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dm_Rdate_FPR creates design matrices for false positive rate regressions; can also be used to standardize dates.


dm_Rdate_FPR(Rdate, Y, effect = "fixed", num_knots_FPR = NULL)



a vector of dates of R format


binary case/control status; 1 for case; 0 for controls


The design matrix for "random" or "fixed" effect; Default is "fixed". When specified as "fixed", it produces standardized R-format dates using control's mean and standard deviation; When specified as "random", it produces num_knots_FPR columns of design matrix for thin-plate regression splines (TPRS) fitting. One needs both "fixed" and "random" in a FPR regression formula in model_options to enable TPRS fitting. For example, model_options$likelihood$FPR_formula can be

~ AGECAT+HIV+dm_Rdate_FPR(ENRLDATE,Y,"fixed")+dm_Rdate_FPR(ENRLDATE,Y,"random",10)

means FPR regression with intercept, main effects for 'AGECAT' and 'HIV', and TPRS bases for 'ENRLDATE' using 10 knots placed at 10 equal-probability-spaced sample quantiles.


number of knots for FPR regression; default is NULL to accommodate fixed effect specification.


Design matrix for FPR regression:

  • Z_FPR_ctrl transformed design matrix for FPR regression for controls

  • Z_FPR_case transformed design matrix for borrowing FPR regression from controls to cases. It is obtained using control-standardization, and square-root the following matrix (\(\Omega\)]) with (\(j_1\),\(j_2\)) element being $$\Omega_{j_1j_2}=\|knots_{j_1}-knots_{j_2}\|^3$$.

See also