analysis– Example:
do composites or amalgams last longer in children?
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
The New England Children’s Amalgam Trial
Soncini, et al. (2007) The longevity of amalgam versus compomer/ composite restorations in posterior primary and permanent teeth, JADA, 138: 763-777.
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
What’s the question?
Usually, questions are of the form:– For ___ response variable, is there a
relationship with ___ predictor variable?– For ___ response variable, is there a
difference between the groups/occasions identified by the ___ predictor variable?
But sometimes, you want to conclude “no difference” or “just as good as”.– These require different tests:
Equivalence tests.
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Which statistical method?How to decide if the correct statistical test was used? Questions are of the form: For ___ response
variable, is there a relationship with ___ predictor variable?
For ___ response variable, is there a difference between the groups identified by the ___ predictor variable?
See the “decision matrix”.
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
The correct initial statistical test All of the above are ONLY for the case of
ONE outcome variable and ONE predictor. Think about multiplicity, especially
multiple teeth/surfaces/implants/restorations or time points– Look for some indication that a more
complex analysis was done– An author with PhD or MPH is a good
sign
V I R G I N I A C O M M O N W E A L T H U N I V E R S I T Y
Good: “multi-way ANOVA”, “multiple regression”, “multiple logistic regression”, “multiple comparison”, “repeated-measures ANOVA”, “proportional hazards”, “adjusted analysis.”
Bad: more variables than subjects, “multiple t-tests”
(likely) Bad: claims of “same” “similar” or “equivalent”
Signs and Symptoms
Recommended