coxmeta.fixed: Mixed data fixed effects meta-analysis with survival data

Description

Combined estimation of parameters of hazard model for a survival meta-analysis when the meta dataset had both patient-level and study-level evidence (mixed data). The fixed effects model assumes homogeneity between studies.

Usage

coxmeta.fixed(
    ipd.formula,
    meta.formula,
    ipd.data,
    meta.data,
    sigma2,
    study.group.interaction,
    beta.ad,
    beta.ipd,
    error=1/1000
)

Arguments

ipd.formula

Formula for patient-level Cox model as would be supplied to coxph, Surv(time,event)~trt*x

meta.formula

Formula for study-level data surv~log(time)+trt*x

ipd.data

Patient-level data frame

meta.data

Study-level data frame containing survival estimates by study and treatment group

sigma2

Estimates variances for aggregate survival estimates of meta.data

study.group.interaction

Factor that is the study and treatment group interaction for meta.data

beta.ipd

Vector of starting values for the individual-level model.

beta.ad

Vector of starting values for the study-level model.

error

Newton-Raphson stopping rule criterion based on change in log-likelihood

Value

A list with components coef, var, loglik, and a list monitor which shows the Newton-Raphson changes in coef and loglik.

Details

The estimation is based on likelihood methods for the combined likelihood contributions of the individual and aggregate data. The individual-level model is a Cox proportional hazards model with fixed effects of covariates. The aggregate data are assumed to be a set of survival estimates and their variance (e.g. KM estimates) for each cluster of the meta dataset, i.e. treatment group within study.

The aggregate model is a multivariate GLM on the log-negative-log transform of the survival estimates. The mean of the transformed survival is linear in the covariate model of meta.formula. The transformed estimates are assumed to have an MVN distribution where the covariance-variance matrix is regarded as known and is determined by the variances sigma2 and the correlation between surival estimates within the same cluster.

Shared parameters between the individual-level and study-level models are determined by common term.labels for ipd.formula and meta.formula. So, for example, if ipd.formula was Surv(time,event)~trt*x and meta.formula was surv~log(time)+trt*x then the shared terms are trt,x and trt:x and these would be combined. If instead meta.formula was surv~log(time)+trt*x.bar, then only trt would be common, and only study level data would be used to estimate x.bar and trt:x.bar factors.

Examples

Run this code

data(ipd.data)
data(meta.data)

#SHARED COVARIATE ~TRT+X
#SURV BASELINE HAZARD COMPONENT OF MODEL ~LOG(TIME)

fit <- coxmeta.fixed(
    Surv(time,event)~trt,surv~log(time)+trt,
    ipd.data,
    meta.data,
    meta.data$sigma2,
    meta.data$sub.group,
    beta.ipd = runif(1),
    beta.ad = c(1,0,runif(1)),
    )

fit$coef		#MODEL FIT

sqrt(diag(fit$var))	#STANDARD ERROR

###SEPARATION OF STUDY-LEVEL AND PATIENT-LEVEL COVARIATE

ipd.data$x.bar <-
rep(tapply(ipd.data$x,ipd.data$group,mean),table(ipd.data$group))
ipd.data$x.c <- ipd.data$x-ipd.data$x.bar
meta.data$x.bar <- meta.data$x

fit <- coxmeta.fixed(
    Surv(time,event)~trt+x.c+x.bar,surv~log(time)+trt+x.bar,
    ipd.data,
    meta.data,
    meta.data$sigma2,
    meta.data$sub.group,
    beta.ipd = runif(3),
    beta.ad = c(1,0,runif(2)),
    )

fit$coef		#MODEL FIT

sqrt(diag(fit$var))	#STANDARD ERROR