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


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


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.


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”


Types of data

Qualitative (named categories):– Nominal– Ordinal

Quantitative (numeric):– Continuous, Discrete, Interval– Time to event


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


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


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.

http://jama.jamanetwork.com/article.aspx?articleid=195841


What is your age?

Rank Responses

1

2

3

4

5

6

1 2 3 4 5 6

0% 0% 0%0%0%0%


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


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

http://www.ncbi.nlm.nih.gov/pubmed/21317246



Predictor variable

Recall that the main summary of results appeared as:

– BP use: Yes or No– ONJ group: Case or Control


Which is the Predictor Variable?

A. BP useB. ONJ group

BP use

ONJ

group

0%0%


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.


Predictor variable:

Decide which row? Quantitative (numeric)

continuous or discrete Qualitative

nominal or ordinal


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%



Questions are of the form:– For ___ response variable,

is there a relationship with ___ predictor variable?


Now look at the outcome variable next.


Which is the Response Variable?

A. BP useB. ONJ group

BP use

ONJ

group

0%0%


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


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%


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%


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


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.






The predictor variable and type: The response variable and type:


For mortality as a response and smoking as a predictor, what statistical test should be

used?A. Linear regression,



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%


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.






The predictor variable and type: The response variable and type:


For Nobel laureates as a response and chocolate as a predictor, what stat. test

should be used?A. Linear regression,



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%


Continuous predictor,Continuous response:

Q: is there a correlation between two numeric variables?

Answer with: Correlation,Simple linear regression


“… 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



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.


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.


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.


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%


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%


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%






The predictor variable and type: – Group (dexamethasone vs control) —

nominal The response variable and type:

– “degree of mouth opening” Trismus — ???


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


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) —


– “mouth opening (trismus) in mm — continuous


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



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%


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


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


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) —


– mouth opening (trismus) in mm— continuous


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



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%


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


Continuous predictor,Nominal response:

Q: Does probability of the response change across the numeric predictor?

A: Logistic regression(which yields a chi-square statistic)


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


Nominal predictor (paired occasions or measures),Nominal response: Q: Are paired

nominal outcomes different?

McNemar’s chi-square

Dental example: a split-mouth design


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?


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.



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.


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”.


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


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

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