Sent: March 1, 2010 3:46 PM
To: James Hanley, Dr.
Subject: EPIB 634 Asst 4

Hey,

We have a question in regards to Q3ii. We have attempted to calculate the person time for everolimus and the number of people in which the primary endpoint occurred. The number of events at 10 days is not given, is this supposed to be read off of figure 2a.

If so, is there a more efficient way then expanding the image and using graphics editor program to make an educated guess as to the number of events and total person time in this interval.

If so, the number at risk below figure 2a, for everolimus, the numbers given below (the number who survived) does not correspond with the number of primary end point events in the abstract at 12 months...

Q2

Sent: March 1, 2010 12:05 PM
To: James Hanley, Dr.
Subject: Question regarding the assingment for Thursday

Professor Hanley,

In question 1, part i of the assignment, we wanted to see if we are on the right track:

In calculating the five-year risk, we used the fifth year incidence density (despite the fact that the ID changes between time intervals) and multiplied this number by five (5 years) to estimate # of events over five year period (mu = 0.025 events per year, over five years, we would have 0.125 events per 5 year period).

To get S(t), we took the negative exponent of the above figure and got 0.88. Obviously, based on the equations provided, we calculated CI as 0.12, where we explained that there is 12% risk in individuals not treated with Rosuvastatin in the five year period. Is this a right approach?

Or should we have taken into consideration of two other ID given in the question (first two years, year 3 and 4)?

If so, how should we factor two other ID along with the fifth year ID into calculating an overall ID for the five year period (and ultimately calculating S(t))?

And for the question 1, part iii, we were hoping to answer this question by suggesting that the event rate in part i is based on the fifth year incidence density to predict the five year survival/risk whereas in part ii we estimated the incidence density based on the 12-month average (where in fact, on the 12th month, the actual incidence density of PI may be lower than 0.0975 due to the gain in intern experience). Basically, in part ii, we are assuming constant rate of incidence density (obviously averaged rates of ID over the 12 month period - some months will be higher, some months will be lower than the average) in predicting S(t) for the 12 months of experience. The reason for CI in part i being similar to ID is the fact that we are using fifth year ID to calculate S(t) for a five year period, where, in fact, the ID rates change over the five year period. In part ii, we take this into a consideration by using the averaged ID per month.

Are we on the right track?

Q2

On 3/16/08 2:40 AM, "Student X.Y" wrote:

Dr.Hanley hello

I have frustrated myself trying to figure out how to do question 2i of the assignment: I can't make the command work for summing all 'dac' limited to year 71 AND also limited to ages 40-85. ....so that after having this sum and that for the Person years, I can calculate the crude all cause mortality rate..

will you please let me know how to do this? I know i can manually sum it up to come up with crude rates but I would really like to know the R code.

much appreciated

http://132.206.244.30/~jameshanley/c634/rates/q_fm_mortality_R.txt


One way is to extract the data fist, as is done there in the code

females=read.table("q_f_mortality_data.txt",header=TRUE)

ds = females[

          (females$year==71 | females$year==02 ) &
          (females$agefrom >= 40 & females$agefrom <= 80 ) ,
          
          c(2,3,4,7,8)
                     ] ; 
                     
ds[ds$year==71,"yrs.since71"] = 0 ;
ds[ds$year== 2,"yrs.since71"] = 31 ; ds

If really want to, can extract each year separately 

The code above (with the | for 'or' ) extracts both

To extract one, use e.g. 

ds71 = females[

          (females$year==71  ) &
          (females$agefrom >= 40 & females$agefrom <= 80 ) ,
          
          c(2,3,4,7,8)
                     ] ;

Now you can

 sum(ds71$dac)  

Etc

Q1

My first questions are regarding question 1.

1 )

When I compare the expected rate of my multiplicative model to my additive model for a specific category, let's say the exposed group in the 60-69 age category, the estimated rates are slightly different.

Is this to be expected or should they be the same?

E[y= body surface area]  = height to some power P 

and 

E [log body weight ] =  B0 + B1 x height

and

log { E [body weight ] } =  C0 + c1 x height

Clayton and Hill write: "[...] but because the estimated values of the parameters in the additive model must be restricted so that they predict positive rates." Is the imposed restriction the cause of the observed difference in rates?

X = concentration of alcohol in a drink

y = 1 you can tell that the drink has alcohol , 0 if not 

you might well be able to fit a binomial model with identity link

ie prob[y=1] = B0 + B1 X

2) When I compare the coefficients in the categorical model vs the continuous models, I find all coefficients in the categorical model to correspond, in some way, to the coefficients in the continuous models. However, the coefficients of the categorical model always end up with a slightly higher value than those in the continuous models.

Why is that?

