Package 'bigtcr'

Title: Nonparametric Analysis of Bivariate Gap Time with Competing Risks
Description: For studying recurrent disease and death with competing risks, comparisons based on the well-known cumulative incidence function can be confounded by different prevalence rates of the competing events. Alternatively, comparisons of the conditional distribution of the survival time given the failure event type are more relevant for investigating the prognosis of different patterns of recurrence disease. This package implements a nonparametric estimator for the conditional cumulative incidence function and a nonparametric conditional bivariate cumulative incidence function for the bivariate gap times proposed in Huang et al. (2016) <doi:10.1111/biom.12494>.
Authors: Chenguang Wang [aut, cre], Chiung-Yu Huang [aut], Mei-Cheng Wang [aut]
Maintainer: Chenguang Wang <[email protected]>
License: GPL (>= 3)
Version: 1.1
Built: 2024-12-11 06:57:57 UTC
Source: CRAN

Help Index


Bivariate Gap Time with Competing Risks

Description

This package implements the non-parametric estimator for the conditional cumulative incidence function and the non-parametric conditional bivariate cumulative incidence function for the bivariate gap times proposed in Huang et al. (2016).

Conditional Cumulative Incidence Functions

Denote by TT the time to a failure event of interest. Suppose the study participants can potentially experience any of several, say JJ, different types of failure events. Let ϵ=1,,J\epsilon=1, \ldots, J indicate the failure event type.

The cumulative incidence function (CIF) for the jjth competing event is defined as

Fj(t)=pr(Tt,ϵ=j),    j=1,,J.F_j(t)=\mbox{pr}(T\leq t, \epsilon =j), \;\; j=1,\ldots, J.

Huang et al. (2016) proposed a non-parametric estimator for the conditional cumulative incidence function (CCIF)

Gj(t)=pr(TtTη,ϵ=j),    t[0,η],    j=1,,J,G_j(t) = \mbox{pr}(T\le t \mid T\le \eta, \epsilon =j), \;\; t\in[0,\eta],\;\; j=1,\ldots, J,

where the constant η\eta is determined from the knowledge that survival times could potentially be observed up to time η\eta.

To compare the CCIF of different failure types jkj\neq k, we consider the following class of stochastic processes

Q(t)=K(t){G^j(t)G^k(t)},Q (t) = K(t)\{\widehat G_j(t) - \widehat G_k(t)\},

where K(t)K(t) is a weight function. For a formal test, we propose to use the supremum test statistic

supt[0,η]Q(t),\sup_{t\in [0,\eta] } \mid Q(t) \mid,

an omnibus test that is consistent against any alternatives under which Gj(t)Gk(t)G_j(t) \neq G_k(t) for some t[0,η]t\in [0,\eta].

An approximate pp-value corresponding to the supremum test statistic is obtained by applying the technique of permutation test.

Bivariate Gap Time Distribution With Competing Risks

For bivariate gap times (e.g. time to disease recurrence and the residual lifetime after recurrence), let VV and WW denote the two gap times so that V+WV+W gives the total survival time TT. Note that, given the first gap time VV being uncensored, the observable region of the second gap time WW is restricted to CVC-V. Because the two gap times WW and VV are usually correlated, the second gap time WW is subject to induced informative censoring CVC-V. As a result, conventional statistical methods can not be applied directly to estimate the marginal distribution of WW.

Huang et al. (2016) proposed non-parametric estimators for the cumulative incidence function for the bivariate gap time (V,W)(V, W)

Fj(v,w)=pr(Vv,Ww,ϵ=j)F_j (v,w)=\mbox{pr}( V\le v, W\le w, \epsilon=j )

and the conditional bivariate cumulative incidence function

Hj(v,w)=pr(Vv,WwTη,ϵ=j).H_j(v, w)=\mbox{pr}(V\le v, W\le w \mid T \le \eta, \epsilon=j).

To compare the joint distribution functions Hj(v,w)H_j(v, w) and Hk(v,w)H_k(v, w) of different failure types jkj\neq k, we consider the supremum test supv+wηQ(v,w)\sup_{v+w\le\eta}\mid Q^*(v, w)\mid based on the following class of processes

Q(v,w)=K(v,w){H^j(v,w)H^k(v,w)},Q^*(v, w) = K^*(v, w) \{\widehat H_j(v, w) - \widehat H_k(v, w)\},

where K(v,w)K^*(v, w) is a prespecified weight function.

The approximate pp-value can be obtained through simulation by applying the technique of permutation tests.

Nonparametric Association Measure for the Bivariate Gap Time With Competing Risks

To evaluate the association between the bivariate gap times, Huang et al. (2016) proposed a modified Kendall's tau measure that was estimable with observed data

τj=4×pr(V1>V2,W1>W2V1+W1η,V2+W2<η,ϵ1=j,ϵ2=j)1.\tau_j^*= 4\times \mbox{pr}(V_1>V_2, W_1>W_2\mid V_1+W_1\le\eta, V_2+W_2< \eta,\epsilon_1=j, \epsilon_2=j)-1.

References

Huang CY, Wang C, Wang MC (2016). Nonparametric analysis of bivariate gap time with competing risks. Biometrics. 72(3):780-90. doi: 10.1111/biom.12494


Conditional Cumulative Incidence Function (CCIF) Estimation

Description

Estimate the conditional cumulative incidence function. See bigtcr-package.

