O RGANIZING & DISPLAYING DATA Dr. Omar Al Jadaan Assistant Professor – Computer Science & Mathematics

S UMMARIZING AND DISPLAYING BINARY AND CATEGORICAL DATA Binary data: data which takes two values. Example of binary data is yes/no, … etc Summary of binary: First step in analyzing categorical data is to count the number of observations in each category Express them in proportions of the total sample size. Then calculate the following metrics : ratio, proportion, percentage, risk and rates.

Ratio: is simply one number divided by another. Example : Weight of person (in kg) and height (in meters) then the ratio of weight and height is Body Mass Index. Proportions: are ratio of counts where the numerator (the top number) is subset of the denominator ( the bottom number). Example: in study of 50 patients, 30 are depressed, the the proportion is 30/50 or 0.6. Percentage : is the proportion multiplied by * 100 = 60% of the patients are depressed. Risk : is a proportion if the numerator counts events which happens prospectively (likely ) Example: 300 students start nursing school and 15 drop out before final, the risk of dropping is 15/300=0.05 or 5%.

Rates: it is proportion where time period is attached to it. Example people die in one year out of population of the death rate is / = 0.01 death per person per year. This known as crude death rate ( ignoring important factors like age).

Type of delivery FrequencyPercentageGender Male n (%) Female n (%) Standard Vaginal delivery (33)23 (43) Assisted vaginal delivery10 4 (9)6 (11) Elective caesarean section884 (9)4 (8) Emergency caesarean section13 6 (13)7 (13 ) Emergency caesarean section not in labour (36)13 (25) Total (100)53(100) Distribution of modes of delivery within gender

Contingency table OutcomeTreatment TestControl PositiveAB NegativeCD A+CB+D

C OMPARING BINARY DATA We use the summary measures to show how the groups differ. By using the difference in proportions and relative risk Proportion for positive outcome is

The difference in proportion is In prospective (likely) studies the proportion is known as a risk. If we ignore the sign we got the absolute risk difference (ARD) If we anticipate that the treatment to reduce some bad outcome (negative) (such as death) then it may be known as absolute risk reduction (ARR)

Risk Ratio or relative risk (RR) Inverse of ARD is the number needed to treat/harm

E XAMPLE SUMMARIZING RESULTS OF S MOKING CESSATION Stopped Smoking Nurse led InterventionUsual care (Control group) N%N% Yes No Smoking cessation rates at one year in the coronary heart disease Proportion values are 57/100 = 57% and 44/118 = 37% and the difference is 20%. If we started with 100 women we expect 20 patients between two groups.

Relative Risk is 57/37=1.5 this is the risk of stopping smoking (a good thing) with the intervention compared to the control group. Thus patients with coronary heart disease are 1.5 times more likely to stop smoking in the intervention group than the control group.

S UMMARIZING BINARY DATA - ODDS AND ODDS RATIO Instead of using the probability we use the odds which defined as the ratio of the probability of occurrence of the event to the probability of non- occurrence

From the contingency table we can find the odds ratio When the probability of an event happened is rare, the odds and probability are close, because a is much smaller than c. Thus OR approximate RR when the success are rare.

C OMPARISON OF RR AND OR FOR DIFFERENT BASE LINE P(test)P(control)RRORRR and OR Close Close Not close Not close Close Close

E XAMPLE (2437 RANDOM SAMPLE, 4 YEARS ) PsychosisCannabisTotal YesNo Yes No The risk of non-cannabis users is 342/2117 = 0.16 while the risk of cannabis users is 82/320 =0.26 Thus the relative risk of psychosis is 0.26/0.16= or an increased risk of 62.5% (1/1.6525) The odds ratio of psychosis for cannabis smokers is (82 * 1175 )/ (238 * 342 ) = 1.79, which is close to relative risk. Because the chance of getting psychosis is reasonably small. The OR of not developing psychosis is 1/1.79 = 0.56.

D ISPLAYING CATEGORICAL DATA Categorical data can be displayed either by bar charts or pie chart