Chi Square Tests PhD zgr Tosun IMPORTANCE OF EVIDENCE BASED MEDICINE The Study Objective: To determine the quality of health recommendations and claims made on popular medical talk shows. Sources: Internationally syndicated medical television talk shows that air daily (The Dr Oz Show and The Doctors). Interventions: Investigators randomly selected 40 episodes of each of The Dr Oz Show and The Doctors from early 2013 and identified and evaluated all recommendations made on each program. A group of experienced evidence reviewers independently searched for, and evaluated as a team, evidence to support 80 randomly selected recommendations from each show. Main outcomes measures: Percentage of recommendations that are supported by evidence as determined by a team of experienced evidence reviewers. Results On average, The Dr Oz Show had 12 recommendations per episode and The Doctors 11. At least a case study or better evidence to support 54% (95% confidence interval 47% to 62%) of the 160 recommendations (80 from each show). For recommendations in The Dr Oz Show, evidence supported 46%, contradicted 15%, and was not found for 39%. For recommendations in The Doctors, evidence supported 63%, contradicted 14%, and was not found for 24%. The most common recommendation category on The Dr Oz Show was dietary advice (39%) and on The Doctors was to consult a healthcare provider (18%). The magnitude of benefit was described for 17% of the recommendations on The Dr Oz Show and 11% on The Doctors Conclusions Recommendations made on medical talk shows often lack adequate information on specific benefits or the magnitude of the effects of these benefits. Approximately half of the recommendations have either no evidence or are contradicted by the best available evidence. The public should be skeptical about recommendations made on medical talk shows. A Fictional Answer for a Random Dr. Ozs Recommendation Dr Oz: "Saturated fat is solid at room temperature, so that means it's solid inside your body." Patient: Thanks, Dr. Oz. You give the best advice. Carrots are very hard and dense, so they'll petrify (transform into stone) your body, turning you into an orange statue. Am I doing it right? Pull down that bread, kiddo!!! CATEGORICAL ONE SAMPLETWO SAMPLES>2 SAMPLES CATEGORICAL ONE SAMPLETWO SAMPLES>2 SAMPLES IndependentPairedIndependent CATEGORICAL ONE SAMPLE TWO SAMPLES>2 SAMPLES IndependentPairedIndependent 2 x 2 Chi Square Test Mc Nemar Test N x M Chi Square Test One Sample Chi Square Test Fishers Exact Test Nonparametric One sample difference of proportions test Parametric Cross Table (Contingency Table) enables showing two or more variables simultaneously in table format a table of counts cross-classified according to categorical variables best way to include sub-group descriptive statistics simplest contingency table is a 2 x 2 table is good for demonstrating possible relationships among variables Cross Table (Contingency Table) An r X c contingency table shows the observed frequencies for two variables. The observed frequencies are arranged in r rows and c columns. The intersection of a row and a column is called a cell Misreading the Table it is important to correctly read the information given in a table although the original data do not change at all, tables can be arranged in several different views looking at the table does not necessarily show the reader about possible relationships among variables in order to decide on the existence of relationship, statistical hypothesis testing is required Observed versus Expected In a cross tabulation, the actual numbers in the cells of the table are called the observed values Observed Frequencies are obtained empirically through direct observation Theoretical, or Expected Frequencies are developed on the basis of some hypothesis Expected Frequencies Assuming the two variables are independent, you can use the contingency table to find the expected frequency for each cell. Finding the Expected Frequency for Contingency Table Cells The expected frequency for a cell E r,c in a contingency table is Example : Find the expected frequency for each Male cell in the contingency table for the sample of 321 individuals. Assume that the variables, age and gender, are independent Female and older Total Male Total51 6041 5031 4021 3016 20Gender Age Expected Frequency Example continued : Female and older Total Male Total51 6041 5031 4021 3016 20Gender Age Chi-Square Independence Test A chi-square independence test is used to test the independence of two variables. Using a chi-square test, you can determine whether the occurrence of one variable affects the probability of the occurrence of the other variable. For the chi-square independence test to be used, the following must be true. 1.The observed frequencies must be obtained by using a random sample. 2.Each expected frequency must be greater than or equal to 5. Chi-Square Independence Test We are looking for significant differences between the observed frequencies in a table (f o ) and those that would be expected by random chance (f e ) 2 x 2 Chi Square df = (r-1)(c-1)= O 11 2 TotalN First criteria Total Second Criteria O 12 O 21 O 22 O.1 O.2 O1.O1. O 2. E ij should be greater than or equal to 5. Is squint more common among children with a positive family history? Is there an association between squint and family history of squint? Total Squint ( alk) Total Family History 2 (1,0.025) =5.024 > Accept H 0. There is no relation between squint and family history Attention In 2 X 2 contingency tables, if any expected frequencies are less than 5, then alternative procedure to called Fishers Exact Test should be performed. An Example A study was conducted to analyze the relation between coronary heart disease (CHD) and smoking. 40 patients with CHD and 50 control subjects were randomly selected from the records and smoking habits of these subjects were examined. Observed values are as follows: Observed and expected frequencies + - Yes No Total 90 Smoking Total CHD df = (r-1)(c-1)=(2-1)(2-1)=1 2 (1,0.05) =3.841 Conclusion: There is a relation between CHD and smoking. 2 =4. 95 > reject H 0 An Example for Fishers Exact Test Research question: does positive BRCA1 gene actually affects the occurrence of breast cancer? Since the percentage of the cells which have expected count < 5 is 50%, Fishers exact test should be applied. According to Fishers test, p value is p> Fail to reject H 0 BRCA1 gene has no affect on breast cancer McNemar Test 35 patients were evaluated for arrhythmia with two different medical devices. Is there any statistically significant difference between the diagnose of two devices? Device I Device II Total Arrhythmia (+)Arrhythmia (-) Arrhythmia (+)10313 Arrhythmia (-)13922 Total231235 The significance test for the difference between two dependent population / McNemar test H 0 : P 1 =P 2 H a : P 1 P 2 Critical z value is 1.96 Reject H 0 McNemar test approach: 2 (1,0.05) =3.8413518 (9.8)16 (24.2) Reject H 0 Congenital abnormality22 PresentAbsent Age groups 253 (7.2)22 (17.8) (12.1)34 (29.9)1,95 >3518 (9.8)16 (24.2)9,64 Omit the >35 age group Congenital abnormality PresentAbsent Age groups H 0 is accepted At the end of the analysis, we should conclude that the risk of having a baby with congenital abnormality is significantly higher for >35 age group. However, risk is not differing significantly between