Nervous system: BiostatisticsMin-Kyung Jung, Ph.D.Biostatisticianmjung01@nyit.eduNYCOM I Room 314E

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ObjectivesState chi-square test, McNemars test, and Fishers exact test as major statistical procedures for comparing proportions

Choose a right test among them for a given study design

Interpret odds ratios to measure effect sizes and their confidence intervals to describe precision

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Chi-square test: Statistical Procedure for Comparing ProportionsChi-square tests are performed to compare proportions of two (or more) independent groups

e.g.) If you want to compare the proportions of having headache between the group of chronic caffeine users and the group of non-caffeine users, which statistical test would you perform?

Important to check assumptions prior to employing a chi-square test

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Assumptions for chi-square testIndependence of the data

2. Expected counts greater than 5 for all cells - acceptable in larger contingency table to have up to 20% of expected counts below 5 - loss of power when violated (the test may fail to detect a genuine effect)Use McNemars testUse Fishers exact test

when violatedwhen violated

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Suppl: Procedure of Chi-square testCheck assumptionsCompute the chi-square test statisticCompute the degree of freedom (df): degree of freedom = (number of rows 1) * (number of columns 1)4. Determine the significance level of alpha ()Find a look-up value from the chi-square table depending on the df and the alpha ()Report the result of whether or not the two groups are significantly different by comparing the test statistic to the look-up value: significant if the test statistic value > the look-up value

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Suppl: Chi-square test statistic formula

where O is the observed count, E is the expected count for each cell, and the sum is made for all of four cellsHave caffeine-withdrawal headaches?

e.g.)

Caffeinerelieved headaches?YesNoTotalYesNoTotal

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Suppl: Steps to compute the chi-square statistic1. Find the observed counts O:2. Compute the expected counts E: E = (row sum) * (column sum) / (total)2. Compute the deviations of observed counts from expected counts: (deviation) = (observed count) - (expected count) = O - E3. Determine the contribution to chi-square: (contribution to chi-square) = 4. Compute the chi-square statistic: (test statistic) =

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Suppl: Observed/Expected counts

Observed counts (O) Expected counts (E)Headache/ReliefYes/Yes cell:Yes/No cell:No/Yes cell:No/No cell:Have headaches? 1626810224 * 42 / 152 = 6.6128 * 42 / 152 = 35.424 * 110 / 152 = 17.4128 * 110 /152 = 92.6

Caffeinerelieved headaches?YesNoTotalYes16824No26102128Total42110152

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Suppl: Contributions to chi-square

Observed(O) Expected(E) Contrib. to chi-square Headache/ReliefYes/Yes cell:Yes/No cell:No/Yes cell:No/No cell:Have headaches? 162681026.635.417.492.6(16 - 6.6)2 / 6.6 = 13.4(26 35.4)2 / 35.4 = 2.5(8 17.4)2 / 17.4 = 5.1(102 92.6)2 / 92.6 = 1.0

Caffeinerelieved headaches?YesNoTotalYes16824No26102128Total42110152

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Suppl: Chi-square statistic

Contrib. to chi-square test statistic Headache/ReliefYes/Yes cell:Yes/No cell:No/Yes cell:No/No cell:Have headaches? (16 - 6.6)2 / 6.6 = 13.4(26 35.4)2 / 35.4 = 2.5(8 17.4)2 / 17.4 = 5.1(102 92.6)2 / 92.6 = 1.013.4 + 2.5 + 5.1 + 1 = 22

Caffeinerelieved headaches?YesNoTotalYes16824No26102128Total42110152

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Suppl: Degree of freedom

Have headaches? Degree of freedom = (number of rows 1) * (number of columns 1)= (2 1) * (2 1) = 1

Caffeinerelieved headaches?YesNoTotalYes16824No26102128Total42110152

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Suppl: Alpha (); level of significance

Level of significance, notated alpha (), is one of the key concepts in hypothesis testing that specifies the probability level for our evidence to be an unreasonable estimate

A recommended standard, or decision criterion:

= 0.05

Be cautious about the blind adoption of this level

Can be adjusted when multiple comparison correction has to be made

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Suppl.

