# Adjustment of Rates by Hand / Calculator

NAME ____________________

ASSIGNMENT 3

Due in Class October 25th

38 Points + Extra Credit

Adjustment of Rates by Hand / Calculator

Suppose we have a “Small” Population and a “Large population and it is decided to use the Large Population as the Reference Population.

Below is the Data You will need to complete the blank squares of the table First to Answer the Questions: (1 POINT FOR TABLE)

|CATEGORYa |SMALL POPULATION |LARGE POPULATION |

| |di |Ni |[pic] |di |Ni |[pic] |

|1 |5 |100 | |6,000 |40,000 | |

|2 |20 |500 | |7,200 |60,000 | |

|3 |60 |2,000 | |9,000 |100,000 | |

|4 |80 |4,000 | |24,000 |400,000 | |

|OVERALL | |7,600 | | |600,000 | |

a. i.e., Category Could be and age range and/or something else

Here is the “Category Distribution” of the Reference Population which again is the the Larger Population

|CATEGORY |Ni |

|1 |40,000 |

|2 |60,000 |

|3 |100,000 |

|4 |400,000 |

1. Direct Adjust the Incidence for both the Small Population and the Large Population to the Reference Population and fill in the Table ON THE NEXT PAGE I am not asking you to find the variance. (2 POINTS)

SHOW DETAILS OF YOUR CALCULATIONS AND FILL IN TABLE ON NEXT PAGE:

|POPULATION |Crude Rate |Adjusted Rate |

|SMALL | | |

|LARGE | | |

2. Explain the Relationship Between the Crude Rate and the Adjusted Rate of the Large Population and why this occurred (1 POINT)

3. Indirect Adjust the Small Population to the Large Population to the Reference Population and find the SMR. (Again I am not asking you to find the variance). (2 POINTS)

[Remember SMR = 100 *

[pic]

Adjustment of Rates by SAS

SAS does not have a formal procedure to adjust rates (at least as far as I know). However, one of the nice things about SAS is that it is possible for a user to write a program on their own to perform simple analyses such as age adjustment. [You could also use other programs such as SPlus, Fortran, or even Excel to do this].

Suppose for example, we wished to obtain age adjusted rates of new Coronary Heart Disease for the following groups of men and women aged 55 – 74.

o Men with SBP < 165

o Men with SBP ≥ 165

o Women with SBP < 165

o Women with SBP ≥ 165

You have started a new job and have been given the following data stratified into age groups

|Group |# New Cases / # Persons in 2004 |

| |55 - 59 |60-64 |55-69 |70-74 |

|Men |36 / 1830 |35 / 1661 |36 / 1410 |13 / 470 |

|SBP < 165 | | | | |

|Men |9 / 260 |14 / 350 |16 / 350 |5 / 100 |

|SBP ≥ 165 | | | | |

|Women |13 / 1890 |15 / 1680 |18 / 1380 |7 / 350 |

|SBP < 165 | | | | |

|Women |7 / 420 |16 / 610 |25 / 690 |3 / 180 |

|SBP ≥ 165 | | | | |

You are told to age adjust the rates in 2004 for each of these groups to the Age distribution of New Jersey Adults from 55 – 64 which is:

Portion of New Jersey Adults 55 – 74 in Each Age Range During 2004

|Range |Portion |

|55-59 | 0.32 |

|60-64 | 0.32 |

|65-69 | 0.28 |

|70-74 | 0.08 |

(i.e. in 2004 32% of 55-74 year old adults in New Jersey are 55-59, etc.)

Now your boss also gives you a documented SAS program (as3.sas on the class website) that gives direct age adjusted rates along with confidence intervals for the “men with SBP < 165” and “Men with SBP ≥ 165” to the New Jersey age Distribution. But the previous worker made a mistake and assumed that 25% of New Jersey 55-74 year olds fell into each age range rather than the correct portions given in the previous table.

A. Read the Program in as3.sas to figure out how it works. Correct the mistake about the age distribution of 55 – 74 year olds in New Jersey and include the “women with SBP < 165” and “women with SBP ≥ 165” into the program. Show the changes you made to the program to correct it in the space below. I only need to see the changes not the entire program. (2 POINTS)

B. Write down the point estimates and 95% confidence intervals for each group in the Table Below. (2 POINTS)

New Coronary Heart Disease Cases Direct Adjusted to 55-74 NJ Population

|GROUP |Point Estimate |95% Confidence Interval |

|Men SBP < 165 | | |

|Men SBP ≥ 165 | | |

|Women SBP < 165 | | |

|Women SBP ≥ 165 | | |

C. From the results of the program develop a simple statistical approach to test Ho the direct age adjusted rates are the same for “55-74 men with SBP < 165” and “55-74 men with SBP ≥ 165”. Would you reject Ho at a two sided α=0.05? show your work. (2 POINTS)

*EXTRA CREDIT - Write a program that indirect adjusts the following age-specific rates of CHD for New Jersey to each of the target Populations. Give each SMR and a 95% confidence interval. NOTE – Assume that the population of New Jersey is large enough that the variance of the age specific CHD rates for New Jersey is ignorable. Attach Program and Write down SMR and Confidence Intervals in the Space Below (3 POINTS)

Age Specific 55 – 74 CHD for New Jersey

|Range |New CHD Portion |

|55-59 | 0.015 |

|60-64 | 0.019 |

|65-69 | 0.025 |

|70-74 | 0.032 |

INTERACTION

Describe the Following Interaction Patterns in terms of whether they are i) Qualitative, ii) Additive-Synergistic, iii) Additive-Antagonistic, iv) and/or v) Multiplicative-Synergistic, Multiplicative-Antagonistic. Use all terms that apply and explain your answers.

