Displaying Your Results

Dr Tarek AminProfessor of Public Health

Cairo Universityamin55@myway.com

Are youCurrently engaged in research?Intention to publish in indexed journals?

Mistakes Could Happen!!!

Confusing between data and information in the results section.

Inclusion of too many pieces of data which may obscure the important stuff.

Inclusion of the mean, median, standard deviation, range, confidence interval, standard error and others for every measured variable studied.

Writing a manuscript around a significant P value.

Relying on statistical jargon instead of English to describe the results.

Prepare the stage

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Cameo appearance of the carrier-fading P value.

Presenting Your Results

Statistics Figures Tables

Analytic Descriptive

List

Subjects characteristics

Multi-variate

Comparison Numerical

Cartoon

Photographs

DichotomousCategoricalContinuous

Comparison

Statistics: Descriptive ResultsInvolve only one variable, either predictor or an

outcome

Types of descriptive data

Follow a logical order or rank

Ordinal

DichotomousBinary data

CategoricalLimited number ofmutually exclusive

possibilities

Continuous dataData having > 6 ordered values

Do not have a logical sequence

Nominal

1-Describing Dichotomous and

Categorical Variables

PercentageStandardize your data for easy

comparison

Risks, rates and OddsProportions

Provide both the numerator and denominator: (4/10 and 400/1000) = 40%Indicate precision using appropriate number of digits: (4/22 = 18.2% not 18.0%)Do not use % when the denominator is small: (< 50 subjects).With dichotomous variables only one value is needed: (after 3 years, 44% (86/196) of the subjects were still alive)For categorical variables, provide all % within categories: (we found that 12 % of the subjects had poor health, 23% had fair health and 41% had good health).

Numerical expression compares one part of the studyunits to the whole “expressed in fractions or decimals”(male patients represented 2/3 of our study subjects)

Risks, Rates, and OddsAre estimates of the frequency of a dichotomous outcome in a group of subjects

who have been followed for a period of time.

A study of 5000 people who were followed for 2 years to see who developed lung cancer, and among them 80 new cases occurred.

Risk

Number who develop outcome 80 = = 0.016Number at risk 5000

In cross-sectional study = prevalence = Number with a characteristic

Total number

Odds

Number who develop outcome 80 = = 0.0163Number at risk who do not develop outcome 4920

Rate

Number who develop outcome 80 = = 0.008 /person-yearPerson-time at risk 4920 *2 = 9940

Used in case-control study / in performing logistic regression.

Risk and Odds are roughly the same if the outcome occur in less 10 %, and similar to rate multiplied by the average amount of follow up.

Going little more deeper

2- Describing Continuous

Variables

0

50

100

Number of men

0 1 2 3 4 5 6 7 8 9

Triglyceride level

0

5

10

No. of women

15.01-17.5

17.51-20.00

20.01-22.50

22.51-25.00

25.01-27.50

27.51-30.00

30.01-32.50

32.51-35.00

35.51-37.50

37.51-40.00

age of the mother

Using Measures of average and spread

1- Examine your data

Using a graphMeasures of

skewness

Non-normal distribution Normal distribution

Measures of skewness or

symmetry Pearson’s skewness

Coefficient Fisher’s measure

of skewness

Skewness = (mean-median)/SD0 = perfectly symmetrical> + 0.2 or < - 0.2 indicate severe skewness

Deviation of the mean to the third power, done by computer.A value close to 0 = normal distribution> + 1.96 or < - 1.96 indicate significant skewness2- Description

Normal distribution Non-normal distribution

Mean Standard deviation

Median Inter-quartile range

Measures of average and spread: Provide information about the population from which your sample was chosen, and to which your results may apply.

Statistics: Analytic Results

Rules Compare two or more variables or groups.

First decide who should be compared “intention to treat” or “once randomized always analyzed”.

Comparing “like with like”. Making comparison between groups rather

within groups “placebo versus study groups rather than change occurred within study group after intervention”

Compare independent sampling units “five episodes of angiodema in a single patient should not be counted as a five sampling units”

Compare the effect size.

