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Dear All,

A colleague of mine in the Dept of Biology is working on gastrointestinal motility. He is studying gastrointestinal motility using the zebrafish.  He want to know if gastrointestinal transit  changes after an experimental ‘condition (he knocks out genes).  GI transit is  the time it takes for food to pass through the gut.  They merely feed zebrafish food with a marker and actually look at every fish at time intervals.  They can see the marker in the GI tract, and therefore they know how much it has moved.  They measure it at specific times.  The data is scored- so if marker is in zone 1 we call it ‘1’, and if it is moved nearly all of the way through the GI tract they call it ‘4’.  Once the GI tract is empty they call it ‘5’.  So, for every fish they have numbers like 1,2,3,5.  That would indicate the food moved progressively through the GUI tract and at the end of the experiment (24 hours) it is empty.

They want to know  if the pattern, or transit changes with an experimental condition?  The only paper using this technique used a Pearson’s Chi Square.  They had between 500 and 1400 observations at every time point. 

Here is a sample of their  data:

An X means the fish died. 

I do feel we can do much better than a simple chi-squared tests or a perhaps a Wilcoxon test. Any suggestions/ comments would be really appreciated.

Best Regards,

Tasneem

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[Tasneem] [Zaihra]
[Post Doctoral Fellow]
[McGill University]
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Tasneem,

You can do "better".

Off the top of my head:

(1) Time to '5' 

(2) Markov chain with 5 states (compare vectors of transition probabilities)

(3) Isotonic regression for ordinal data.

Deaths are an issue with (2) and (3)

David

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David Bristol
Statistical Consulting Services
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Although at first glance it looks like nonparametric longitudinal data, I'm thinking No, Not Really. It actually looks like time-to-event data. For example if 5 means Expelled, then one could ask, how long did it take to observe a 5 in each zebrafish, and how many zebrafish are right-censored for achieving a 5 after 24 hours. I appreciate there appears to be a whole lot of interval-censoring going on in addition to the right-censoring, but I might still start with Kaplan-Meier curves to create the initial picture, and I might still use a log-rank test to compare the curves.   

I imagine one could adopt the same analysis approach with respect to the time it takes each fish to to achieve a 4, a 3, or a 2. But if one pursued the times to achieve those events, then I would need to ask: does the food ever move backwards in any of the fish? 

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Eric Siegel
Biostatistician
Univ of Arkansas for Medical Sciences of Biostatistics
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Why was the experimental group injected with 25 µM TB/SA Mix?

The injection could have been intended to either accelerate or slow down the passing of the food through the gut.

The comparison of "patterns" across groups should ultimately reflect the purpose of the injection. 

If the injection was intended to accelerate the passing of food through the gut, one could compare the two groups with respect to the outcome "The first time the food reached zone 5 of the GI tract". This outcome will be censored for fish who died or who did not reach zone 5 of the tract. 

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Isabella Ghement
Ghement Statistical Consulting Company Ltd.
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I agree that a time-to-event approach would be helpful, and would also support looking at time to achievement of movement to each zone.  I believe you would need to use interval censoring in this case, since you do not have exact time of food arriving in a particular zone, but identify status at specific time intervals.

You might take a look at the "interval" package in R (see Fay and Shaw reference below). 

I believe SAS can also be used, based on a paper by So, Johnston and Kim in SAS Global Forum 2010; there is also a procedure called ICLIFETEST, although I have not used it myself.

Some references:

 Chen D-G, Sun J, Peace KE (2013). Interval-Censored Time-to-Event Data: Methods and Applications. Chapman and Hall.

Fay, MP (1996). "Rank invariant tests for interval censored data under the grouped continuous

model". Biometrics, 52: 811-822.

Fay, MP (1999). "Comparing Several Score Tests for Interval Censored Data." Statistics in Medicine,

18: 273-285 (Correction: 1999, 18: 2681).

Fay, MP and Shaw, PA (2010). Exact and AsymptoticWeighted Logrank Tests for Interval Censored

Data: The interval R package. Journal of Statistical Software. http://www.jstatsoft.org/v36/

i02/. 36 (2):1-34.

Fay, MP and Shih JH. (2012). Weighted Logrank Tests for Interval Censored Data when Assessment

Times Depend on Treatment. Statistics in Medicine 31, 3760-3772.

