Use of excel curves as a valid way to estimate unmeasured data

[EBL]

Hi--
I am reviewing a scientific manuscript for publication. In the
article, they graph data in excel and use the curve fitting function
to estimate days when nadirs are reached. To me, that seems like a
misuse of trendlines, but I'm appealing to the statistically savvy
people on this group. Here is the type of data--

Day Result
1 114%
4 107%
8 92%
13 81%
28 79%
42 92%
68 84%
91 89%
112 92%

Based on an excel curve, the authors estimated that the actual nadir
occurred on day 24. However, in my mind, that's an inappropriate use
of the curve fitting function. Comments?
Thanks.

 

[Jon Peltier]

What kind of model did they fit their data to? Excel has none that is
valid and comes up with 24.

I get a fit that comes very close (R^2 > 0.99) to each point if I use a
polynomial fit of order 6. Of course, this sets up an oscillating curve
with minima at about 22 (75%) and 79 (78%), and maxima at 51 (96%) and
105 (111%). When plotted, this is clearly an unrealistic fit and should
be discarded.

I can fit a line to the first four points, and another line to the last
5 or 6 points (doesn't make much difference) and these lines intersect
at 12-13. If I ignore the bump at the 6th point and fit points 5 and
7-9, this intersects the first line at 14. Both of these fits are better
than a poly fit.

The best way to fit this data is to come up with a physical mechanism
that describes the process that produced the data, and use appropriate
coefficients in the related model.

- Jon

 

[EBL]

Thanks for the reply.

Their M&M just says that curves were fit using excel. I think they
picked an XY chart and the option of scatter with data points
connected with smoothed lines (at least--when I do that, I get a curve
that looks identical to the one that they provided in the draft
manuscript).

I think you're confirming what I thought but couldn't articulate--that
this is a simplistic and scienfitically unacceptable way to estimate a
value at an unmeasured time point because a model to fit the data
needs to be based on measured or estimated parameters/coefficients
describing the biological process that they are attempting to model.

Correct?

 

[Jon Peltier]

Oh yeah, I didn't even consider the "smoothed line" method. This in no
way follows the path of the data. The curves are bezier curves
connecting adjacent points, and can stray far from the position of
actual data.

Using smoothed lines is as invalid as using a polynomial fit.

- Jon

 

[Herbert Seidenberg]

Excel 2007
Curve Fitting.
A better fit.
http://www.mediafire.com/file/neojzj0lymj/10_14_09b.xlsx

 

[Jerry W. Lewis]

Plus, Excel's Bezier curve seems to have its minimum on day 23, not day 24.

Any idea what Herbert Seidenberg is talking about? He claims a "better fit"
in 2007 but does not say better in what way, and like the authors of the
paper, fails to say what kind of fit. Also his download link is useless to
those of us who do not use 2007.

Jerry

 

[Jon Peltier]

Jerry -

I hate the way he just posts an undocumented link to an xlsx file. I
prefer seeing a description in an html page, without having to download
and open a whole workbook. This is the first of his links I've ever
bothered to follow, and I'm in no hurry to follow another.

Anyway, he linked to a site called http://zunzun.com, which I gather he
used to fit the meager data to a function of the form

y = x / (a * exp(-exp(b - c * x))) + d

- Jon

 

[Lori Miller]

I agree, the analysis is sloppy and more info is needed.

Three common interpolation methods for smooth functions give very
different values for minima around the interval of interest.

Using the formulae below the global minima were found, with the aid
of solver, to be at x = 23.25, 20.65 and 31.74 respectively.

Data range=A2:B10, first is ctrl+shift+entered in two cells, (0 < t <= 1):

"Smooth line":
=MMULT(t^{0,1,2,3},MMULT({0,2,0,0;-1,0,1,0;2,-5,4,-1;-1,3,-3,1}/2,A4:B7))

Cubic: =TREND(B4:B7,A4:A7^{3,2,1},x^{3,2,1})

Lagrange: =TREND(B2:B10,A2:A10^{8,7,6,5,4,3,2,1},x^{8,7,6,5,4,3,2,1})

 

[zunzun.com]

I agree, the analysis is sloppy and more info is needed.

There is a rather obvious outlier at;

Day Result
42 92%

which I saw by scatterplotting the raw data. Try removing this point.

James Phillips
http://zunzun.com

 

[Lori Miller]

The observation on day 42 is only outlying if you're bound by simple
parametric models and shouldn't necessarily be excluded. In fact it
forms a significant part of the basis for the nadir estimate and i
doubt the authors of the paper would have included it otherwise.

In the absence of an underlying theoretical model, any inference on
scarce data is necessarily vague, and the practice of trying arbitrary
data models until you find one that fits is not generally recommended
due to the problems of overfitting and data snooping.

PS. To clarify the remark was directed at the OP: chart-based
estimates should be avoided in any scientific paper, in addition an
inaccurate value is given without a mitigating explanation it seems.