Mood changes of residents and interns on the day after being on call.

Characteristics Characteristics Interns Interns (n=40)(n=40)

Residents Residents (n=20)(n=20)

P P value value

Alert in roundsAlert in rounds

MoodMood

HappyHappy

NeutralNeutral

Sad Sad

Sleep (mean hr Sleep (mean hr /night)/night)

40 %40 %

20%20%

30%30%

50%50%

4.2 4.2

60%60%

40%40%

30%30%

30%30%

6.86.8

0.0200.020

0.0300.030

--

0.0120.012

0.0010.001

Effect size:Residents are 1.5 times as likely to be alert (60% / 40%=1.5) or 20% more likely to be alert.Interns are 0.67 times as likely to be alert.

Avoid writing the results section around a significant P value.

Effect Size “approach”

¶ List the 5 or 10 most essential analytic ‘key’ results in your study “brevity is a virtue”.

¶ Decide which is the predictor (independent) variable, and which is the outcome variable, for each.

¶ Decide whether predictor and outcome variables are dichotomous, categorical, or continuous.

¶ Decide what sort of effect size to use, based on the type of predictor, outcome variables and study design.

Predictor Predictor variable variable

Outcome Outcome variablevariable

Effect size Effect size Formula Formula

DichotomoDichotomous us

Dichotomous Dichotomous Relative Relative prevalence prevalence

Difference in Difference in prevalence prevalence

= proportion of men “hypertensive”= proportion of men “hypertensive”

proportion of women proportion of women “hypertensive“hypertensive

= proportion of hypertensive men – = proportion of hypertensive men –

proportion of proportion of hypertensive womenhypertensive women

Male (vs. Male (vs. female) female)

Hypertension Hypertension

(SBP > 160 or (SBP > 160 or DBP >90)DBP >90)

‘‘Cross-Cross-sectionalsectional’’

Antistroke Antistroke drug (vs. drug (vs. placebo)placebo)

Stroke in the Stroke in the next 2 years next 2 years

Clinical trial Clinical trial

Relative risk Relative risk (risk ratio)(risk ratio)

Risk Risk difference difference

= risk of stroke in persons treated = risk of stroke in persons treated with drugwith drug

risk of stroke in placebo group risk of stroke in placebo group

= risk of stroke in the treated – risk = risk of stroke in the treated – risk in placebo in placebo

Use of Use of saccharine saccharine (vs. non-(vs. non-use)use)

Bladder Bladder cancer (vs. cancer (vs. control)control)

Vertebral Vertebral fracture (vs. fracture (vs. no vertebral no vertebral fracture)fracture)

Bladder Bladder cancer in the cancer in the next 20 years next 20 years

Use of Use of saccharine in saccharine in the previous the previous 20 years 20 years

Hip fracture in Hip fracture in the next 5 the next 5 years years

Survival Survival analysisanalysis

Cohort studyCohort study

Odds ratio / Odds ratio / RR*RR*

Case-controlCase-control

Odds ratio Odds ratio

Rate ratio Rate ratio (relative (relative hazard)hazard)

Rate Rate difference difference

= odds of cancer in users of = odds of cancer in users of saccharinesaccharine

odds of cancer in non-usersodds of cancer in non-users

= odds of saccharine use in cases of = odds of saccharine use in cases of cancercancer

odds of saccharine use in odds of saccharine use in controlscontrols

= hip fracture rate in those with = hip fracture rate in those with vertebral fracturesvertebral fractures

hip fracture rate in those w/o hip fracture rate in those w/o vertebral fracturesvertebral fractures

= rate of hip fracture in those with = rate of hip fracture in those with vertebral fracture – rate of hip vertebral fracture – rate of hip fracture in those w/o vertebral fracture in those w/o vertebral

fracture.fracture.

Effect size measurements

*In cohort design: relative risk and Odds ratio could be used.