Usage

get.ccif(obs.y, event, tau = Inf)

Arguments

obs.y

YY: time to failure events or censoring

event

0: censored; 1,J1, \ldots J: type of failure events

tau

Conditioning time τ\tau under which the CCIF is defined

Value

A matrix with class ccif that has JJ columns. Columns 1 to JJ correspond to G1(t)G_1(t) to GJ(t)G_J(t). Each row represents a distinct observed time point tt and the row name contains the value of tt.

Examples

Gj <- get.ccif(obs.y = pancancer$obs.y, event = pancancer$min.type, tau   = 120);

Conditional Bivariate Cumulative Incidence Function Estimation

Description

Estimate the conditional bivariate cumulative incidence function. See bigtcr-package.

Usage

get.gap.ccif(obs.y, event, v, tau = Inf)

Arguments

obs.y

YY: time to failure events or censoring

event

0: censored; 1,J1, \ldots J: type of failure events

v

Time to the first failure event (e.g. disease recurrence)

tau

Conditioning time τ\tau under which the CCIF is defined

Value

A matrix with class gap.ccif that has J+2J+2 columns. Column 1 and 2 are (v,w)(v,w). The rest columns correspond to H1(v,w)H_1(v,w) to HJ(v,w)H_J(v,w). Each row represents a distinct observed time point and the row name contains the value of this time point.

Examples

Hj <- get.gap.ccif(obs.y=pancancer$obs.y, event=pancancer$min.type, v=pancancer$v, tau=120)

Cause-Specific Kendall's tau Estimation

Description

Estimate the modified cause-specific Kendall's tau for the evaluation of association for bivariate gap time with competing risks. See bigtcr-package.

Usage

get.gap.kt(obs.y, event, v, tau = Inf, nbs = 0)

Arguments

obs.y

YY: time to failure events or censoring

event

0: censored; 1,J1, \ldots J: type of failure events

v

Time to the first failure event (e.g. disease recurrence)

tau

Conditioning time τ\tau under which the CCIF is defined

nbs

Number of bootstrap samples for bootstrap variances. When nbs is smaller than 1, bootstrap variances are not evaluated.

Value

A list of the estimation and variances of modified casue-specific Kendall's tau

Examples

Kt <- get.gap.kt(obs.y=pancancer$obs.y, event=pancancer$min.type,
               v=pancancer$v, tau=120, nbs=5)

Comparison of Bivariate CCIF

Description

Compare the bivariate CCIF of different failure typess by applying the technique of permutation test. See bigtcr-package.

Usage

get.gap.pval(obs.y, event, v, tau = Inf, comp.event = c(1, 2), np = 1000,
  Kt = function(x) {     1 })

Arguments

obs.y

YY: time to failure events or censoring

event

0: censored; 1,J1, \ldots J: type of failure events

v

Time to the first failure event (e.g. disease recurrence)

tau

Conditioning time τ\tau under which the CCIF is defined

comp.event

Failure events for CCIF comparison

np

Number of permutations

Kt

A weight function that takes one parameter tt and return the weight for tt. Default weight function is constant 11

Value

P-value of the hypothesis test H0:Hj=Hk==HlH_0: H_j = H_k = \ldots = H_l.

Examples

gap.pval <- get.gap.pval(pancancer$obs.y, pancancer$min.type, pancancer$v,
                         tau=120, comp.event=c(1,2), np=20);

Kendall's tau Estimation

Description

Estimate Kendall's tau association between two random variables

Usage

get.kendalltau(v, w)

Arguments

v

Vector of numeric values. Missing values will be ignored.

w

vector of numeric values. Missing values will be ignored.

Examples

kt <- get.kendalltau(pancancer$v, pancancer$w);

Comparison of CCIF

Description

Compare the CCIF of different failure typess by applying the technique of permutation test. See bigtcr-package.

Usage

get.pval(obs.y, event, tau = Inf, comp.event = c(1, 2), np = 1000,
  Kt = function(x) {     1 })

Arguments

obs.y

YY: time to failure events or censoring

event

0: censored; 1,J1, \ldots J: type of failure events

tau

Conditioning time τ\tau under which the CCIF is defined

comp.event

Failure events for CCIF comparison

np

Number of permutations

Kt

A weight function that takes one parameter tt and return the weight for tt. Default weight function is constant 11

Value

P-value of the hypothesis test H0:Gj=Gk==GlH_0: G_j = G_k = \ldots = G_l.

Examples

pval <- get.pval(pancancer$obs.y, pancancer$min.type,
                 tau=120, comp.event=c(1,2), np=20);

Example Pancreatic Cancer Dataset

Description

Simulated data used in bigtcr examples.

Format

A dataframe with 3 variables:

obs.y

Observed time to failure events or censoring in months

min.type

Type of failure events

0

Censored

1

death with metastasis limited to lung only

2

death with metastasis that involves sites other than lung (e.g. liver)

3

death without disease recurrence

v

Time to recurrence. NA if no recurrence observed

Details

Data simulated based on the patients who had surgical resection of pancreatic adenocarcinomas and had postoperative follow-up at the Johns Hopkins Hospital between 1998 and 2007.