- On 18 Aug 1997 at 15:48:02, rajesh krishna (rkrishna.aaa.unixg.ubc.ca) sent the message

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I have some questions on the application of statistical methodology to a

tumor efficacy study involving measurement of tumor volumes as a function

of time (days) following administration of specific drug treatment groups

(solid tumor growth inhibition measurements). If somebody in this group

could render their views, it would be awesome!

Experimental design: Studies involved solid tumor bearing mice. Once

these solid tumors reached about 100 mg (measurable size), treatment was

initiated with the anticancer drug injected on days 1, 5, and 9. Tumor

size was measured daily until conclusion of study at 15 days. We

performed statistical comparisons using ANOVA (between various treatment

groups). Now, the specific questions we have are:

[1] Is it appropriate to perform ANOVA on each's days data? If not, then

would performing ANOVA on the final times for statistical inference with

just description of the curves prior to that time point is considered

appropriate?

[2] What are the accepted procedures for analysis using methods for

longitudinal data?

[3] What does non-monotonicity of data and generalized estimating

equations (GEE) mean? How do they apply in such toxicological and

efficacy studies?

[4] It is likely that in such toxicological studies, one would have to

appropriately deal with missing data. What patterns of missingness

dictate the appropriate statistical interpretation of such results?

Any response on the above will be welcome and appreciated.

Regards,

Rajesh Krishna

Department of Advanced Therapeutics

BC Cancer Agency

600 West 10 Avenue

Vancouver, BC

V5Z 4E6 Canada

604/877 6010 ext. 3051

604/877 6011 (Fax)

http://members.tripod.com/~rkrishna/ - On 19 Aug 1997 at 12:09:13, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message

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rajesh krishna wrote:

> I have some questions on the application of statistical methodology to

> a

> tumor efficacy study involving measurement of tumor volumes as a

> function

> of time (days) following administration of specific drug treatment

> groups

> (solid tumor growth inhibition measurements).

> [1] Is it appropriate to perform ANOVA on each's days data? If not,

> then

> would performing ANOVA on the final times for statistical inference

> with

> just description of the curves prior to that time point is considered

> appropriate?

>

I would suggest you consider a different question. You have data that

describe the time course of drug effect so why not use a PKPD model to

describe it? ANOVA is the last resort of intellectually challenged

statisticians who have no understanding of biology and no interest in

using methods which are more revealing than a P value.

> [2] What are the accepted procedures for analysis using methods for

> longitudinal data?

>

NONMEM is a method which can describe PKPD and take into account

differences between individuals. There are other methods but NONMEM is

the most readily available.

> [3] What does non-monotonicity of data and generalized estimating

> equations (GEE) mean? How do they apply in such toxicological and

> efficacy studies?

>

Non-monotonicity means the time course of the observations can go up and

down. This means to me that you need to describe your data with a

non-linear model. GEE are still only used by statisticians (as far as I

know) and I think they are restricted to linear models. NONMEM has no

such restriction and has lots of people who know how to apply it to

understanding pharmacology.

> [4] It is likely that in such toxicological studies, one would have

> to

> appropriately deal with missing data. What patterns of missingness

> dictate the appropriate statistical interpretation of such results?

>

There is no simple answer to this. Broadly, missingness can be

considered uninformative (eg data are missing at random of for reasons

quite unrelated to the drug effect) or informative (eg data are missing

because a patient dropped out because of treatment related side

effects). The former can essentially be ignored. The latter is harder to

deal with and is the subject of state of the art investigation by

workers such as Lew Sheiner and Don Rubin.

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, Private Bag 92019, Auckland, New Zealand

email:n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556

http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html - On 20 Aug 1997 at 13:44:12, Shawn Johnson (sjohnson.-at-.mga.com) sent the message

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***************************************************

Per Dr. Krishna's request I have posted my response to him below.

***************************************************

Dear Dr. Krishna:

I am not the right person to answer your statistical questions, since I

am an engineer and only a recent convert to pharmacology. But I thought

I would provide my thoughts which you are certainly welcome to dismiss

as nonsense if you so choose.

question 1: performing ANOVA on each day's data.... Certainly you could

do this. Presumably the reason would be to estimate the variability in

the rate of efficacy (and toxicity perhaps) across your population. The

first question I would have is "is your sample population large enough

to provide you a reasonable confidence interval on this estimate of rate

of efficacy (toxicity)?".... I would at least do it if the data are

readily available.

Just using the endpoint is probably more meaningful since this is what

will likely be the most important clinical endpoint when you take the

drug into humans....i.e. did my tumor get smaller (or larger) and if so

by how much and what were the side effects? I would perform both

analyses but concentrate my efforts on the later.

question 2: I will leave this for the pure statisticians in the group.

My only insight is that I use the sampled data you have (it is

essentially discrete samples) to build a model of the time-continuous

function of tumor growth. I use a maximum likelihood estimation method

to calculate the curve parameters using a Gompertz model for tumor

growth. I then use this model (basically the differential equations for

the PK and PD models and clinical endpoint models) to simulate the

results of a planned clinical trial for the new drug. Last Fall I

presented a poster session on this process at a conference in Geneva for

a "psuedo" cancer drug (to show people how to do it). I would be glad

to send you a copy of the paper if you are interested.

question 3: I will leave this for the statistics professionals.

question 4: The issue of missing data (or incorrect data) is always a

difficult thing to address. Perhaps this is where the science of

statistics meets the art of applied math.

First you may want to consider a filter on the data you have collected

(which may not sit to well with the statisticians in the audience). I

have used a windowed median approach in the past as a way to filter

sampled data of time continuous functions (such as tumor growth) but

have not applied it to cancer modeling as yet. Once you have filtered

out bad data, the question becomes what do we do with the gaps. If the

data are extremely sparse there are some algorithms for bridging them,

but they all make some assumptions about the behavior of the underlying

function you are trying to model, so you will have to choose wisely.

Essentially, your sparse data will mostly impact your confidence

intervals when you try to estimate the underlying function. At some

point, and it depends on the function, the confidence interval becomes

so large (because of sparse data) that your conclusions become

unwarranted. This will become apparent during your ANOVA.

Like I said, I am not a statistician. I just use statistics in my

work. Hopefully, these few words shed some light on the issues you

face.

Please feel free to contact me directly if I can be of any assistance.

Best regards,

Shawn Johnson

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