Suppl: Look up value from chi-square table

3.84The look up value with df = 1 and = 0.05 from the chi-square table is

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Suppl: Report the result whether or not significantReport the result of whether or not the two groups are significantly different by comparing the test statistic to the look-up value:

significant if the test statistic value > the look-up value

computed statistic: 22 Look up value with df = 1 and = 0.05: 3.84

Thus, the proportions of the two groups are significantly different.

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Review: Odds, Odds ratioOdds = A/B, C/D: the odds in favor of having disease with the factor: the odds in favor of having disease without the factorOdds ratio = (OR)=

FactorDiseaseYesNoExposedABUnexposed C D

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ExerciseA group of researchers conducted a survey study about caffeine-withdrawal headache with 152 subjects. They compared caffeine-withdrawal headache subgroup to non-headache subgroup regarding various caffeine self-report items including whether they agree that caffeine relieved headaches. The result was presented in a 2X2 table as below:

Calculate the odds ratio associated with having headaches and being relieved by caffeine

(16 / 8) / (26 / 102) = 7.85Odds of believing that caffeine relieves headaches is about 8 times higher in the caffeine-withdrawal headache group than in the non-headache group.Have caffeine-withdrawal headaches?

Caffeinerelieved headaches?YesNoTotalYes16824No26102128Total42110152

Review: CONFIDENCE INTERVALA range of values that tries to quantify the uncertainty, a range of plausible valuesA narrow interval implies high precisionA wide interval implies poor precisionCheck if the interval contains a value of no change /effect for interpretationThe end points of the confidence interval are referred to as the upper and lower confidence limits.

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Review: 95% CONFIDENCE INTERVALfor a population odds ratio :

The sample odds ratio does not assume the approximate normal distribution Transform using Ln (natural log, log with base e)

Standard error of Ln(OR)=

95% CI of Ln(OR) = Ln(OR) 1.96

95% CI of OR = exp[Ln(OR) 1.96 ]

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95% Confidence Interval of OR

Odds ratio (OR) =

Standard error of Ln(OR)=

95% CI of Ln(OR) = Ln(7.85) 1.96

95% CI of OR = exp[Ln(7.85) 1.96 ]

95% Confidence interval of OR 7.85 is (3.03, 20.33) which does not contain the null value 1.Have headaches? (16 / 8) / (26 / 102) = 7.85

Caffeinerelieved headaches?YesNoTotalYes16824No26102128Total42110152

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How to interpret?OR = 1 means no increased riskOR > 1 means an increased riskOR < 1 means a protective effect

e.g. 1) OR = 0.56 in the study of effect of low-dose aspirin on cardiovascular disease means a protective effect of having aspirin

e.g. 2) OR = 3.9 in the study of effect of helmet wearing on head injury at bike ride means an increased risk of not wearing helmet

How to check significance?Check if the associated 95% confidence interval contains 1OR is not significant if its CI contains 1OR is significant if CI does not contain 1

e.g. 1) OR = 0.48 with 95% confidence interval (0.26, 0.88) means a protective effect that is significante.g. 2) OR = 0.71 with 95% confidence interval (0.48, 1.04) means a protective effect that is not significant e.g. 3) OR = 1.22 with 95% confidence interval (0.86, 1.73) means an increased risk that is not significant e.g. 4) OR = 2.95 with 95% confidence interval (1.73, 3.51) means an increased risk that is significant

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Reference article 1Gender and the functional outcome of elderly ischemic stroke patients. Mizrahi et al.: To compare between the two gender groups, they performed t-test for continuous variables and chi-square test for categorical variables

Reference article 2Gender differences in non-motor symptoms (NMS) in early PD: A 2-yr follow-up study on previously untreated patients. Picillo et al.: To compare NMS frequency between the baseline and the follow-up, they performed McNemars test

Reference article 3Depression in PD is related to a genetic polymorphism of the cannabinoid receptor gene (CNR1). Barrero et al.: To compare genotypes frequency between those with and without depression, they performed Fishers exact test

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