1 in ref (0) category
1.5 in next  so beta_hat_1 = 1og RR  = 0.405
2.25 in next so beta_hat_2 = log RR  = 0.81,
3.375 in next so log = 1.21,
etc

Q2

In Q.2 part iii) Is the intercept of the following glm output a 'corner'?

glm(dac~as.factor(agefrom) + as.factor(yrs.since71),family=poisson,offset=log(pop),data=ds)

Q3

I have been working on question #3 of the assignment and was able to get parts i and ii, but I am having problems with part iii in terms of getting the "cornering" into my R code. I looked up the references by Clayton and Hills from question #2 but, still cannot piece it together.

Rate = Corner x Exposure (Gender) x Age does not make that much sense to me. I cannot flip it to how we have seen regression in 607 and 621.

eg ideal weight 

100 lb + 5 lbs for every inch above 5' + 10 extra lbs if male + (if male) 1 extra lb for every inch above 5' 

corner is the 100 lb for 5' females 

so in a model

   glm(cases~x1+x2 + ...,family=poisson,offset=log(pt))

you are fitting 

log{E[#cases]} = linear predictor           + offset 

                = B0 + B1.X1 + B2.X2 + ..    + log(pt)

back-translate

E[#cases]} = exp[ B0 + B1.X1 + B2.X2 + ..    + log(pt) ]

           = { exp[ B0] x exp[B1.X1] x exp[B1.X1]  ....   x  pt

divide by pt

E[#cases/pt]} = exp[ B0] x exp[B1.X1] + exp[B1.X1]  .... 

ie 

Expected[rate] = corner rate x multiplier associated with X1 x multiplier associated with X2   ...  etc

Q3

A quick question regarding the R code that you gave us: What exactly is the ~1 doing in this model?

glm(cases~-1 + pt+ e.pt + ... , family=poisson(link="identity"))

Q3

I would like to have some clarifications about Question 3 of Assignment. I understand the part where you ask us to rewrite the OR. However, you also asked us to explain why PT1 and PT0 do not appear in eqn 7-5, whereas their counterparts c and d do in eqn 7-6. And I guess you really referred to the equations of SE (and not eqn 8-5 and 8-6). I guess that because you can measure the person-time directly in a cohort study, this does not contribute to your "uncertainty" where as in a case-control study, you have to account for the fact that controls are used. Am I on the right track? How do you demonstrate that mathematically?

I am kind of lost as many others. It would be great if we can focus on one thing for a week, so that we can understand it. You might have to pick ONLY those few things which are important from an Epidemiology master's student point of view. We are not learning anything like this. I hope you understand.

I have a question about Q. 4 part ii. In the Wilson formula on page 132 of Rothman, do I use N=1084 and a=6, as there are 6 people with infection and 1084 w-y at risk?

I am a little confused about question 2. I arrived at the CI in part (i), namely by using a probability of 0.8 x 10(-6), and n of 3 million odd. However, since the probability is expressed as 0.8 per 100,000 persons (call it a unit), and there are 33 such units in the total population, could I not have used the binomial setting, pie= .8, n=33. I do, but the CI I get when I do this is much smaller. (approx, 0.66 to 0.94).Ê Perhaps this is because the probability is close to the extremes of the probability range and the number of trials too small. Does that make any sense?

I have tried to access material from your other courses on your webpage (such as EPIB 607), but the M-H password doesn't give me access. Can you help? Thanks

Q4

I have a quick question about the confidence interval on the IDR in question 4(ii), safe-pilots. Because it is a ratio, I do not have a 'count' to plug in the Poisson CI spread sheet. Is that correct. I am not able to calculate the confidence interval, hence.

Q5

I was reading the Miettinen paper. While I understood the last two columns of the table-1 after reading the original formulas from his paper, I do not understand why he multiplies by 5-years in the foot note to calculate 30-year risk. Please explain.

I do not understand what question 5i) is asking. Where are the 30-year risk of bladder cancer, calculated by Miettinen, in the article? Are you refering to the exposure-specific incidence density?

4.1. The parameters. Even though the source population of subjects tends to constitute a (dynamically) static group in each category of age (figure 1), with new people continually entering it at the lower bound (and within the range) of age and others exiting it (within the range and) at the upper bound, the data from successive age categories may be used to make inferences about an aging cohort of fixed membership and homogeneous, though continually increasing, age. With regard to such an age-cohort, the interest is, firstly in the cumulative incidence of the group as it passes from one age to another, and, secondly, in the corresponding risks of its individual members.

The cumulative incidence-rate for a span of age is the proportion of the group developing the illness in that period, while the risk for an individual is the probability of his developing the illness in the particular span of age.

I understand why the multiplier time is there in calculating cumulative risk. However, I do not understand why Miettinen multiplies it by 5 years to calculate 30-year risk and does not multiply by 30 years?