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Background When quantifying the probability of survival in cancer patients using cancer registration data, it is common to estimate marginal relative survival, which under assumptions can be interpreted as marginal net survival. Net survival is a hypothetical construct giving the probability of being alive if it was only possible to die of the cancer under study, enabling comparisons between populations with differential mortality rates due to causes other the cancer under study. Marginal relative survival can be estimated non-parametrically (Pohar Perme estimator) or in a modeling framework. In a modeling framework, even when just interested in marginal relative survival it is necessary to model covariates that affect the expected mortality rates (e.g. age, sex and calendar year). The marginal relative survival function is then obtained through regression standardization. Given that these covariates will generally have non-proportional effects, the model can become complex before other exposure variables are even considered. Methods We propose a flexible parametric model incorporating restricted cubic splines that directly estimates marginal relative survival and thus removes the need to model covariates that affect the expected mortality rates. In order to do this the likelihood needs to incorporate the marginal expected mortality rates at each event time taking account of informative censoring. In addition time-dependent weights are incorporated into the likelihood. An approximation is proposed through splitting the time scale into intervals, which enables the marginal relative survival model to be fitted using standard software. Additional weights can be incorporated when standardizing to an external reference population. Results The methods are illustrated using national cancer registry data. In addition, a simulation study is performed to compare different estimators; a non-parametric approach, regression-standardization and the new marginal relative model. The simulations study shows the new approach is unbiased and has good relative precision compared to the non-parametric estimator. Conclusion The approach enables estimation of standardized marginal relative survival without the need to model covariates that affect expected mortality rates and thus reduces the chance of model misspecification.

In a competing risks analysis, interest lies in the cause-specific cumulative incidence function (CIF) which can be calculated by either (1) transforming on the cause-specific hazard (CSH) or (2) through its direct relationship with the subdistribution hazard (SDH). We expand on current competing risks methodology from within the flexible parametric survival modelling framework (FPM) and focus on approach (2). This models all cause-specific CIFs simultaneously and is more useful when we look to questions on prognosis. We also extend cure models using a similar approach described by Andersson et. al. for flexible parametric relative survival models. Using SEER public use colorectal data, we compare and contrast our approach with standard methods such as the Fine & Gray model, and show that many useful out-of-sample predictions can be made after modelling the cause-specific CIFs using a FPM approach. Alternative link functions may also be incorporated such as the logit link. Models can also be easily extended for time-dependent effects.

Hearing over a wide range of sound intensities is thought to require complementary coding by functionally diverse spiral ganglion neurons (SGNs), each changing activity only over a subrange. The foundations of SGN diversity are not well understood but likely include differences among their inputs: the presynaptic active zones (AZs) of inner hair cells (IHCs). Here we studied one candidate mechanism for causing SGN diversity—heterogeneity of Ca(2+) influx among the AZs of IHCs—during postnatal development of the mouse cochlea. Ca(2+) imaging revealed a change from regenerative to graded synaptic Ca(2+) signaling after the onset of hearing, when in vivo SGN spike timing changed from patterned to Poissonian. Furthermore, we detected the concurrent emergence of stronger synaptic Ca(2+) signals in IHCs and higher spontaneous spike rates in SGNs. The strengthening of Ca(2+) signaling at a subset of AZs primarily reflected a gain of Ca(2+) channels. We hypothesize that the number of Ca(2+) channels at each IHC AZ critically determines the firing properties of its corresponding SGN and propose that AZ heterogeneity enables IHCs to decompose auditory information into functionally diverse SGNs.