Hi Katrine,

Do I understand correctly that you did not receive just cumulative mortality but year-by-year mortality for 10 years?

If you indeed got mortality rates (instead of probability of dying in a year) then you should calculate first the probability of dying in a year and then the probability of dying in 3 months by assuming discrete time steps:

p_3month = 1 - (1 - p_1year)^(1/4)

Unless the mortality rates are high, that would lead to only a small difference compared to what you described.

Therefore, when you say: "completely wrong" I wonder if something else went wrong as well. Perhaps you can give a complete example of calculations and comparison with data.

Question 2 seems to be about uncertainty/probabilistic sensitivity analysis, right?

I think that estimating the uncertainty around mortality data is generally not simple. I get the impression that you are extrapolating to life time from 10 years of observed mortality. If you can assume that the mortality from the disease you are modeling has stopped by the end of the 10 years, you may want to assume general population life table mortality after that time. Have you considered bootstrapping the mortality data you got for the 10 years?

It also seems that your model may be similar to partitioned survival models that are often used for evaluation of oncology drug. Perhaps you can look up some papers on how they deal with uncertainty in mortality data.

Best regards,

Rob

Hi Rob,

Thank you so much for the answer. It is really helpful.

Thank you so much again!

1.

Do I understand the first figure correctly and it shows % deaths with the number alive at baseline as denominator? Then you should account for the fact that a Markov model calculates probability of death with number alive at start of a model cycle instead of at baseline.

2.

It is possible to reconstruct/'estimate' individual records for the mortality data you received if you know the population size at baseline. Then you can bootstrap that reconstructed data set, calculate the 3 month cycle probabilities of death for each bootstrap draw and feed that into your model's uncertainty analysis.

3.

It is possible to change cycle length. However, it is rather unorthodox, to an extent that some people may think it is wrong to do so; and you should be really careful with counting correctly, particularly the life years will easily go wrong.

Hi Rob,

Aw, thank you so much!

1. Yes it is at baseline as a denominator. And yes I accounted for that. Thank you!

2. Unfortunately it it not possible to get the population size at the baseline. But the idea is very good. Will look for more ideas how to find CI.

3. Now I am changing all the other parameters to get the 3 month cycle as RCT measurements were each 3 month, but just up to 3 years. Then I think it it easier to change to 1 year cycle.

What do you think about EIGENDECOMPOSITION APPROACH instead of traditional?

You answers is greatly appreciated! Thank you again!

Best regards,

Katrine

Without any knowledge of the population size, it seems not possible to estimate the uncertainty of the mortality data you received.

I don't know of an eigendecomposition approach in this context.

I thought so too. Thank you a lot. I really appreciate your advice!

I read that if there is more than 2 states t is better to apply this decomposition. I will look in to it as well.

Thank you!

Hi Katrine,

1.

Your problem is of the class of such problems: restore the reliability function (in medicine called survival function

Some add some adjectives, which are not very important if all arround know the issue. However, just for rigorousness, let us introduce our notions in a uniquely determined way.

-- Thus, let the basic notion survival function be given by:

R(t) = Pr{ a single patient survives at least till t}, t > 0.

-- Then the cumulative distribution function (cpdf) is given by

F(t) = 1-R(t) = Pr{ a sigle patient dies before t}, t>0.

-- And finaly let us define rate of mortality in the usual way by

r(t) = - [ln ( R(t) ]' i.e. as the logaritmic derivative of the survival function.

-- A closely related is the density probability function (dpf) given equivalently by either one of three formulas (prime ' stands for the derivative):

f(t) = F'(t), . . . f(t) = r(t)* R(t) . . . . f(t) = - R'(t)).

2.

Now, the empirical data did not fit the expectation, which ususally is that they form a regularly decreasing graphic of the survival function. We have them in a table of 10 values of the OBSERVED values of R at t=1,2,3,...,10 (collected in table "got"). There are years without death, which is obviously very good, but this fact destroyes regularity!). Your natural proposal accepts this irregularity by assumed homogeneity of every quater of the year. But between years you have obtained unbelievable "jumps" of the rate of mortality. Let us try to improve this just a little, which seemingly you want to achieve suggesting some two stage processes. This would require some additional understanding of the features of the corresponding models.

3.

But before any further steps, let me make sure about the following. If I understood well the result of your discussion with Robert, your problem/goal is

to infere from the given data th values of the rate of mortality somehow averaged within 40 consecutive 3-month periods.

Please accept my break and answer whether this is correct before further advices, which I will supply with a teacher's pleasure, ok?

Best, Joachim

Oops! there is a mistake in my point 2. The erratum is as follows.

THERE IS:

We have them in a table of 10 values of the OBSERVED values of R at t=1,2,3,...,10 (collected in table "got").

TO BE REPLACE BY:

We have them in a table of 10 values of the OBSERVED values of F at instants t=1,2,3,...,10 y (collected in the central column of table "got").