1 דר' רונית קלדרון אוקטובר 2014

נושאי השיעור  מדדי סיכום לשכיחות ארועים באוכלוסיה  יחס, פרופורציה, שיעור  תכונות ודוגמאות  תקנון  תקנון ישיר  תקנון עקיף 2

מדדי סיכום לשכיחות אירועים באוכלוסייה. 1 יחס – Ratio חלוקה של שני מספרים מהצורה c/d כאשר c ו- d מתייחסים לשכיחות של מאורע כלשהו.

Properties of Ratios  R= (c/d)* k. Often the ratio is multiplied by a value k where k is 1000, etc.  R > 0  R may or may not have units.

Ratio, Examples יחס מיטות אשפוז כלליות למיטות אשפוז פסיכיאטרי: # beds per doctor –850 beds/10 doctors –R = 85 beds for 1 doctor Sex Ratio:Male / Female Female / Male Odds ratio Rate ratio 5

6

7 מקור: הלשכה המרכזית לסטטיסטיקה היחס בין גברים לנשים, ישראל, 2011

מדדי סיכום לשכיחות אירועים באוכלוסייה 2. פרופורציה - Proportion יחס שבו המונה הוא תת-קבוצה של המכנה.c/(c+d)

Properties of Proportions n - individuals in a population x - individuals in the populations have characteristics C p = x/n proportion in the population with C Range=?

Properties of Proportions 0  p  1 p has no units p can be expressed as kp per k where k is a number such as 1000,10000 in order to avoid very small numbers.   

Example In 2009, among Israeli women 19% of all deaths from cancer were from breast cancer p=0.19 or 190 per Properties of Proportions

12

3. שעור - Rate יחס שבו מופיע אלמנט הזמן במונה וגם במכנה: a*/(a+b) כאשר : a* = מספר האירועים במשך תקופת זמן מסוימת (a+b) = גודל האוכלוסייה בסיכון לאירוע במשך תקופת הזמן. מדדי סיכום לשכיחות אירועים באוכלוסייה השיעור יכול להיות, אך אינו בהכרח, פרופורציה.

Properties of Rates Express relative frequency of an event per unit time. Person years and rates.  

Properties of Rates N(t) = number of people exposed to risk of event during a time period of length T. T j = number of time units (years) that person j is exposed to risk. A(t)=  (T j ) = person-years of exposure for the N(T) individuals D(T) = number of people with event in the time period.

Properties of Rates R = D(T) / A(T) = The rate of event is :

Properties of Rates Example 0 time 10y T 1 =5 T 2 =9 T 3 =5 T 4 =5 T 5 =3 * * * * = event

Properties of Rates- Example R = D(T)/A(T) = 3/( ) = 3/27 = 0.11 In vital statistics, we rarely know the exact exposure times. Instead we approximate A(T) by NT where N= mid period population size. Then: R = D(T)/NT = 3/(3x10) = 3/30 = 0.10

Examples of rates in vital statistics 1). Annual crude death rate = 2). Annual age-specific death rate. e.g. death rate ages 1- 4 =

Examples of rates in vital statistics 3). Percent of all deaths which are aged 1- 4= 4). Percent of all death due to cancer =

Examples of rates in vital statistics 5). Infant mortality rate =

Example of Age Adjustment 1. Comparison of Total Death Rates in a Population at Two Different Time Periods Early PeriodLater Period PopulationNo. of Deaths Death Rate per 100,000 PopulationNo. of Deaths Death Rate per 100, , ,0001,130126

Example of Age Adjustment 2). Comparison of Age-Specific Death Rates in Two Different Time Periods Early PeriodLater Period Age Group (yr) Pop.No. of Deaths Death Rate per 100,000 Pop.No. of Deaths Death Rate per 100,000 All ages 900, ,0001, , , , , , ,

Example of Age Adjustment 3). Carrying Out an Age Adjustment Using the Total of the Two Populations as the Standard Age Group (yr) Standard Population “Early” Rate per 100,000 Expected No. of Deaths Using “Early” Rate “Later” Rate per 100,000 Expected No. of Deaths Using “Later” Rate All 1,800, , , , , ,050 Total no. of deaths expected2,238 1,830

In the standard population age-adjusted rates (per population): “Early”= “Later”= Example - Age adjustment

26 Example - Age adjustment שיעורי התמותה הגולמיים ל-1,000 תושבים במדינת ישראל בשנת 2011 היו 5.9 ליהודים ו-2.9 למוסלמים

(0.1) שיעורי תמותה ספציפיים לגיל, ישראל 2011 יהודיםמוסלמים

30

31 השיעורים המתוקננים לגיל ל-1000 תושבים (אוכלוסיית התקן: מפקד 2008) היו 5.6 ביהודים ו-7.9 בקרב מוסלמים

32 Indirect Standatrdization תקנון עקיף

Age group (yr) Mortality per million men per year Number of men Number of doctors ,584, ,065,10012, ,876,17011, ,965,88010, ,756, Age-specific mortality rates due to cirrhosis.

Age group Standard mortality rate, all men (a) Observed pop. Number of doctors (b)(a) x (b) Total

By indirect standardization  Number expected =  Number observed=14  Ratio observed/expected = 3.1

Standardized Mortality Ratio Frequently used statistic in epidemiology SMR =

Cause-specific Mortality of Grand Multiparous Women in Finland. Hinkula, Am J Epidemiol, 2006

Types of Adjustment Procedures  Stratified or subgroup analysis  Direct or indirect standardization of rates  Multivariate statistical analysis

Example - Israeli Data שנתון סטטיסטי Period: Mortality rates to 1000 persons, men Overall: Jews-5.8; Arabs-3.1 Age group: 70-74: Jews-22.7; Arabs-35.7 Age group: 75-79: Jews-39.6; Arabs-60.8

תמותה לפי מין, קבוצת אוכלוסיה ושנה שיעורים גולמיים

תמותה לפי מין, קבוצת אוכלוסיה ושנה שיעורים מתוקננים למאה אלף

Example - Israeli Data Deaths, crude rate per 100,000, women =571 Adjusted* mortality rate per 100,000: Spain 438 Italy 444 Sweden 491 Israel 512 * Standard population = European population

Example - Israeli Data Deaths, crude rate per 100,000, among men =597 Adjusted* mortality rate per 100,000: Iceland 681 Israel 723 Sweden 740 Italy 751 EU * Standard population = European population

Direct method - Properties Calculate what rates in each group would be if the groups had the same age distribution or composition (that of the standard population) Results : 1.Actual values of adjusted rates are meaningless 2.Compare directly adjusted rates to each other.  

Direct method - Properties Does require the 1.Age-specific rates for each group. 2.Age distribution of the standard population. 

Indirect method - Properties  Calculate how many deaths would be expected in each group if the age-specific rates of the reference population were applicable  Results: 1.Actual values of adjusted rates are meaningless 2.Compare indirectly standardized (adjusted) rates to the crude rate for the reference population.

Indirect method - Properties  Does not require age-specific rates for each group  Does require: 1.Age distribution of each group 2.Total deaths in each group 3.Age-specific rates for a standard population.