Regularized parametric survival modeling to improve risk prediction models.

We propose to combine the benefits of flexible parametric survival modeling and regularization to improve risk prediction modeling in the context of time-to-event data. Thereto, we introduce ridge, lasso, elastic net, and group lasso penalties for both log hazard and log cumulative hazard models. The log (cumulative) hazard in these models is represented by a flexible function of time that may depend on the covariates (i.e., covariate effects may be time-varying). We show that the optimization problem for the proposed models can be formulated as a convex optimization problem and provide a user-friendly R implementation for model fitting and penalty parameter selection based on cross-validation. Simulation study results show the advantage of regularization in terms of increased out-of-sample prediction accuracy and improved calibration and discrimination of predicted survival probabilities, especially when sample size was relatively small with respect to model complexity. An applied example illustrates the proposed methods. In summary, our work provides both a foundation for and an easily accessible implementation of regularized parametric survival modeling and suggests that it improves out-of-sample prediction performance.

Developing a Natural History Model for Duchenne Muscular Dystrophy.

BACKGROUND: The aim of this study was to pool multiple data sets to build a patient-centric, data-informed, natural history model (NHM) for Duchenne muscular dystrophy (DMD) to estimate disease trajectory across patient lifetime under current standard of care in future economic evaluations. The study was conducted as part of Project HERCULES, a multi-stakeholder collaboration to develop tools to support health technology assessments of new treatments for DMD. METHODS: Health states were informed by a review of NHMs for DMD and input from clinicians, patients and caregivers, and defined using common outcomes in clinical trials and real-world practice. The primary source informing the NHM was the Critical Path Institute Duchenne Regulatory Science Consortium (D-RSC) database. This was supplemented with expert input obtained via an elicitation exercise, and a systematic literature review and meta-analysis of mortality data. RESULTS: The NHM includes ambulatory, transfer and non-ambulatory phases, which capture loss of ambulation, ability to weight bear and upper body and respiratory function, respectively. The NHM estimates patients spend approximately 9.5 years in ambulatory states, 1.5 years in the transfer state and the remainder of their lives in non-ambulatory states. Median predicted survival is 34.8 years (95% CI 34.1-35.8). CONCLUSION: The model includes a detailed disease pathway for DMD, including the clinically and economically important transfer state. The NHM may be used to estimate the current trajectory of DMD in economic evaluations of new treatments, facilitating inclusion of a lifetime time horizon, and will help identify areas for further research.

Jointly modelling longitudinally measured urinary human chorionic gonadotrophin and early pregnancy outcomes.

Human chorionic gonadotrophin (hCG) is largely used to confirm pregnancy. Yet evidence shows that longitudinal hCG profiles are distinguishable between healthy and failing pregnancies. We retrospectively fitted a joint longitudinal-survival model to data from 127 (85 healthy and 42 failing pregnancies) US women, aged 18-45, who were attempting to conceive, to quantify the association between longitudinally measured urinary hCG and early miscarriage. Using subject-specific predictions, obtained uniquely from the joint model, we investigated the plausibility of adaptively monitoring early pregnancy outcomes based on updating hCG measurements. Volunteers collected daily early morning urine samples for their menstrual cycle and up to 28 days post day of missed period. The longitudinal submodel for log hCG included a random intercept and slope and fixed linear and quadratic time terms. The survival submodel included maternal age and cycle length covariates. Unit increases in log hCG corresponded to a 63.9% (HR 0.36, 95% CI 0.16, 0.47) decrease in the risk of miscarriage, confirming a strong association between hCG and miscarriage. Outputted conditional survival probabilities gave individualised risk estimates for the early pregnancy outcomes in the short term. However, longer term monitoring would require a larger sample size and prospectively followed up data, focusing on emerging extensions to the joint model, which allow assessment of the specificity and sensitivity.

Adjusting for treatment switching in randomised controlled trials - A simulation study and a simplified two-stage method.

Estimates of the overall survival benefit of new cancer treatments are often confounded by treatment switching in randomised controlled trials (RCTs) - whereby patients randomised to the control group are permitted to switch onto the experimental treatment upon disease progression. In health technology assessment, estimates of the unconfounded overall survival benefit associated with the new treatment are needed. Several switching adjustment methods have been advocated in the literature, some of which have been used in health technology assessment. However, it is unclear which methods are likely to produce least bias in realistic RCT-based scenarios. We simulated RCTs in which switching, associated with patient prognosis, was permitted. Treatment effect size and time dependency, switching proportions and disease severity were varied across scenarios. We assessed the performance of alternative adjustment methods based upon bias, coverage and mean squared error, related to the estimation of true restricted mean survival in the absence of switching in the control group. We found that when the treatment effect was not time-dependent, rank preserving structural failure time models (RPSFTM) and iterative parameter estimation methods produced low levels of bias. However, in the presence of a time-dependent treatment effect, these methods produced higher levels of bias, similar to those produced by an inverse probability of censoring weights method. The inverse probability of censoring weights and structural nested models produced high levels of bias when switching proportions exceeded 85%. A simplified two-stage Weibull method produced low bias across all scenarios and provided the treatment switching mechanism is suitable, represents an appropriate adjustment method.

Should relative survival be used with lung cancer data?

BACKGROUND: Under certain assumptions, relative survival is a measure of net survival based on estimating the excess mortality in a study population when compared with the general population. Background mortality estimates are usually taken from national life tables that are broken down by age, sex and calendar year. A fundamental assumption of relative survival methods is that if a patient did not have the disease of interest then their probability of survival would be comparable to that of the general population. It is argued, as most lung cancer patients are smokers and therefore carry a higher risk of smoking-related mortalities, that they are not comparable to a population where the majority are likely to be non-smokers. METHODS: We use data from the Finnish Cancer Registry to assess the impact that the non-comparability assumption has on the estimates of relative survival through the use of a sensitivity analysis. RESULTS: Under realistic estimates of increased all-cause mortality for smokers compared with non-smokers, the bias in the estimates of relative survival caused by the non-comparability assumption is negligible. CONCLUSION: Although the assumption of comparability underlying the relative survival method may not be reasonable, it does not have a concerning impact on the estimates of relative survival, as most lung cancer patients die within the first 2 years following diagnosis. This should serve to reassure critics of the use of relative survival when applied to lung cancer data.