# 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 (22)

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 KhanAll 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

Edgar Meza· Instituto del Mar del PerúHi

In my research I compared two curves (data vs model) and I used the weighted least squares (WLS)

For the WLS method it was defined as the sum of the absolute differences between observed and expected values, divided by the observed values (Lika et al. 2011).

The second part is to analyze the correlation (Matlab= corrcoef).

Regards

## Article: The “covariation method” for estimating the parameters of the standard Dynamic Energy Budget model II: Properties and preliminary patterns

ABSTRACT:The covariation method for estimating the parameters of the standard Dynamic Energy Budget (DEB) model provides a single-step method of accessing all the core DEB parameters from commonly available empirical data. In this study, we assess the robustness of this parameter estimation procedure and analyse the role of pseudo-data using elasticity coefficients. In particular, we compare the performance of Maximum Likelihood (ML) vs. Weighted Least Squares (WLS) approaches and find that the two approaches tend to converge in performance as the number of uni-variate data sets increases, but that WLS is more robust when data sets comprise single points (zero-variate data). The efficiency of the approach is shown to be high, and the prior parameter estimates (pseudo-data) have very little influence if the real data contain information about the parameter values. For instance, the effects of the pseudo-value for the allocation fraction κ is reduced when there is information for both growth and reproduction, that for the energy conductance is reduced when information on age at birth and puberty is given, and the effects of the pseudo-value for the maturity maintenance rate coefficient are insignificant. The estimation of some parameters (e.g., the zoom factor and the shape coefficient) requires little information, while that of others (e.g., maturity maintenance rate, puberty threshold and reproduction efficiency) require data at several food levels. The generality of the standard DEB model, in combination with the estimation of all of its parameters, allows comparison of species on the basis of parameter values. We discuss a number of preliminary patterns emerging from the present collection of parameter estimates across a wide variety of taxa. We make the observation that the estimated value of the fraction κ of mobilised reserve that is allocated to soma is far away from the value that maximises reproduction. We recognise this as the reason why two very different parameter sets must exist that fit most data set reasonably well, and give arguments why, in most cases, the set with the large value of κ should be preferred. The continued development of a parameter database through the estimation procedures described here will provide a strong basis for understanding evolutionary patterns in metabolic organisation across the diversity of life.François Anton· Technical University of DenmarkCan you help by adding an answer?