markPH.ipw2: Approach 2: IPW Estimation and Hypothesis Testing of...

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

Approach 2: IPW 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.ipw2(
  cmprskPHformula,
  trtpos = 1,
  strata,
  causelevels = NULL,
  missmodel = T,
  missformula,
  data = parent.frame(),
  VEnull = 0.3,
  maxit = 15
)

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.
missmodel	indicates whether a logistic regression model is applied to predict the probability of being not missing for each type of causes under the missing at random (MAR) assumption. If not, a logical vector is needed. TRUE: fit a logistic regression model; FALSE: that cause is not missing, i.e. the probability of being not missing for that cause is 1. For example, we have three types of causes: c("cause A", "cause B", "cause C"). missmodel=c(T,T,F) means that the probability of being not missing for cause C is 1, and the logistic regression model is fitted for cause A and cause B. The default value is T.
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.
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.

Details

Approach 2: Failure endpoint = COVID. Cause/mark V=0: vaccine-matched genotype AND viral load above minimum threshold; Cause/mark V=1: vaccine-mismatched genotype AND viral load above minimum threshold; Cause/mark V=2: viral load below minimum threshold. In Approach 2, we only care about V=0 and V=1; V=2 is a competing risk for both V=0 and V=1.

Let R be the indicator of whether all possible data are observed for a subject; R = 1 if either \delta=0 (right-censored) or if \delta=1 (a failure is observed) and the cause is not missing; and R = 0 otherwise. Let VL be the viral load and h_0 the minimum threshold. Missing at random (MAR) assumption is valid using Approach 2: P(R=1|\delta=1,T,Z,VL,h_0,V)=P(R=1|\delta=1,T,Z,VL,h_0) =I(VL<h_0)+P(R=1|\delta=1,T,Z,VL,VL \ge h_0)I(VL\ge h_0)

Value

returns an object of type 'markPH.ipw2'. With the following arguments:

causes	types of causes
misscauses	types of causes which are subject to missingness
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	estimates of covariate coefficients using IPW method
se	estimates of standard errors of estimators for covariate coefficients using IPW method
coef.VE	estimates of the strain-specific vaccine efficacy to reduce susceptibility to strain j using IPW 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 IPW method, j=1,...,J
coef.VD	estimates of VD using IPW method
se.VD	estimates of standard errors of estimators for VD using IPW method
U1	test statistic for testing against the alternative hypothesis HA1: VE(j)>=VEnull with strict inequality for some j in misscauses
U2	test statistic for testing against the alternative hypothesis HA2: VE(j) is not equal to VEnull for some j in misscauses
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(misscauses[1]) \ge \dots \ge VE(misscauses[I]) 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 in misscauses
pval.A1	p value for testing against the alternative hypothesis HA1: VE(j)>=VEnull with strict inequality for some j in misscauses
pval.A2	p value for testing against the alternative hypothesis HA2: VE(j) is not equal to VEnull for some j in misscauses
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(misscauses[1]) \ge \dots \ge VE(misscauses[I]) 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 in misscauses
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 IPW 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)

threshold <- 0.5
sim2cs$cause[(sim2cs$delta==1)&(sim2cs$A<threshold)] <- 3

res.ipw2 <- markPH.ipw2(cmprskPHformula=cbind(time,delta,cause)~z1+z2,
                        trtpos=1,
                        strata="strata",
                        causelevels=c(1,2,3),
                        missmodel=c(TRUE,TRUE,FALSE),
                        missformula=~z1+A,
                        data=sim2cs,
                        VEnull=0.3,
                        maxit=15)
res.ipw2 # print the result

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

threshold <- 0.5
sim3cs$cause[(sim3cs$delta==1)&(sim3cs$A<threshold)] <- 4

res.ipw2 <- markPH.ipw2(cmprskPHformula=cbind(time,delta,cause)~z1+z2,
                        trtpos=1,
                        strata="strata",
                        causelevels=c(1,2,3,4),
                        missmodel=c(TRUE,TRUE,TRUE,FALSE),
                        missformula=~z1+A,
                        data=sim3cs,
                        VEnull=0.3,
                        maxit=15)
res.ipw2 # print the result

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