# 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.

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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, PhD David 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 Threats to validity –Bias –Confounding –Chance –Multiplicity Some solutions Some solutions –Study design –Randomization –Masking (AKA blinding) –Analysis 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? 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 relationship with ___ predictor variable? For ___ response variable, is there a difference between the characteristic identified by the ___ 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? Q: Are the predictor variable’s values related to the response variable’s values? –Is the predictor related to the response? Variables have values Variables have values –What type of values does the variable have? Which variable is the predictor, and which the response? 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” 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): Qualitative (named categories): –Nominal –Ordinal Quantitative (numeric): 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 CharacteristicsExamples Discrete or qualitative Observations grouped into distinct classes NominalClasses without a natural order or rank Sex, treatment group, presence or absence OrdinalClasses 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 classification Type of data Distinguishing CharacteristicsExamples Continuous or quantitative (numeric) Observation may assume any value on a continuous scale IntervalNumeric 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. Female B. Male 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.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? RankResponses 1 2 3 4 5 6

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): Qualitative (named categories): –Nominal –Ordinal Quantitative (numeric): 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.) 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 DataDescriptive statistic Test statistic & 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,…” “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 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: 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 use B. ONJ 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’s the question? “Outcomes” are related to “Predictors” “Outcomes” are related to “Predictors” Questions are of the form: 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. 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 Quantitative (numeric) continuous or discrete Qualitative nominal or ordinal 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 Quantitative (numeric) continuous or discrete Qualitative nominal or ordinal 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

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: 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. 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 use B. ONJ 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 Response variable: Decide which column? Quantitative (numeric) continuous or discrete Quantitative (numeric) continuous or discrete Qualitative nominal or ordinal Qualitative nominal or ordinal Time to event Time to event Quantitative (numeric), continuous or discrete Qualitative, 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

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, correlation B. Logistic regression C. Proportional hazards D. Two group t-test E. ANOVA F. Chi-square G. Kaplan-Meier survival analysis H. Paired t-test I. Repeated measures ANOVA J. McNemar’s chi-square

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 there an association between two nominal variables? Q: is the % on one variable different across the groups of the other variable? Q: is the % on one variable different across the groups of the other variable? Chi-square test of association 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: 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 predictor variable and type: The response 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, correlation B. Logistic regression C. Proportional hazards D. Two group t-test E. ANOVA F. Chi-square G. Kaplan-Meier survival analysis H. Paired t-test I. Repeated measures ANOVA J. McNemar’s chi-square

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. 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. 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. 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. 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: 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 predictor variable and type: The response 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, correlation B. Logistic regression C. Proportional hazards D. Two group t-test E. ANOVA F. Chi-square G. Kaplan-Meier survival analysis H. Paired t-test I. Repeated measures ANOVA J. McNemar’s chi-square

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? Q: is there a correlation between two numeric variables? Answer with: Correlation, Simple linear regression 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 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 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. 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. 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. 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

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 pain B. Swelling, less swelling C. Dexamethasone, none D. Removal of 3 rd molar, no removal

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 above

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: 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 predictor variable and type: –Group (dexamethasone vs control) — nominal The response variable and type: 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 2 nd 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 2 nd 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: 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: The predictor variable and type: –Group (dexamethasone vs control) — nominal The response variable and type: 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 regression C. Proportional hazards D. Two group t-test E. ANOVA F. Chi-square G. Kaplan-Meier survival analysis H. Paired t-test I. Repeated measures ANOVA J. McNemar’s chi-square

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? Q: is there a mean difference between the groups? For two groups: a t- test For two groups: a t- test For more than two groups: Analysis of Variance 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 2 nd 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: 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: The predictor variable and type: –Postoperative day (Pre-op vs Day 2) — nominal The response variable and type: 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 regression C. Proportional hazards D. Two group t-test E. ANOVA F. Chi-square G. Kaplan-Meier survival analysis H. Paired t-test I. Repeated measures ANOVA J. McNemar’s chi-square

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 mean change across time? Q: is there a difference between two paired measures? Q: is there a difference between two paired measures? Two: paired t-test Two: paired t-test More than two: repeated-measures ANOVA More than two: repeated-measures ANOVA 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? Q: Does probability of the response change across the numeric predictor? A: Logistic regression (which yields a chi-square statistic) 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? Q: Are paired nominal outcomes different? McNemar’s chi- square 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? Q: Is the survival time different between groups? Kaplan-Meier survival analysis 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: 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”. 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 relationship with ___ predictor variable? For ___ response variable, is there a difference between the groups identified by the ___ 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. 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 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.” 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” Bad: more variables than subjects, “multiple t-tests” (likely) Bad: claims of “same” “similar” or “equivalent” (likely) Bad: claims of “same” “similar” or “equivalent” Signs and Symptoms

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