NOTE – I am only asking you to consider the point estimates. Do not think about P-values, confidence intervals, or statistical significance

PATTERN A [CASE CONTROL STUDY] (2 POINTS)

Men Women

Put Your Answer Here:

PATTERN B [CROSS SECTIONAL STUDY] (2 POINTS)

Boys Girls

Put Your Answer Here:

STATISICAL INTERPRETATION AND CAUSAL INFERENCE

I. In addition to developing AIDS, Homosexual men in infected with HIV-1 are also very likely to be infected with a different virus known as Zoster which causes a disease called shingles. It has been long known that a drug called Acyclovir is very useful in treating shingles once they occur. In the mid 1990s several articles suggested that Acyclovir may also counteract HIV-1 and delay AIDS in persons infected with HIV-1. At this point some (but not all) persons infected with HIV-1 began using Acyclovir to prevent AIDS. Of course, homosexual men also would use Acyclovir to treat shingles as well. Dr. HS was aware of this and wondered whether taking acyclovir to prevent AIDS might prevent shingles form occurring in homosexual men. For example, if a homosexual man began taking Acyclovir to prevent AIDS in January of 2004, maybe the fact that he was taking Acyclovir at the time would prevent an outbreak of Shingles that would have otherwise occurred in February 2004. In order to test this assumption Dr. HS went to the SCAM study which had recruited 150 HIV infected homosexual men in January 2004 and at enrollment had asked them numerous questions including:

o Did you use Acyclovir in 2003

o Did you develop Shingles in 2003

Dr. HS analyzed the data and from this obtained the following 2 x 2 Table:

|Used Acyclovir in 2003 |Zoster in 2003 |

| |Yes |No |

|Yes |40 |10 |

|No |30 |70 |

To his surprise, Acylovir was associated with higher (RR=9.33, p < 0.001) not lower risk of Zoster. He did further types analyses (which we will learn later in this class) to rule out the possibility of confounding so assume confounding does not exist. His Colleague Dr AC has a theory that Acyclovir actually activates Zoster in persons infected with HIV-1. Can you think of other causal reasons that this association was observed?

Write Your Answer Here (3 POINTS)

Mantel-Haenszel Adjustment by Hand / Calculator

Stratavarius is conducting a case-control study of whether attending musical concerts is associated with loss of hearing. He samples 200 adult cases 20 – 49 years old who had some loss of hearing and 200 adult controls 20 – 49 years old with no loss of hearing. For the purpose of this problem assume that the age distribution is similar between the cases and controls and there is no other potential confounder except for gender where it turns out that 140 of the 200 cases were men compared to only 95 / 200 controls.

Therefore, Stratavarius decides he must stratify the analysis by gender and obtains the following 2 x 2 Tables.

STRATA A = MEN

|Attended a Musical Concert |Hearing Loss |

| |Yes |No |

|Yes |110 |33 |

|No |30 |62 |

STRATA B = WOMEN

|Attended a Musical Concert |Hearing Loss |

| |Yes |No |

|Yes |40 |15 |

|No |30 |80 |

You have been hired by Stratavarius to analyze the data so do the following:

A. Find the pooled Mantel-Haenszel Odds Ratio (2 POINTS)

B. Construct a 95% confidence interval for the MH odds ratio Using Hauk’s method taught in class. (2 POINTS)

C. Use the asymptotic approach to test Ho: OR = 1. Give the test statistic and P-value. (2 POINTS)

D. Now pool the data together into one table and compute the Crude Odds Ratio. Qualitatively compare this crude odds ratio to the Mantel-Haenszel odds ratio and explain why you think these ORs are (or are not) that different. (2 POINTS)

Mantel-Haenszel Adjustment by Computer

You may remember from Assignment 2 that we looked at the association between low birth weight and smoking in a data set that had some other variables including race. It is well known that both smoking habits and birth rates differ by race in America. So a reasonable question exists as to whether race could confound smoking.

For the purposes of this assignment assume the data was collected from a case-control study of an uncommon outcome. You are now going to run a SAS program to undertake an analysis of low birth weight versus smoking stratified by race.

Repeat the Unstratified analysis of smoking Vs low birth weigth you did last time and also run an analysis of smoking versus low birth weight stratified by race. The commands are in as3b.sas. at the class web site. This is the same data you used in Assignment 2. See page 5 of Assignment 2 for a description of the variables.

E. Write down the following from the stratified analyses (6 POINTS)

o Pooled Mantel Haenszel (MH) Odds Ratio

o The 95% Confidence Interval for the pooled MH Odds Ratio

o The MH P-value for the pooled Odds Ratio to be 1

o The Breslow-Day test for homogeneity of OR across strata

F. Assume the Pooled Mantel-Haenszel Odds-Ratio from the output holds for each strata and use this to, estimate the Within Strata Percent Risk and PAR for low birth weight from Smoking for each Racial group. (4 POINTS)

|STRATA |Percent Risk from Smoking |Within Strata PAR From Smoking |

|RACE 1 | | |

|RACE 2 | | |

|RACE 3 | | |

SHOW DETAILS OF YOUR WORK ON NEXT PAGE

G. Compare the stratified OR to the unstratified OR from Assignment 2. What do you think caused the OR to change after adjustment (describe the specific mechanisms in detail). (1 POINT)

I. On your own do not turn in. Try running different programs requesting different options and different combinations of stratification variables and predictors.

-----------------------

|Exposure |Disease |

| |+ |- |

|+ |50 |50 |

|- |50 |50 |

|Exposure |Disease |

| |+ |- |

|+ |75 |25 |

|- |50 |50 |

|Exposure |Disease |

| |+ |- |

|+ |16 |112 |

|- |48 |80 |

|Exposure |Disease |

| |+ |- |

|+ |32 |96 |

|- |64 |64 |

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