# Is there any statistical method to compare two curves in a graph? e.g. quantifying how similar/different they are.

I want to compare the dose-volume curve of a organ from two different radiotherapy plans

I want to compare the dose-volume curve of a organ from two different radiotherapy plans

## All Answers (20)

István Németh· Gedeon Richter PlcFirst your dataset is suitable created (it contains two additive 0-1 coded collumn) to be implementd into a simple nonlinear least sqares method. Than you pick the appropriate parameter(s) from your model (eg. ED50, Emax etc) and you describe it as a linear function of your additive collumn (Emax=a+b*x where ix is your 0-1 coded collumn)

Second you use nonlinear mixed effects modeling ie nlme package in R or PROC NLMIXED in SAS

Hope it helps,

I

Jochen Wilhelm· Justus-Liebig-Universität Gießenhttp://www.sciencedirect.com/science/article/pii/S0360301607036620

http://www.translational-medicine.com/content/8/1/29/

Winky Wing Ki Fung· Hong Kong Sanatorium & HospitalSorry I am a statistics geek, thanks Lstvan and Jochen!

Jochen Wilhelm· Justus-Liebig-Universität GießenTo my opinion, it will be most instructive to compare the curves visually.

István Németh· Gedeon Richter PlcMohammad Firoz Khan· Jamia Millia IslamiaAll the above scholarly suggestions are quite valid, however, your problem is not well-defined. Your latter response, "You can imagine they are only two curves which should be quite similar to each other" suggests that dose-volume in the two cases should be similar. In this case, tow methods:one parametric and a non-parametric may be used. In the first case differences in response variable in two curves may be considered and their significance may be tested as in bi-variate regression models. In the second case Chi-Square test may be applied.

Jun Niu· China Agricultural UniversityVladimir Bakhrushin· Classic Private University1. The Kolmogorov-Smirnov and omega-squared tests, which are used for comparison of sample homogeneity. The essence of the criteria is to compare the distribution functions, which is a particular case of your problem.

2. Methods for analysis of residues in checking of the models adequacy. They suggest verification of the hypothesis that the model residuals have a normal distribution with zero mean and are independent random variables. In your case, as the residues You can used the differences of the functions for a set of the independent variable values.

Abdolrahman Khezri· Norwegian School of Veterinary ScienceLuis Enrique Ortiz-Vidal· University of São PauloI have the same problem. Did you solve it? how?

Thanks.

Winky Wing Ki Fung· Hong Kong Sanatorium & HospitalI still have not solve the problem stated. Alternatively I record points on the two curves for comparison now…

Luis Enrique Ortiz-Vidal· University of São PauloIn my case, I have several curves and I need to quantify their shapes. So, I am trying with statistical parameters like Kurtosis, RMS, Peak, etc.

My goal is to propose a simple identification method. I know that there are sophisticated methods in the literature, but... for now, it is not my way...

Winky Wing Ki Fung· Hong Kong Sanatorium & Hospitalyou mind further elaborate? ;)

Thanks.

Luis,

Can you name those methods you have come across? I would like to see if those are suitable in my study.

Thanks!

Luis Enrique Ortiz-Vidal· University of São PauloIt's about pattern recognition. You can check these two documents:

http://www.acoustics.asn.au/conference_proceedings/ICSVS-1997/pdf/scan/sv970356.pdf

http://cdn.intechopen.com/pdfs-wm/10675.pdf

The analysis are done in time domain, initially; however, I am using these parameters for data in frequency domain.

Jochen Wilhelm· Justus-Liebig-Universität GießenWinky Wing Ki Fung· Hong Kong Sanatorium & HospitalThanks Sean, really appreciated!!

Wenhai Zhang· University of Albertayou can consider Fréchet distance

Mateusz Wyrzykowski· Empa - Swiss Federal Laboratories for Materials Science and TechnologyThe problem is not trivial at all (it has to do with patent recognition). If your y values are at the same x for each curve, you can still try some non-parametric statistical tests. The problem is when the curves come at non coherent x sets. Of course the easiest way is to replace the curves with some characteristics (like area underneath suggested before, moments of distribution, etc.) and then run multivariate ANOVA on them. If you really want to asses the similarity between the curves, you may want to check theses papers:

http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=1E626E76AA499B64ED0D34C40C524B62?doi=10.1.1.118.5078&rep=rep1&type=pdf

http://onlinelibrary.wiley.com/doi/10.2307/3316142/pdf

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