Predictor Predictor variable variable

Outcome Outcome variablevariable

Effect size Effect size Formula Formula

DichotomoDichotomous us

Continuous Continuous Mean Mean differencedifference

Mean % Mean % difference” difference”

Mean Mean difference in difference in change change

= mean SBP in whites – mean SBP = mean SBP in whites – mean SBP in non whitesin non whites

= mean SBP in white – mean SBP in = mean SBP in white – mean SBP in non whitesnon whites

mean SBP in non whitemean SBP in non white

= mean change in DBP in treatment = mean change in DBP in treatment group – group –

mean change in DBP in placebo mean change in DBP in placebo group group

White (vs. White (vs. non white)non white)

New drug New drug (vs. (vs. placebo) placebo)

Systolic blood Systolic blood pressure pressure (SBP)(SBP)

Case-control / Case-control / CohortCohort

Change in Change in diastolic blood diastolic blood pressure pressure (DBP)(DBP)

Clinical trialClinical trial

ContinuouContinuous s

Continuous Continuous

Regression/Regression/Slope Slope

Proportion of Proportion of variance variance explained explained

Change in 1, 25 Vitamin D level per Change in 1, 25 Vitamin D level per change in creatinine clearancechange in creatinine clearance

Correlation between lead level and Correlation between lead level and IQ IQ

Creatinine Creatinine clearanceclearance

Serum lead Serum lead level level

1, 25- vitamin 1, 25- vitamin D level D level

IQ IQ

Effect size measurements

Simple effect size for dichotomous predictor

and dichotomous outcome variables

Depends primarily on the study design:

Cross-sectional = prevalence Case-control = Odds ratios Cohort or randomized trial =

risk, rate, Odds, or risk or rate differences.

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Risk ratio: how many times more likely an event was to occur in one group than in another: a risk ratio of 2.23 (123%) greater risk (or 2.23 folds).

Risk ratios (odds ratio and rate ratios) that are less than 1 can be difficult to interpret.

Risk difference: how much more likely an outcome is to happen in one group than in another ‘a risk difference of 1 % means that of 100 subjects, one less event occurred in one of the group’.

Number needed to treat= 1/ risk difference.

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Odds difference do not make Odds difference do not make sensesense, , when comparing odds, when comparing odds, only the odds ratio is useful.only the odds ratio is useful.When the outcome is rare (< When the outcome is rare (< 10%):10%): Odds ratios, risk ratios, Odds ratios, risk ratios, and rate ratios are similar. and rate ratios are similar. When the outcome is > 30 %:When the outcome is > 30 %: the three measures are very the three measures are very different.different.

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More complicated ways for

dichotomy Logistic regression Cox proportional

hazard model Survival analysis

When the time to the outcome is not known or does not matter.Used to delineate the possible predictor for the outcome It yields Odds ratios.

Used when the time to the eventis known and matters.Useful when the amount of follow up varies among the subjects “Enrolled at different times, dropped out or died of unrelated causes”.

It yields rate (hazard) ratio.

Nothing to do with living or dying. Remaining free of the outcome of interestUsed whether the outcome is fatal or not

“disease free survival”.

Now, I know how you feel.

Effect size for Dichotomous predictors and Continuous outcome

variable Distribution

Normal Non-normal

Compare meansMean difference is the effect sizeAbsolute or % difference could be used

Compare medians

Or use non-parametric tests

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Effect size for Continuous predictor

and Continuous outcome

Linear regressionCorrelationOr others

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Indicating the precision of your estimates with Confidence

Intervals.• It is the range of values that are

consistent with your estimate.• 95% CI= repeating of bias-free study

many times, 95 % of all the CI for the point estimate “your finding” will contain the true value of the population.

• The wider a CI, the less precise is the point estimate.