Fay, MP and Hunsberger, SA. (2012). Practical Issues on Using Weighted Logrank Tests with

Interval Censored Events in Clinical Trials. Chapter 13 in Interval-Censored Time-to-Event Data:

Methods and Applications, Chen, D-G, Sun, J, and Peace, KE (editors) Chapman and Hall/CRC.

Finkelstein, DM (1986). "A proportional hazards model for interval censored failure time data"

Biometrics, 42: 845-854.

Huang, J, Lee, C, Yu, Q (2008). "A generalized log-rank test for interval-censored failure time data

via multiple imputation" Statistics in Medicine, 27: 3217-3226.

Sun, J (1996). "A non-parametric test for interval censored failure time data with applications to

AIDS studies". Statistics in Medicine, 15: 1387-1395.

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Deborah Dawson
Director of Biostatistics
University of Iowa
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1) TE using lifetable method would do trick...but will likely experience resistance to distance between conventional approach and descriptions. Also more challenging for higher-order effects or linear contrasts...limiting.

2) Alternative...probably what I'd do: Binomial...0-5 successes out of 5 trials...watch your residuals, though...obviously not the exact right distribution to arise out of phenomenon, but proportions with 95%CI can easily be back-translated to original scale by multiplying by 5...and get to use standard linear modeling (in SAS, proc glimmix would handle easily).

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Jason T. Machan
Director, Lifespan Biostatistics Core,
Lifespan Hospital System
Research Scientist, Biostatistics, Research
Rhode Island Hospital
Assistant Professor, Departments of Orthopaedics and Surgery
The Warren Alpert Medical School, Brown University
Director Biostatistics Externship, Adjunct Assistant Professor, Department of Psychology
University of Rhode Island
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Additionally, someone sent me a note after I'd replied. Part of that note made me realize I didn't address the repeated measures nature of the data.

I suspect the function will be close enough to linear (in logit-scale) to use a growth model for binomial data (g-side, random intercept and slope). If not, could treat each assessment time as categorical and use correlated error model (r-side, correlated error across assessment times with 1^st order autoregressive or otherwise).  …throwing classical sandwich estimation at it for good measure.

Will need to reformat data to be long, rather than wide...one observation per fish per assessment time (make a variable). Also add a denominator for the binomial model (e.g. max_score=5; in the datastep somewhere). Then,

Growth Model

proc glimmix plots=(ResidualPanel PearsonPanel) empirical;

   class Fish Group;

   model score/max_score = Group | Assessment_Time

          /dist=binomial;

   estimate "slope in group 1" Assessment_Time 1 Group*Assessment_Time 1 0,

                "slope in group 2" Assessment_Time 1 Group*Assessment_Time 1 0

         /cl adjdfe=row stepdown ilink;

   random intercept Assessment_time/subject=Fish type=csh;

run;

...tweak variance-covariance matrix if necessary, though classic sandwich estimation (empirical) will "fix" a lot.

...graph to get a gut-check.

Correlated Residual Error model

proc glimmix plots=(ResidualPanel PearsonPanel) empirical;

   class Fish Group Assessment_time;

   model score/max_score = Group | Assessment_Time

          /dist=binomial;

    lsmeans Group*Assessment_Time

         /cl adjdfe=row stepdown ilink;

   random Assessment_time/subject=Fish type=ar(1) residual;

run;

...tweak variance-covariance matrix if necessary, though classic sandwich estimation (empirical) will "fix" a lot.

...graph to get a gut-check.

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Jason T. Machan
Director, Lifespan Biostatistics Core,
Lifespan Hospital System
Research Scientist, Biostatistics, Research
Rhode Island Hospital
Assistant Professor, Departments of Orthopaedics and Surgery
The Warren Alpert Medical School, Brown University
Director Biostatistics Externship, Adjunct Assistant Professor, Department of Psychology
University of Rhode Island
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"slope in group 2" Assessment_Time 1 Group*Assessment_Time 1 0

should be

"slope in group 2" Assessment_Time 1 Group*Assessment_Time 0 1

Sorry!

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Jason T. Machan
Director, Lifespan Biostatistics Core,
Lifespan Hospital System
Research Scientist, Biostatistics, Research
Rhode Island Hospital
Assistant Professor, Departments of Orthopaedics and Surgery
The Warren Alpert Medical School, Brown University
Director Biostatistics Externship, Adjunct Assistant Professor, Department of Psychology
University of Rhode Island
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