Empirical study of the dependence of the results of multivariable flexible survival analyses on model selection strategy

Assessing the time dependence of prognostic values of cytology and human papillomavirus testing in cervical cancer screening

Accurate assessment of risks for developing cervical intraepithelial neoplasia of grade 2 or worse (CIN2+) after a given set of screening test results is instrumental to reaching valid conclusions and informing cervical cancer screening recommendations. Using data from the Canadian Cervical Cancer Screening Trial (CCCaST), we assessed prognostic values of enrollment screening test results to predict CIN2+ among women attending routine cervical screening using multivariable Cox proportional hazards (PH) regression and its flexible extension during each of two follow-up periods (protocol-defined and extended). Nonproportional (time-dependent (TD)) and/or nonlinear effects were modeled, as appropriate. Women with abnormal cytology had hazard ratios (HRs) for CIN2+ detection of 17.61 (95% CI: 11.25-27.57) and 10.46 (95% CI: 5.41-20.24) relative to women with normal cytology during the protocol-defined and extended follow-up periods, respectively. High-risk human papillomavirus (HR-HPV) positivity was an even stronger predictor of CIN2+ risk, with significant TD effects during both follow-up periods (p <0.001 for both TD effects). Risks among women co-testing HR-HPV+ with and without abnormal cytology (relative to women co-testing negative) were highest immediately after baseline, and decreased significantly thereafter (p <0.001 for both TD effects). HRs for HPV16+ and HPV18+ women (relative to those testing HR-HPV-) did not vary significantly over time (HR = 182.96; 95% CI: 95.16-351.77 and HR = 111.81; 95% CI: 44.60-280.31, respectively). Due to TD effects, conventional Cox model estimates considerably underestimated adjusted HRs associated with positive HR-HPV testing results early on in the follow-up periods.

Multiple imputation in Cox regression when there are time-varying effects of covariates

In Cox regression, it is important to test the proportional hazards assumption and sometimes of interest in itself to study time-varying effects (TVEs) of covariates. TVEs can be investigated with log hazard ratios modelled as a function of time. Missing data on covariates are common and multiple imputation is a popular approach to handling this to avoid the potential bias and efficiency loss resulting from a "complete-case" analysis. Two multiple imputation methods have been proposed for when the substantive model is a Cox proportional hazards regression: an approximate method (Imputing missing covariate values for the Cox model in Statistics in Medicine (2009) by White and Royston) and a substantive-model-compatible method (Multiple imputation of covariates by fully conditional specification: accommodating the substantive model in Statistical Methods in Medical Research (2015) by Bartlett et al). At present, neither accommodates TVEs of covariates. We extend them to do so for a general form for the TVEs and give specific details for TVEs modelled using restricted cubic splines. Simulation studies assess the performance of the methods under several underlying shapes for TVEs. Our proposed methods give approximately unbiased TVE estimates for binary covariates with missing data, but for continuous covariates, the substantive-model-compatible method performs better. The methods also give approximately correct type I errors in the test for proportional hazards when there is no TVE and gain power to detect TVEs relative to complete-case analysis. Ignoring TVEs at the imputation stage results in biased TVE estimates, incorrect type I errors, and substantial loss of power in detecting TVEs. We also propose a multivariable TVE model selection algorithm. The methods are illustrated using data from the Rotterdam Breast Cancer Study. R code is provided.

Flexible modeling of disease activity measures improved prognosis of disability progression in relapsing-remitting multiple sclerosis

OBJECTIVES

To illustrate the advantages of updating time-varying measures of disease activity and flexible modeling in prognostic clinical studies using the example of the association between the frequency of past relapses and occurrence of ambulation-related disability in multiple sclerosis (MS).

STUDY DESIGN AND SETTING

Longitudinal population-based study of 288 patients from Burgundy, France, diagnosed with relapsing-remitting MS in 1990-2003. The end point was a nonreversible moderate MS disability (European Database for Multiple Sclerosis score ≥ 3.0 derived from Extended Disability Status Scale). Alternative time-varying measures of attacks frequency included (1) conventional number of early MS attacks in the first 2 years after diagnosis; and two new measures, continuously updated during the follow-up; (2) cumulative number of past attacks; and (3) number of recent attacks, during the past 2 years. Multivariate analyses used Cox proportional hazards model and its flexible generalization, which accounted for time-dependent changes in the hazard ratios (HRs) for different attack frequency measures.

RESULTS

HRs for all measures decreased significantly with increasing follow-up time. The proposed updated number of recent attacks improved model's fit to data, relative to alternative measures of attack frequency, and was associated with a statistically significantly increased hazard of developing ambulation-related MS disability in the next 2 years during the entire follow-up period.

CONCLUSION

Updated measures of recent disease activity, such as frequency of recent attacks and modeling of their time-dependent effects, may substantially improve prognosis of clinical outcomes, such as development of MS disability.

A flexible alternative to the Cox proportional hazards model for assessing the prognostic accuracy of hospice patient survival

Prognostic models are often used to estimate the length of patient survival. The Cox proportional hazards model has traditionally been applied to assess the accuracy of prognostic models. However, it may be suboptimal due to the inflexibility to model the baseline survival function and when the proportional hazards assumption is violated. The aim of this study was to use internal validation to compare the predictive power of a flexible Royston-Parmar family of survival functions with the Cox proportional hazards model. We applied the Palliative Performance Scale on a dataset of 590 hospice patients at the time of hospice admission. The retrospective data were obtained from the Lifepath Hospice and Palliative Care center in Hillsborough County, Florida, USA. The criteria used to evaluate and compare the models' predictive performance were the explained variation statistic R², scaled Brier score, and the discrimination slope. The explained variation statistic demonstrated that overall the Royston-Parmar family of survival functions provided a better fit (R² = 0.298; 95% CI: 0.236–0.358) than the Cox model (R² = 0.156; 95% CI: 0.111–0.203). The scaled Brier scores and discrimination slopes were consistently higher under the Royston-Parmar model. Researchers involved in prognosticating patient survival are encouraged to consider the Royston-Parmar model as an alternative to Cox.

Flexible modeling improves assessment of prognostic value of C-reactive protein in advanced non-small cell lung cancer

Background:

C-reactive protein (CRP) is gaining credibility as a prognostic factor in different cancers. Cox's proportional hazard (PH) model is usually used to assess prognostic factors. However, this model imposes a priori assumptions, which are rarely tested, that (1) the hazard ratio associated with each prognostic factor remains constant across the follow-up (PH assumption) and (2) the relationship between a continuous predictor and the logarithm of the mortality hazard is linear (linearity assumption).

Methods:

We tested these two assumptions of the Cox's PH model for CRP, using a flexible statistical model, while adjusting for other known prognostic factors, in a cohort of 269 patients newly diagnosed with non-small cell lung cancer (NSCLC).

Results:

In the Cox's PH model, high CRP increased the risk of death (HR=1.11 per each doubling of CRP value, 95% CI: 1.03–1.20, P=0.008). However, both the PH assumption (P=0.033) and the linearity assumption (P=0.015) were rejected for CRP, measured at the initiation of chemotherapy, which kept its prognostic value for approximately 18 months.

Conclusion:

Our analysis shows that flexible modeling provides new insights regarding the value of CRP as a prognostic factor in NSCLC and that Cox's PH model underestimates early risks associated with high CRP.