| Usage: |
z = harefit(data{, delta, covars, ipenalty, maxdim, exclude, include, prophaz, additive, linear, fit})
|
| Input: |
| data | n x 1 vector of observations. Observations may or may not
be right censored. All observations should be nonnegative.
|
| delta | binary n x 1 vector with the same length as data. Elements of data
for which the corresponding element of delta is 0 are assumed to be
right censored, elements of data for which the corresponding element
of delta is 1 are assumed to be uncensored. If delta is missing,
all observations are assumed to be uncensored.
|
| covars | n x k matrix of covariates with as many rows as the length of data.
May be omitted if there are no covariates.
|
| ipenalty | an optional scalar parameter to be used in the AIC criterion. The method chooses
the number of knots that minimizes -2*loglikelihood+ipenalty*(dimension).
The default is to use ipenalty=log(samplesize) as in BIC.
|
| maxdim | a scalar, maximum dimension of splines (default is 6*length(data)^0.2).
|
| exclude | an optional m x 2 matrix of combinations to be excluded from interactions.
If for example exclude[1,1]=2 and exclude[1,2]=3, no
interaction between covariate 2 and 3 is included. 0 represents time.
Exclude can be specified only if include is not.
|
| include | an optional m x 2 matrix of combinations to be included as interactions.
If for example exclude[1,1]=2 and exclude[1,2]=3,
interaction term between covariate 2 and 3 is included. 0 represents time.
Include can be specified only if exclude is not.
|
| prophaz | an optional scalar (default is 0); if non-zero, a proportional
hazard model is fitted (instead of non-proportional).
|
| additive | an optional scalar (default is 0); if non-zero, an aditive
hazard model is fitted, which means that no interaction terms
between covariates are included and include and exclude should not be
specified.
|
| linear | an optional vector indicating for which of the variables
no knots should be entered. For example, if linear=c(2,3),
no knots for covariates 2 or 3 are entered. 0 represents time.
|
| fit | an optional object created by harefit. If a fit is specified,
harefit adds basis functions starting with those in the specified fit.
|
| Output: |
| z.ncov | number of covariates |
| z.ndim | number of dimensions of the fitted model |
| z.fcts | ndim x 6 matrix; each row is a basis function;
the first element is first covariate involved (0=time);
the second element means which knot (0 means constant (time), else linear (covariate));
the third element is second covariate involved (NaN means: this is a function of one variable);
the fourth element is knot involved (if the third element is NaN, of no relevance);
the fifth element is beta;
the sixth element is standard error of beta. |
| z.knots | a matrix of size ncov x v, one row for each dimension.
Covariate i has row i+1, time has row 1.
First element is the number of knots in this dimension,
the other elements are the knots, appended with NaNs to make it a matrix. |
| z.penalty | the parameter used in the AIC criterion |
| z.max | maximum element of data |
| z.ranges | column i gives the range of the i-th covariate |
| z.logl | matrix with two columns. The i-th element of the first column
is the loglikelihood of the model of dimension i. The second
column indicates whether this model was fitted during the addition
stage (1) or during the deletion stage (0). |
| z.sample | sample size |
- Example:
library("hazreg")
randomize(111)
n = 500
p = 2
beta = 1|2 ; regression parameter
z = 1 + uniform(n,p) ; covariates
y = -log(1-uniform(n)) ; exponential survival
y = y./exp(z*beta) ; covariate effects
c = 4*uniform(n) ; uniform censoring
t = min(y~c,2) ; censored time
delta =(y<=c) ; censoring indicator
fit=harefit(t,delta,z)
haresummary(fit)
plothare(fit,1.1~1.4,"p,s")
- Result:
Along with the summary, the estimated distribution and
survival functions are plotted.
Contents of sum
[ 1,] "dim A/D loglik AIC penalty "
[ 2,] " min max"
[ 3,] " 0 Add -1.6e-46 -9.2e+102 1.4e+02 1.4e+02"
[ 4,] " 0 Add 5.6e+175 -5.9e-144 42 42"
[ 5,] " 0 Add 9.7e+43 -6.2e-127 1.3 1.3"
[ 6,] " 0 Add -7.3e-252 2.7e-273 0.00"
[ 7,] " "
[ 8,] "the present optimal number of dimensions is 3."
[ 9,] "penalty(AIC) was the default: BIC=log(samplesize): log(500)=6.2"
[10,] " "
[11,] " dim1 dim2 beta SE Wald"
[12,] "Constant 0.21 0.32 0.64"
[13,] "Co-2 linear 1.8 0.16 11"
[14,] "Co-1 linear 1 0.16 6.5"
- Example:
library("hazreg")
randomize(11)
n = 500
p = 2
beta = 1|2 ; regression parameter
z = 1 + uniform(n,p) ; covariates
y = -log(1-uniform(n)) ; exponential survival
y = y./exp(1 + z*beta + 5*z[,1].*z[,2]) ; covariate effects
c = 4*uniform(n) ; uniform censoring
t = min(y~c,2) ; censored time
delta =(y<=c) ; censoring indicator
fit=harefit(t,delta,z)
haresummary(fit)
- Result:
Contents of sum
[ 1,] "dim A/D loglik AIC penalty "
[ 2,] " min max"
[ 3,] " 0 Add -3.5e+46 5.3e+83 Inf"
[ 4,] " 0 Add -8.9e-287 -2.1e-212 NaN NaN"
[ 5,] " 0 Add -8.5e-101 3.1e+11 70 70"
[ 6,] " 0 Add 2e+75 1.2e+224 0.00"
[ 7,] " "
[ 8,] "the present optimal number of dimensions is 4."
[ 9,] "penalty(AIC) was the default: BIC=log(samplesize): log(500)=6.2"
[10,] " "
[11,] " dim1 dim2 beta SE Wald"
[12,] "Constant 0.25 1.3 0.19"
[13,] "Co-2 linear 2.4 0.89 2.7"
[14,] "Co-1 linear 1.4 0.85 1.7"
[15,] "Co-1 linear Co-2 linear 4.8 0.58 8.3"