Yang-Jin Kim, Chung Mo Nam, Youn Nam Kim, Eun Hee Choi and Jinheum Kim have a new paper in the Journal of the Korean Statistical Society. This concerns the analysis of tumorigenicity data where a three-state model with states representing tumour-free, with tumour and death is used. The main characteristic of the data is that disease status (presence of tumour) can only be determined at either death or sacrifice - meaning we have data with possible observations: sacrifice without tumour, sacrifice with tumour, death without tumour and death with tumour.
Note that while the time of the tumour is always interval censored, if the mouse dies before sacrifice this death time is taken to be known exactly.
Kim et al extend the model proposed by Lindsey and Ryan (1993, Applied Statistics) by allowing a shared-frailty term that affects both tumour onset rate and the hazard of death given the presence of a tumour. Like Lindsey and Ryan, piecewise constant intensities are used to model the baseline intensities, with a Cox proportional hazards model for the effect of covariates. The same baseline hazard is used for pre- and post-tumour hazard of death, with the presence of tumour changing the effect of covariates. For some reason the introduction talks about n^{1/3} convergence rates of the non-parametric survival distribution for current status data. This doesn't seem relevant here given that the piecewise constant intensities model is parametric.
An EM algorithm is used to maximize the likelihood. Gauss-Hermite quadrature is required to perform the M-step due to the presence of the frailty terms. The authors appear to be basing standard error estimates on the complete data (rather than observed data) likelihood.
The new model is applied to the same data as used in Lindsey and Ryan. In addition, in a simulation it is shown that there is some reduction in bias compared to Lindsey and Ryan's method is the proposed model is correctly specified.
Sunday 21 November 2010
Monday 8 November 2010
Accounting for bias due to a non-ignorable tracing mechanism in a retrospective breast cancer cohort study
Titman, Lancaster, Carmichael and Scutt have a new paper in Statistics in Medicine. This applies methods developed by Copas and Farewell (Biostatistics, 2001) to data from a retrospective cohort study where patients were traced conditional on survival up to a certain time. The authors note that the resulting observed process can be viewed as a purged process (Hoem, 1969). In addition to the pseudo-likelihood method of Copas and Farewell (which requires specification of the entry time distribution of patients), a full likelihood approach based on piecewise constant intensities under a Markov assumption is also applied. The term to take into account the conditional survival involves a transition probability, so estimation has similar difficulties to interval-censored data. For the breast cancer study considered, the two methods give very similar results.
A semi-competing risks model for data with interval-censoring and informative observation
Jessica Barrett, Fotios Siannis and Vern Farewell have a new paper in Statistics in Medicine. Essentially the paper uses similar methods as in Siannis et al 2006, to investigate informative loss-to-follow-up (LTF) in a study of aging and cognitive function.
LTF, refers to loss-to-follow-up of monitoring cognitive impairment - crucially survival continues to be monitored. LTF (from healthy) is modelled as a separate state in the process with its own transition intensity. Once LTF, the subject experiences different intensities of becoming cognitive impaired or dying. An unidentifiable parameter k determines the relative rate at which people who are lost to follow-up (before becoming cognitively impaired) proceed to the cognitively impaired state rather than the death state, compared to those not lost to follow-up.
k can be varied to see what impact assumptions about those LTF have on overall estimates. In the current study k has quite a large impact on estimates of cumulative incidence of cognitive impairment. This is in contrast to the Whitehall study where these methods were applied to right-censored data, where k had little effect.
A parametric Weibull intensities Markov model is used to model the data. Due to the interval censoring, computation of the likelihood requires numerical integration.
As an informal goodness-of-fit test the authors compare on Cox model of overall survival, with the corresponding survival estimates for the multi-state model with proportional intensity models on each intensity. The authors note that the Cox proportional hazards model for overall survival should be unbiased. Of course, it is only unbiased if the proportional hazards assumption holds on the overall hazard of death. If, however, the covariates are proportional on the individual intensities, as assumed in the multi-state model, the Cox model on overall survival will be biased. This approach is therefore more of a test of robustness to assumptions about the covariates than a goodness-of-fit test because the models aren't nested. The same method was used in Siannis et al 2006 and in Van den Hout et al, 2009.
LTF, refers to loss-to-follow-up of monitoring cognitive impairment - crucially survival continues to be monitored. LTF (from healthy) is modelled as a separate state in the process with its own transition intensity. Once LTF, the subject experiences different intensities of becoming cognitive impaired or dying. An unidentifiable parameter k determines the relative rate at which people who are lost to follow-up (before becoming cognitively impaired) proceed to the cognitively impaired state rather than the death state, compared to those not lost to follow-up.
k can be varied to see what impact assumptions about those LTF have on overall estimates. In the current study k has quite a large impact on estimates of cumulative incidence of cognitive impairment. This is in contrast to the Whitehall study where these methods were applied to right-censored data, where k had little effect.
A parametric Weibull intensities Markov model is used to model the data. Due to the interval censoring, computation of the likelihood requires numerical integration.
As an informal goodness-of-fit test the authors compare on Cox model of overall survival, with the corresponding survival estimates for the multi-state model with proportional intensity models on each intensity. The authors note that the Cox proportional hazards model for overall survival should be unbiased. Of course, it is only unbiased if the proportional hazards assumption holds on the overall hazard of death. If, however, the covariates are proportional on the individual intensities, as assumed in the multi-state model, the Cox model on overall survival will be biased. This approach is therefore more of a test of robustness to assumptions about the covariates than a goodness-of-fit test because the models aren't nested. The same method was used in Siannis et al 2006 and in Van den Hout et al, 2009.
Monday 1 November 2010
A regression model for the conditional probability of a competing event: application to monoclonal gammopathy of unknown significance
Arthur Allignol, Aurélien Latouche, Jun Yan and Jason Fine have a new paper in Applied Statistics (JRSS C). The paper concerns competing risks data and develops methods for regression analysis of the probability of a competing event conditional on no competing event having occurred. In terms of the cumulative incidence functions, for the case of two competing events, this can be written as  "\inline CPF_1 = CIF_1/(1-CIF_2)")
. In some applications this quantity may be more useful than either the cause-specific hazards or the cumulative incidence functions themselves. One approach to regression is this scenario might be to compute pseudo-observations and perform the regression using those. The authors instead propose use of temporal process regression (Fine, Yan and Kosorok 2004), allowing estimation of time dependent regression parameters, by considering the cross-sectional data at each event time.
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