Institut de Santé Publique,
d'Épidémiologie et de Développement

Centre Inserm U897
Equipe Biostatistique

Asymptotically Exact Corrected P-value for a finite number of tests.

Correction asymptotiquement exacte de la P_value pour un nombre fini de tests.


We consider a situation which is common in epidemiology, in which several transformations of an explanatory variable are tried in a Cox model and the most significant test is retained. The p-value should then be corrected to take account of the multiplicity of tests. Bonferoni mthod is often too conservative because the tests my be highly positively correlated. We propose an asymptotically exact correction of the p-value. The method uses the fact that the tests are asymptotically normal to compute numerically the distribution of the maximum of several tests. Counting processes theory is used to drive estimators of the correlations between tests. 

Dichotomous transformation   \begin{displaymath}z_p(k)=\left\{\begin{array}{c}0 \ \textrm{si} \ z_p\leq c_k\\1 \ \textrm{si} \ z_p> c_k\end{array}\right .\end{displaymath}


Strategy for dichotomous transformations 

Number of transformations

c1 c2 c3 c4 ... c7
1 median          
2 1st tercile 2nd tercile        
3 1st quartile 2nd quartile 3rd quartile      
4 1st quintile 2nd quintile 3rd quintile 4th quintile    
7 1st octile 2nd octile 3rd octile 4th octile   7th octile

Box-Cox transformation 

\begin{displaymath}z_p(k)=\left\{\begin{array}{c}\lambda_k^{-1}(z_p^{\lambda_k}......z_p \hspace{+4mm} \textrm{si} \lambda_k =0\end{array}\right .\end{displaymath}



Particularly $\lambda_k=1$ implies no transformation, and $\lambda_k=0$ implies the log, $\lambda_k=0.5$ gives a square root transformation.

Strategy for Box-Cox transformations

Number of transformations λ1 λ2 λ3 λ4 λ5
1 1        
2 1 0      
3 1 0 2    
4 1 0 2 0.5  
5 1 0 2 0.5 1.5

Downlables files

AEFNCP.tar.gz which involves following files:

aefncp.f fortran 77 source file
aefncp1 executable file (Unix)
aefncp2 executable file (Windows PC)
exdata example of data file
text.inf names of explanatory variables
aefncp.res results file
results of example


The program gives the following results:

  • the correlation matrix of transformed variables
  • the corrected p-value 

Data file

This ascii file contains the data set and must be given in the following structure:


The data file must be arranged by columns:
  • first one contains age at time of entry in study
  • the second one contains age at time of exit (dementia)
  • other columns are the explanatory variables
- Remarks : 
  • each variable must be separated with one (or more) space
  • the program do not take in account missing values.


Haschemi R, Commenges D. 
Correction of p-values after multiple tests in Cox regression. Lifetime Data Anal 2002 8(4): 335-348.


Reza Hashemi
Daniel Commenges

Inserm U897
146 rue Léo Saignat
33076 Bordeaux Cedex


We are interested in feed-back but can not guarantee support.


The authors are not in business of writing software packages and can not garantee that the program is error free. The main purpose of this program is for our own use in analyzing data. It is distributed free of charge for use by non-programmers and for programmers who would like to extract parts and possibly modify the program.

Downloading: aefncp.tar.gz (Unix version)

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