markPH.aipw: AIPW Estimation and Hypothesis Testing of Strain-Specific...

In fei-heng/cmprskPH: Cause-specific proportional hazards model for competing risks analysis

AIPW Estimation and Hypothesis Testing of Strain-Specific Vaccine Efficacy Adjusted for Covariate Effects with Missing Causes

Description

Fit a stratified cause-specific proportional hazards regression model postulates that the conditional cause-specific hazard function for cause j for an individual in the k-th stratum with the covariate value z equals

\lambda_{kj}(t|z)=\lambda_{0kj}(t)\exp(\beta_j^{T}z)

for j=1,...,J and k=1, ..., K, where \lambda_{0kj}(\cdot) is an unspecified cause-specific baseline hazard function for the k-th stratum and K is the number of strata.

Usage

markPH.aipw(
  cmprskPHformula,
  trtpos = 1,
  strata,
  causelevels = NULL,
  missformula,
  markformula,
  data = parent.frame(),
  VEnull = 0.3,
  maxit = 15,
  ipw = T,
  cc = T,
  lambda0 = T
)

Arguments

cmprskPHformula	a formula object with the response on the left of a '~' operator, and the independent terms on the right as covariates in the cause-specific proportional hazards regression model. The response must be in the format of cbind(time, delta, cause), where time is the minimum of the failure time and the censoring time, delta specifies the censoring status (1: failure is observed; 0: right-censored), cause is the cause of failure. If cause is missing, cause=NA.
trtpos	the position of the treatment group indicator in the RHS of the formula object cmprskPHformula. The default value is 1.
strata	the column name of the strata variable in the data.
causelevels	types of causes.
missformula	a formula object started with a '~' operator, and the independent terms on the right of '~' are variables used for predicting the probability of being not missing under a logistic regression model.
markformula	a formula object started with a '~' operator, and the independent terms on the right of '~' are variables used for predicting the probability of being cause j under a multinomial log-linear regression model (function multinom() in nnet package).
data	a data.frame with the variables.
VEnull	the assumed VE value in the null hypothesis. The default value is 0.3.
maxit	Maximum number of iterations to attempt for convergence. The default is 15.
ipw	Whether to conduct the IPW estimation. The default value is TRUE.
cc	Whether to conduct the complete-case estimation. The default value is TRUE.
lambda0	Whether to estimate the cumulative baseline hazard. The default value is TRUE.

Value

returns an object of type 'markPH.aipw'. With the following arguments:

causes	the types of causes of failure
coef.cc	estimates of covariate coefficients using a complete-case analysis
se.cc	estimates of standard errors of estimators for covariate coefficients using a complete-case analysis
coef.ipw	estimates of covariate coefficients using IPW method
se.ipw	estimates of standard errors of estimators for covariate coefficients using IPW method
coef	estimates of covariate coefficients using AIPW method
se	estimates of standard errors of estimators for covariate coefficients using AIPW method
coef.VE	estimates of the strain-specific vaccine efficacy to reduce susceptibility to strain j using AIPW method, j=1,...,J
se.VE	estimates of standard errors of estimators for the strain-specific vaccine efficacy to reduce susceptibility to strain j using AIPW method, j=1,...,J
coef.VD	estimates of VD using AIPW method
se.VD	estimates of standard errors of estimators for VD using AIPW method
U1	test statistic for testing against the alternative hypothesis HA1: VE(j)>=VEnull with strict inequality for some 1<=j<=J
U2	test statistic for testing against the alternative hypothesis HA2: VE(j) is not equal to VEnull for some 1<=j<=J
U1j	test statistic for testing against the alternative hypothesis HAj1: VE(j)>VEnull
U2j	test statistic for testing against the alternative hypothesis HAj2: VE(j) is not equal to VEnull
T1	test statistic for testing against the alternative hypothesis HB1: VE(1)>=...>=VE(J) with at least one strict inequality
T2	test statistic for testing against the alternative hypothesis HB2: VE(i) is not equal to VE(j) for at least one pair of i and j, 1<=i<j<=J
pval.A1	p value for testing against the alternative hypothesis HA1: VE(j)>=VEnull with strict inequality for some 1<=j<=J
pval.A2	p value for testing against the alternative hypothesis HA2: VE(j) is not equal to VEnull for some 1<=j<=J
pval.A1j	p value for testing against the alternative hypothesis HAj1: VE(j)>VEnull
pval.A2j	p value for testing against the alternative hypothesis HAj2: VE(j) is not equal to VEnull
pval.B1	p value for testing against the alternative hypothesis HB1: VE(1)>=...>=VE(J) with at least one strict inequality
pval.B2	p value for testing against the alternative hypothesis HB2: VE(i) is not equal to VE(j) for at least one pair of i and j, 1<=i<j<=J
tgrid	specifies the time grids for estimating \lambda_{0kj}(\cdot) , the unspecified cause-specific baseline hazard function for cause j and the k-th stratum.
lambda0	estimates of \lambda_{0kj}(\cdot) using AIPW method
covariates	covariates in the cause-specific proportional hazards model.
trtpos	the position of the treatment group indicator in the RHS of the formula object cmprskPHformula.
VEnull	the assumed VE value in the null hypothesis.
diffsigma	estimates of standard deviation of \hat\alpha_j-\hat\alpha_{j-1}, j=2,...,J.
cov.alpha	estimated covariance matrix of (\hat\alpha_1,\dots,\hat\alpha_J).

Author(s)

Fei Heng

References

(2021+)

Examples

## Example 1: Simulated competing risks data with 2 causes subject to missingness
data(sim2cs)

res.aipw <- markPH.aipw(cmprskPHformula=cbind(time,delta,cause)~z1+z2,
                        trtpos=1,
                        strata="strata",
                        causelevels=c(1,2),
                        missformula=~z1+A,
                        markformula=~time+z1+A,
                        data=sim2cs,
                        VEnull=0.3,
                        maxit=15)
res.aipw # print the result

## Example 2: Simulated competing risks data with 3 causes subject to missingness
data(sim3cs)

res.aipw <- markPH.aipw(cmprskPHformula=cbind(time,delta,cause)~z1+z2,
                        trtpos=1,
                        strata="strata",
                        causelevels=c(1,2,3),
                        missformula=~z1+A,
                        markformula=~time+z1+A,
                        data=sim3cs,
                        VEnull=0.3,
                        maxit=15)
res.aipw # print the result

fei-heng/cmprskPH documentation built on May 24, 2023, 3:54 p.m.