Relation between CI and P value

Effect size measured asEffect size measured as No effect “insignificant P No effect “insignificant P value”value”

Difference in prevalenceDifference in prevalence

Risk differenceRisk difference

Rate differenceRate difference

Number needed to treatNumber needed to treat

Mean differenceMean difference

Mean % differenceMean % difference

Mean changeMean change

Mean % changeMean % change

SlopeSlope

CorrelationCorrelation

Prevalence ratioPrevalence ratio

Risk ratioRisk ratio

Odds ratioOdds ratio

Rate ratioRate ratio

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The concept of NO EFFECT.

ExamplesExamples • Mean difference in serum bicar. level Mean difference in serum bicar. level

between 2 groups is 5 meq/L (95% CI between 2 groups is 5 meq/L (95% CI of 2-8) = of 2-8) = the difference is significant the difference is significant because it does not include the NO because it does not include the NO EFFECT ‘0’.EFFECT ‘0’.

• The relative risk of osteosarcoma in The relative risk of osteosarcoma in smokers is 2.0 (95% CI, 1.0-4.0)= smokers is 2.0 (95% CI, 1.0-4.0)= P P value is > o.o5value is > o.o5..

• Odds ratio is 1.4 (95 % CI= 1.1-3.9)= Odds ratio is 1.4 (95 % CI= 1.1-3.9)= the P value is significant because it the P value is significant because it does not include the no effect= 1. does not include the no effect= 1.

Where the P value come from?

• Statistical tests of significance:• What, when, why and how? Next table.• Actual P value should be provided:

(P= 0.034 rather P < 0.05) or (P = 0.098 rather P > 0.05 or NS).

• Do not compare the P value. • Use the P value wisely: not more than

10-15.

Road map for statistical tests of significance Type of Data

Goal of the test Measurement (continuous)

Rank, Score, or Measurement (non-normal)

Binomial(Two Possible

Outcomes)

Survival Time

Describe one group

Mean, SD Median, interquartile range

Proportion Kaplan Meier survival curve

Compare one group to a hypothetical value

One-sample t test Wilcoxon test Chi-squareorBinomial test **

Compare two unpaired groups

Unpaired t test Mann-Whitney test Fisher's test(chi-square for large samples)

Log-rank test or Mantel-Haenszel*

Compare two paired groups

Paired t test Wilcoxon test McNemar's test Conditional proportional hazards regression*

Compare three or more unmatched groups

One-way ANOVA Kruskal-Wallis test Chi-square test Cox proportional hazard regression**

Compare three or more matched groups

Repeated-measures ANOVA

Friedman test Cochrane Q** Conditional proportional hazards regression**

Quantify association between two variables

Pearson correlation

Spearman correlation

Contingency coefficients**

Predict value from another measured variable

Simple linear regressionorNonlinear regression

Nonparametric regression**

Simple logistic regression*

Cox proportional hazard regression*

Predict value from several measured or binomial variables

Multiple linear regression*orMultiple nonlinear regression**

Multiple logistic regression*

Cox proportional hazard regression*

PARAMETRIC AND NONPARAMETRIC TESTS

You should definitely choose a parametric test if you are sure that your data are sampled from a population that follows a Gaussian “normal” distribution (at least approximately)

Select a nonparametric test in three situations:

Ω The outcome is a rank or a score and the population is clearly not Gaussian. Examples include class ranking of students, Apgar score, visual analogue score for pain, and star*** scale.

Ω Some values are "off the scale" that is, too high or too low to measure. Excess extremes.

Ω The data ire measurements, and you are sure that the population is not distributed in a Gaussian manner “biological fluids or markers”

PARAMETRIC AND NONPARAMETRIC

TESTS: THE HARD WAY.

A formal statistical test (Kolmogorov-Smirnoff test) can be used to test whether the distribution of the data differs significantly from a Gaussian distribution.

Conclusions:

• Identify the type of your variables.• Define which are the predictors and

which are the outcomes.• Use the effect size in description of

your results.• Estimate the 95% confidence

intervals for your estimates for better precision.

• Use the P value wisely and do not let it steal the show.

Thank you