Regression and homoscadasticity test

v9991

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Data :- concentration vs response at 5 levels; and in triplicate measurements for each level. ( i.e., 5_concentrations & 3 measurements at each level, 5-levels of 3 sets each)

Requirement :- required to demonstrate goodness of regression equation., and test for homoscadasticity is recommended.

problem :-
F-Value and Normal plot for residuals is considered qualitative / not-objective and are deemed generally not-acceptable/adequate. and
certain alternatives of ‘White’s’ test and ‘Breusch pagan’ test were tried; but the simulation of results were counter-intuitive. viz., despite highly variable residuals, decreasing residuals leads to still failing of the criteria; and seemingly the tests anticipate certain bias in the residuals. ( viz., higher conc have higher residuals)

references looked up on net are as follows :-
(1)JP xiv :- validation of analytical

Regression and homoscadasticity test

(1`)Development and validation of an analytical method using High Performance Liquid Chromatography (HPLC) to determine ethyl butylacetylaminopropionate in topical repellent formulations

Brazilian Journal of Pharmaceutical Sciences On-line version ISSN 2175-9790
For linear ranges, the deviations should be equally distributed between positive and negative values. Another approach is to divide signal data by their respective concentrations, yielding the relative responses. A graph is plotted with the relative responses on the y-axis and the corresponding concentrations on the x-axis, on a log scale.The obtained line should be horizontal over the full linear range. At higher concentrations, there will typically be a negative deviation from linearity. Parallel horizontal lines are drawn on the graph corresponding, for example, 95 percent and 105 percent of the horizontal line. The method is linear up to the point where the plotted relative response line intersects the 95 percent line.

Regression and homoscadasticity test

(2)A Practical Guide to Analytical Method Validation
(Araujo_LinearitY-sdarticle%20(2).pdf)

Analytical Method Committee suggests using the F-test as a reliable approach to check the linearity of any calibration function.

• The value of F(I–2)/(IJ–I) calculated experimentally is compared against the critical value of F found in statistical tables, generally at the 95% confidence level for I − 2 and IJ − J degrees of freedom in the numerator and denominator respectively. If the experimental data set describes a genuine linear calibration of the form given by Eq.(1)then the condition Ftabulated > F(I–2)/(IJ–I) must be fulfilled. Otherwise there are grounds to suspect that a different model to the described by Eq. (1) must be proposed.

• The estimation of the various error sum squares and the Fisher ratio for testing the acceptability of a linear model proposed in the literature is discussed in Appendix A.

(4)Establishing Acceptance Criteria for Analytical Methods

Regression and homoscadasticity test

(3)ANVISA :- RESOLUTION OF THE COLLEGIATE BOARD - RDC Nº. 166, DATED JULY 24th, 2017 Providing for the validation of analytical methods and other provisions.

Paragraph 1. Data homocedasticity shall be investigated for the use of a proper model.
Paragraph 2. In statistical tests, a significance level of five per cent (5%) shall be used.
Paragraph 3. Correlation coefficient shall be above 0.990.
Paragraph 4. Angular coefficient shall be significantly different from zero.

ANVISA :-

(3)Resolution - RE n. 899, of May 29, 2003 D.O.U. 02/06/2003 - Original link is dead.

GUIDE FOR VALIDATION OF ANALYTICAL AND BIOANALYTICAL METHODS - Original ink is dead (http ://www .anvisa.gov. br/hotsite/ genericos/ legis/ resolucoes/ 2003/899_03re_e.pdf) Available on Scribd (pay site) - 899_03re_e.pdf | Coefficient Of Variation | Detection Limit - 2003

2.2.2. If there is apparent linear relation after visual examination of the graph, the results of the tests must be handled with appropriate statistical methods for determination of the correlation coefficient, intersection with the Y axis, angular coefficient, residual addition of the minimum squares of the linear regression and relative standard deviation. If there is no linear relation, undertake mathematical transformation.
2.2.3. The acceptable minimum criterion of the correlation coefficient (r) must be = 0.99.
2.2.4. The curves obtained must be presented (from the experiment and from the result of the mathematical treatment).
 
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v9991

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problem :-
F-Value and Normal plot for residuals is considered qualitative / not-objective and are deemed generally not-acceptable/adequate. and
certain alternatives of ‘White’s’ test and ‘Breusch pagan’ test were tried; but the simulation of results were counter-intuitive. viz., despite highly variable residuals, decreasing residuals leads to still failing of the criteria; and seemingly the tests anticipate certain bias in the residuals. ( viz., higher conc have higher residuals)

I apologize for not completing the problem statment..., request your guidance on the
A. selection of right test for above scenario., or
more appropriate objective-test for homoscedasticitity.

note :- i see certain constraint on sample size for applying other tests....or ...is sample size really an criteria for selecting an test?

B. are the F-Test and lack of quadratic fit adequate indicators for homoscedasticity.
 
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Miner

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How are you using the results (i.e., internal use only, publication)? I ask, because there is a practical answer suitable for your own internal use, and there are technical answers that only matter to purists.
 

v9991

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How are you using the results (i.e., internal use only, publication)? I ask, because there is a practical answer suitable for your own internal use, and there are technical answers that only matter to purists.
as indicated above, this is for Brazil-regulatory submission., ( so, can be considered for sort of purists!)
 

Miner

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Can you provide the residuals versus fits data? This will allow us to evaluate the suitability of various tests and still keep your raw data and analyses anonymous.
 

v9991

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Can you provide the residuals versus fits data? This will allow us to evaluate the suitability of various tests and still keep your raw data and analyses anonymous.
enclosed data..pl. guide/help.
 

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Miner

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You could perform a test for equal variances on the residuals by x value. reviewing your data, homoscedasticity does not appear to be an issue. However, there does appear to be an issue with your residuals versus the fitted values (your graph in the lower right). The residuals for x = 3.5591 and for x = 4.5971 are statistically significantly larger and smaller than the other x values.
 

v9991

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You could perform a test for equal variances on the residuals by x value. reviewing your data, homoscedasticity does not appear to be an issue. However, there does appear to be an issue with your residuals versus the fitted values (your graph in the lower right). The residuals for x = 3.5591 and for x = 4.5971 are statistically significantly larger and smaller than the other x values.
Agree with your observation; but regulatory agency seems to recommend an "method " to determine heteroscedasticity
can you pll guide me define a general approach towards "defining process steps" towards heteroscadasticity.
viz., as mentioned in first post,
a) criteria to select& defend the method towards assessing heteroscedasticity;
b) suggestion on method to select. ( pagan, white , cochran etc)

thank you.
 
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