Lecture 5. Contingency /incidence tables Sensibility, specificity Relative Risk Odds Ratio CHI SQUARE test

Transcription

1 Lecture 5 Contingency /incidence tables Sensibility, specificity Relative Risk Odds Ratio CHI SQUARE test

2 Contingency tables - example Factor 2 Present + Absent - Total Factor 1 Present + a b a+b Absent - c d c+d Total a+c b+d N=a+b+c+d One way to assess the relationship between two factors (the tendency for to occur or to be missing simultaneously) is to analyze the ratio of the number of individuals that have a match - both factors are present or both are absent and the number of individuals who don t have a match - a factor is present and the other absent =the Diagonal Coefficient. DC = (a+d)/ (b+c)

3 Contingency tables - example CD =( )/(152+36) = 2012/188=10.7 Clinical test Present + Disease Absent - Total Pozitive Negative Total The accuracy of a test represents the ratio between the number of individuals categorized correctly and the total number of individuals tested: Acc = (a+d)/(a+b+c+d) = ( )/2200 = 91.45%

4 Sensibility and Specificity The sensitivity of a clinical test refers to the ability of the test to correctly identify those patients with the disease. It represents the probability of a positive (abnormal) test when the subjects have the disease investigated. The specificity of a clinical test refers to the ability of the test to correctly identify those patients without the disease. It represents the probability of a negative (normal) test when the subjects don t have the disease investigated.

5 Clinical test- example Birth type Premature Normal Total Uterus Cervical Length <26 mm > 26 mm Total Sensitivity Sn= B+/B =33/41=80.4% Specificity Sp=S-/S =53/68=77.9%

6 Comparing clinical tests with the golden standard A clinical trial is as valuable as real sick patients and real healthy patients, are diagnosed by the test as positive and negative, respectively.

7 Positive predictive value PPV=B+/ P Shows the proportion of sick people of all subjects who had a positive result. Can be interpreted as the probability of being sick if the test is positive and represents the ability of a test to identify those individuals who are truly ill.

8 Negative predictive value NPV=S-/ N Shows the proportion of healthy people of all subjects who had a negative result. Can be interpreted as the probability of being healthy if the test is negative and represents the ability of a test to identify those individuals who are truly healthy.

9 Relative Risk - definition It is a measure of the relationship between disease and the presence of a risk factor, presumably influencing the disease. Because it is measured in terms of risk to those exposed and risk to those not exposed a risk factor, you need to know what are these two risks.

10 Risks The risk to those exposed is the likelihood of an exposed individual to get the disease. Present + Disease Absent - Total So, in the table, the risk to those exposed is 48/200, meaning 0.24 or 24%. Risk Factor Exposed + Not exposed Total

11 Risks The risk to those exposed is the likelihood of an exposed individual to get the disease. Present + Disease Absent - Total So, in the table, the risk to those not exposed is 36/2000, meaning 0,018 or 1,8%. Risk Factor Exposed + Not exposed Total

12 Relative Risk Relative risk is the ratio of risk to those exposed and risk to those not exposed. The risk to those exposed is 24%, The risk to those not exposed is 1,8% The relative risk is 24/1,8=13, 3

13 Risk Factor Present + Disease Absent - Total Exposed + a b a+b Not exposed - c d c+d Total a+c b+d N=a+b+c+d The risk to those exposed: R e = a/(a+b) The risk to those not exposed: R n = c/(c+d) Relative risk - RR=R e /R n, or R=(a*(c+d))/(c*(a+b)) The relative risk tells us how many times the likelihood of developing the disease when you are exposed to a risk factor is greater than when you are not exposed.

14 Interpreting the Relative Risk In general, relative risk values close to 1 show approximately the same likelihood of developing the disease, both exposed and unexposed to a factor, and it should be considered that the presumed risk factor does not have a real influence on the occurrence of disease If the relative risk is much higher than 1, it is an indicator that between the presumed risk factor and the disease there is a correlation, a link that usually is interpreted as the cause, although this is not necessarily the case.

15 Observation There are cases where the relative risk is smaller than 1, meaning that the analyzed factor is PROTECTIVE. For these factor, the risk of disease is lesser in those exposed compared to those not exposed.

16 Observation Attributable Risk is the risk difference between those exposed and those not exposed to risk. It is rarely used in practice. It has the advantage that it is expressed as a percentage. Ex.: RA=24%-1.8%=22.2%

17 Odds Ratio - definition Odds Ratio is the ratio between the odds for exposed individuals and the odds for not exposed individuals to develop an illness. The odds for those exposed is the ratio between the number of individuals exposed that are ill and the number of individuals exposed that are not ill. The odds for those not exposed is the ratio between the number of individuals not exposed that are ill and the number of individuals not exposed that are not ill.

18 Present + Disease Absent - Total Risk Factor Exposed + a b a+b Not exposed - c d c+d Total a+c b+d N=a+b+c+d Odds for exposed =a/b Odds for not exposed =c/d Odds Ratio - OR=(a/b) / (c/d)=(a*d)/(b*c)

19 Present + Disease Absent - Total Risk Factor Exposed Not exposed Total Odds for exposed =50/150= 1/3 Odds for not exposed =40/1960=1/49 Odds Ratio - OR=(1/3)/(1/49) = 49/3=16.3

20 Interpreting OR Values close to 1 show similar odds, meaning the exposure means does not affect the disease. Values greater than 1 show a correlation between exposure and disease, correlation which is usually considered as the cause, although this is not always true. Values below 1 show correlation, but in this case, exposure is considered a protective factor In all cases, the confidence with which we interpret the value of OR, is higher if the number of patients included in the table is large

21 Chi Square Test (χ 2 ) When ordinal or nominal data are involved, we need to use tests that analyze contingency tables, generated by "cross tabulation" of pairs of factors. The Chi Square test is a statistical test that shows if there is a relationship (interaction) between the two factors.

22 Age group < > Total Females Males Total % 40% 30% 20% 10% 44.83% 18.00% 22.00% 13.79% 12.00% 10.34% 38.00% 31.03% 6.00% 4.00% 0% 0.00% 0.00% < > Age group (p=0.015 statistically significant dif) The result of the Chi square test shows that there is a significant difference between the age distribution of the two sexes.