# Estimate Cox model hazard ratios for covariates with missing data

### Description

`nested.coxph`

fits the Cox model to estimate hazard ratios
for covariates that are missing data on some cohort members. All
covariates may be continous or categorical.
`nested.coxph`

requires knowledge of the variables that
missingness depends on, with missingness probability modeled through a
`glm`

sampling model. Often, the data is in the form of a
case-control sample taken within a cohort. `nested.coxph`

allows
cases to have missing data, and can extract efficiency from auxiliary
variables by including them in the sampling model. `nested.coxph`

requires `coxph`

from the survival package.

### Usage

1 2 3 4 5 | ```
nested.coxph(coxformula, samplingmod, data, outputsamplingmod = FALSE,
glmlink = binomial(link = "logit"),
glmcontrol = glm.control(epsilon = 1e-10, maxit = 10, trace = FALSE),
coxphcontrol = coxph.control(eps = 1e-10, iter.max = 50),
missvarwarn = TRUE, ...)
``` |

### Arguments

Required arguments:

`coxformula` |
Standard |

`samplingmod` |
Right side of the formula for the |

`data` |
Data Frame that all variables are in |

Optional arguments:

`outputsamplingmod` |
Output the sampling model, default is false |

`glmlink` |
Sampling model link function, default is logistic regression |

`glmcontrol` |
See |

`coxphcontrol` |
See |

`missvarwarn` |
Warn if there is missing data in the sampling variable. Default is TRUE |

`...` |
Any additional arguments to be passed on to |

### Details

If `nested.coxph`

reports that the sampling model "failed to converge",
the sampling model will be returned for your inspection. Note that if
some sampling probabilities are estimated at 1, the model technically
cannot converge, but you get very close to 1, and `nested.coxph`

will not report non-convergence for this situation.

Note these issues. The data must be in a dataframe and specified in the data statement. No variable can be named 'o.b.s.e.r.v.e.d.' or 'p.i.h.a.t.'. Cases and controls cannot be finely matched on time, but matching on time within large strata is allowed. cluster() statements are not allowed in coxformula. Allows left truncation, staggered entry, open cohorts, and stratified baseline hazards. Must use Breslow Tie-Breaking.

### Value

If outputsamplingmod=FALSE, the output are the hazard ratios and the
`coxph`

model. Any
method for `coxph`

objects will work for this so long
as that method only requires consistent estimates of the parameters and
their standard errors.
If outputsamplingmod=TRUE, then the sampling model is also returned, and
the output is a list with components:

`coxmod` |
The Cox model of class |

`samplingmod` |
The sampling model of class |

### Note

Requires the MASS library from the VR bundle that is available from the CRAN website.

### Author(s)

Hormuzd A. Katki

### References

Katki HA, Mark SD. Survival Analysis for Cohorts with Missing Covariate Information. R-News, 8(1) 14-9, 2008. http://www.r-project.org/doc/Rnews/Rnews_2008-1.pdf

Mark, S.D. and Katki, H.A. Specifying and Implementing Nonparametric and Semiparametric Survival Estimators in Two-Stage (sampled) Cohort Studies with Missing Case Data. Journal of the American Statistical Association, 2006, 101, 460-471.

Mark SD, Katki H. Influence function based variance estimation and missing data issues in case-cohort studies. Lifetime Data Analysis, 2001; 7; 329-342

Christian C. Abnet, Barry Lai, You-Lin Qiao, Stefan Vogt, Xian-Mao Luo, Philip R. Taylor, Zhi-Wei Dong, Steven D. Mark, Sanford M. Dawsey. Zinc concentration in esophageal biopsies measured by X-ray fluorescence and cancer risk. To Appear in Journal of the National Cancer Institute.

### See Also

See Also: `nested.stdsurv`

, `zinc`

,
`nested.km`

, `coxph`

, `glm`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | ```
## Simple analysis of zinc and esophageal cancer data:
## We sampled zinc (variable zncent) on a fraction of the subjects, with
## sampling fractions depending on cancer status and baseline histology.
## We observed the confounding variables on almost all subjects.
data(zinc)
coxmod <- nested.coxph(coxformula="Surv(futime01,ec01==1)~
sex+agepill+smoke+drink+mildysp+moddysp+sevdysp+anyhist+zncent",
samplingmod="ec01*basehist",data=zinc)
summary(coxmod)
# This is the output:
# Call:
# coxph(formula = as.formula(coxformula), data = data, weights = 1/p.i.h.a.t.,
# subset = TRUE, na.action = na.omit, control = coxphcontrol,
# x = TRUE, method = "breslow")
# n= 123, number of events= 56
# (308 observations deleted due to missingness)
# coef exp(coef) se(coef) z Pr(>|z|)
# sexMale 0.2953 1.3436 0.5558 0.53 0.5952
# agepill 0.0539 1.0554 0.0275 1.96 0.0499 *
# smokeEver 0.0145 1.0146 0.5870 0.02 0.9803
# drinkEver -0.8548 0.4254 0.5896 -1.45 0.1471
# mildyspMild Dysplasia 0.9023 2.4653 0.3937 2.29 0.0219 *
# moddyspModerate Dysplasia 1.3309 3.7845 0.4212 3.16 0.0016 **
# sevdyspSevere Dysplasia 2.1334 8.4439 0.4615 4.62 3.8e-06 ***
# anyhistFamily History 0.0904 1.0946 0.3896 0.23 0.8165
# zncent -0.2498 0.7789 0.1351 -1.85 0.0645 .
# exp(coef) exp(-coef) lower .95 upper .95
# sexMale 1.344 0.744 0.452 3.99
# agepill 1.055 0.948 1.000 1.11
# smokeEver 1.015 0.986 0.321 3.21
# drinkEver 0.425 2.351 0.134 1.35
# mildyspMild Dysplasia 2.465 0.406 1.140 5.33
# moddyspModerate Dysplasia 3.784 0.264 1.658 8.64
# sevdyspSevere Dysplasia 8.444 0.118 3.417 20.86
# anyhistFamily History 1.095 0.914 0.510 2.35
# zncent 0.779 1.284 0.598 1.02
# Concordance= NA (se = NA )
# Rsquare= NA (max possible= NA )
# Likelihood ratio test= NA on 9 df, p=NA
# Wald test = 65.1 on 9 df, p=1.36e-10
# Score (logrank) test = NA on 9 df, p=NA
``` |