cchs: Cox model for case--cohort data with stratified subcohort-selection

Description

cchs fits a Cox proportional-hazards regression model to case-cohort data where the subcohort was selected by stratified simple random sampling. It uses Estimator III of Borgan et al (2000).

Usage

cchs(formula, data=sys.parent(), inSubcohort, stratum, 
		samplingFractions, cohortStratumSizes, precision=NULL, 
		swap=TRUE, dropNeverAtRiskRows=TRUE, dropSubcohEventsDfbeta=FALSE, 
		adjustSampFracIfAnyNAs=FALSE, keepAllCoxphElements=FALSE, 
		verbose=FALSE, coxphControl, ...)

Arguments

formula

An object of class formula that specifies the terms in the model. The left-hand side must be a Surv object. The special terms cluster and str

data

A data-frame or environment that contains the variables used in the formula. The variables named in inSubcohort, stratum, samplingFractions, and cohortStratumSizes will be looked for first in data<

inSubcohort

A vector of logical variables that shows whether each observation/row is in the subcohort (TRUE) or not (FALSE).

stratum

A vector that defines the strata within which the subcohort was selected. Each element of stratum corresponds to one observation/row in the data. The elements can be character strings, integers, or any other type of variable that can be conve

samplingFractions, cohortStratumSizes

samplingFractions is a vector of the sampling fractions in the different strata, and cohortStratumSizes is a vector of the sizes of the strata in the full cohort. Exactly one of these must be given. There are two possible forms f

precision

For example, if the times were recorded to the nearest day but are stored as numbers of years, then precision should be 1/365.25. If there are no tied event-times, then it makes no difference what precision is. If th

swap

If this is FALSE then the swapping will be omitted (in the formula for Estimator III in Borgan et al 2000, the randomly selected observation/row will not be removed). This is only intended to be used for testing or development.

dropNeverAtRiskRows

If this is TRUE, observations/rows whose at-risk periods do not include any of the event-times will be dropped just before cchs internally calls coxph. These observations/rows make n

dropSubcohEventsDfbeta

If this is FALSE, which is the default, the dfbeta residuals and therefore the variance-estimates will be calculated exactly as described by Borgan et al (2000). If it is TRUE, they will be calculated as described by Langholz & J

adjustSampFracIfAnyNAs

If this is true, and if any observations are dropped because of missing data (NAs), then the sampling fractions will be recalculated using the numbers of observations after those observations are dropped.

keepAllCoxphElements

If this is TRUE, then the object returned by cchs will contain elements such as loglik and linear.predictors from the object that was produced by cchs's internal call to

verbose

If this is TRUE, detailed information about the internal manipulations and calculations will be displayed.

coxphControl, ...

These are optional arguments to control the working of coxph when it is called internally by cchs. If coxphControl is supplied then it must be a list produced by coxph.cont

Value

An S3 object of class cchs. This is a list that contains the following elements:
coefficientsThe vector of coefficients.
varThe variance matrix of the coefficients.
iterThe number of iterations used by coxph.
nThe number of observations (that is, rows), that were used in the call to coxph.
neventThe number of events (also called failures).
callThe call that was used to create the cchs object (an object of mode call).
coeffsTableA summary of the main numerical output. This is a matrix that contains the hazard ratios, 95% confidence intervals for them, p-values for the Wald tests, log hazard ratios (which are the coefficients in the Cox model), and standard errors of the log hazard ratios.
nEachStatusA vector with three elements: the numbers of subcohort non-cases, subcohort cases, and non-subcohort cases. The sum of these is n.
nStrataThe number of strata that appear in the data.
messageA message about observations that have been dropped because of NAs and event-times that have been changed to deal with ties, if either of these happened.
If keepAllCoxphElements is TRUE, then the cchs object will also contain the other elements listed under coxph.object.

encoding

UTF-8

Details

In a case--cohort study, the dataset consists only of the cases (the participants who have an event) and the participants who are in the subcohort, which is a randomly selected subset of the cohort. In a stratified case--cohort study, the subcohort is selected by stratified simple random sampling. This means that the cohort is divided into strata, and from each stratum a proportion of the participants equal to that stratum's sampling fraction is selected to be in the subcohort (and within each stratum, each participant is selected with equal probability). For more on stratified case--cohort studies see any of the references listed below. cchs fits a Cox proportional-hazards regression model to data from a stratified case--cohort study, using the time-fixed version of Estimator III from Borgan et al (2000). Estimators I and II from Borgan et al (2000) are available by using cch with the options method="I.Borgan" and method="II.Borgan", but only Estimator III is score-unbiased, which is the main desirable criterion. The data must be in the usual form where each row corresponds to one observation (that is, one participant). cchs works by manipulating the data in various ways, then passing it to coxph (which is suitable for fitting a Cox model to data from a cohort study), and finally making corrections to the variance-estimates. It is planned that a vignette will be produced and this will contain more detail. For normal use, the logical (boolean) arguments should have their default values. cchs performs a complete-case analysis, meaning that rows will be dropped if they contain NAs in any of the variables that appear in the model, including inside the Surv(), or in inSubcohort or stratum. NAs are not allowed in samplingFractions or cohortStratumSizes, unless that vector has names and any of those names are not equal to values of stratum, in which case the corresponding elements can be NA.

cchs does not normally give replicable results, because the swapping and the small changes to tied event-times are random (see swap and precision in the Argument section). To get exactly the same results every time, use set.seed with a fixed seed just before calling cchs.

References

Borgan, Ø., Langholz, B., Samuelsen S.O., Goldstein, L., Pogoda, J. (2000). Exposure stratified case--cohort designs. Lifetime Data Analysis 6 (1), 39--58. http://tinyurl.com/onc2ual{link} Cologne, J., Preston, D.L., Imai, K., Misumi, M., Yoshida, K., Hayashi, T., Nakachi, K. (2012). Conventional case--cohort design and analysis for studies of interaction. International Journal of Epidemiology 41 (4), 1174--1186. http://ije.oxfordjournals.org/content/41/4/1174.full{link}

Langholz, B., Jiao, J. (2007). Computational methods for case--cohort studies. Computational Statistics and Data Analysis 51 (8), 3737--3748. http://www.sciencedirect.com/science/article/pii/S0167947306005068{link}

Examples

Run this code

# Analyze the relation between survival and three covariates in cchsData. 
# The times are stored as years but were recorded to the nearest month, so 
# precision has to be 1/12. The selection of the subcohort was stratified 
# according to two strata, defined by cchsData$localHistol, and the sampling 
# fractions are stored in cchsData$sampFrac. 

cchs(Surv(time, isCase) ~ stage + centralLabHistol + ageAtDiagnosis, 
      data=cchsData, inSubcohort=inSubcohort, stratum=localHistol, 
      samplingFractions=sampFrac, precision=1/12)

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