An Additive–Multiplicative Restricted Mean Residual Life Model

The mean residual life measures the expected remaining life of a subject who has survived up to a particular time. When survival time distribution is highly skewed or heavy tailed, the restricted mean residual life must be considered. In this paper, we propose an additive–multiplicative restricted mean residual life model to study the association between the restricted mean residual life function and potential regression covariates in the presence of right censoring. This model extends the proportional mean residual life model using an additive model as its covariate dependent baseline. For the suggested model, some covariate effects are allowed to be time‐varying. To estimate the model parameters, martingale estimating equations are developed, and the large sample properties of the resulting estimators are established. In addition, to assess the adequacy of the model, we investigate a goodness of fit test that is asymptotically justified. The proposed methodology is evaluated via simulation studies and further applied to a kidney cancer data set collected from a clinical trial.     

Cox regression with missing covariate data using a modified partial likelihood method

Missing covariate values is a common problem in survival analysis. In this paper we propose a novel method for the Cox regression model that is close to maximum likelihood but avoids the use of the EM-algorithm. It exploits that the observed hazard function is multiplicative in the baseline hazard function with the idea being to profile out this function before carrying out the estimation of the parameter of interest. In this step one uses a Breslow type estimator to estimate the cumulative baseline hazard function. We focus on the situation where the observed covariates are categorical which allows us to calculate estimators without having to assume anything about the distribution of the covariates. We show that the proposed estimator is consistent and asymptotically normal, and derive a consistent estimator of the variance–covariance matrix that does not involve any choice of a perturbation parameter. Moderate sample size performance of the estimators is investigated via simulation and by application to a real data example.     

A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo‐observations

Pseudo‐values have proven very useful in censored data analysis in complex settings such as multi‐state models. It was originally suggested by Andersen et al., Biometrika, 90, 2003, 335 who also suggested to estimate standard errors using classical generalized estimating equation results. These results were studied more formally in Graw et al., Lifetime Data Anal., 15, 2009, 241 that derived some key results based on a second‐order von Mises expansion. However, results concerning large sample properties of estimates based on regression models for pseudo‐values still seem unclear. In this paper, we study these large sample properties in the simple setting of survival probabilities and show that the estimating function can be written as a U‐statistic of second order giving rise to an additional term that does not vanish asymptotically. We further show that previously advocated standard error estimates will typically be too large, although in many practical applications the difference will be of minor importance. We show how to estimate correctly the variability of the estimator. This is further studied in some simulation studies.     

SOCIAL BACKGROUND,EDUCATION, AND INEQUALITY

The role parents' education plays for the educational achievements of children is a source of unequal opportunities. Through this channel the number of educated affects the options of future cohorts, creating a social multiplier effect making improvements in education self‐reinforcing. Policies to compensate for inequalities of opportunities—public education or transfers—have very different implications. Transfers not only reduce inequality on impact but also reduce social mobility, while public education—even if a perfect substitute to private education—works in the opposite direction. Social impediments to education are similar to a market imperfection, and publicly provided education may lead to a Pareto improvement. (JEL D3, I2, H2, H4)     

DOES THE PUBLIC SECTOR IMPLODE FROM BAUMOL'S COST DISEASE?

The root of the Baumol cost disease is higher productivity increases for manufactured goods than for services. The implied increase in relative costs of service production is widely claimed to have devastating implications for the public sector as a provider of tax‐financed services such as health, education, and care. To match the increasing costs it appears inevitable that tax rates would be ever increasing. It is shown that this inference does not follow under standard assumptions when accounting explicitly for service provision from both the private and public sectors. Strikingly under assumptions often made in the literature, the welfare maximizing tax rate for a utilitarian policy maker would remain constant despite the Baumol cost disease, and by implication the share of public employment in total employment will remain constant. (JEL H5, H11, O41)     

A Forecast Model for Unemployment by Education

ABSTRACT We present a dynamic forecast model for the labour market: demand for labour by education and the distribution of labour by education among industries are determined endogenously with overall demand by industry given exogenously. The model is derived from a simple behavioural equation based on a strong relationship between the “strength” in the struggle for jobs of an educational group, and the change in relative supply. This relationship proves to be significant in the data. Furthermore, when used to forecast employment by education on real data, the model predicts reasonably well even for educational groups, where the initial forecast year is a change point for unemployment.     

The additive hazards model with high-dimensional regressors

This paper considers estimation and prediction in the Aalen additive hazards model in the case where the covariate vector is high-dimensional such as gene expression measurements. Some form of dimension reduction of the covariate space is needed to obtain useful statistical analyses. We study the partial least squares regression method. It turns out that it is naturally adapted to this setting via the so-called Krylov sequence. The resulting PLS estimator is shown to be consistent provided that the number of terms included is taken to be equal to the number of relevant components in the regression model. A standard PLS algorithm can also be constructed, but it turns out that the resulting predictor can only be related to the original covariates via time-dependent coefficients. The methods are applied to a breast cancer data set with gene expression recordings and to the well known primary biliary cirrhosis clinical data.     

Estimation of Causal Odds of Concordance using the Aalen Additive Model

A simple summary of a treatment effect is attractive, which is part of the explanation of the success of the Cox model when analysing time‐to‐event data since the relative risk measure is such a convenient summary measure. In practice, however, the Cox model may fail to give a reasonable fit, very often because of time‐changing treatment effect. The Aalen additive hazards model may be a good alternative as time‐changing effects are easily modelled within this model, but results are then evidently more complicated to communicate. In such situations, the odds of concordance measure (OC) is a convenient way of communicating results, and recently Martinussen & Pipper (2012) showed how a variant of the OC measure may be estimated based on the Aalen additive hazards model. In this study, we propose an estimator that should be preferred in observational studies as it always estimates the causal effect on the chosen scale, only assuming that there are no un‐measured confounders. The resulting estimator is shown to be consistent and asymptotically normal, and an estimator of its limiting variance is provided. Two real applications are provided.     

Infants of Depressed Mothers Show Reduced Gaze Activity During Mother–Infant Interaction at 4 Months

Gaze is one of the main means of communication in young infants, and it has been shown to be important for subsequent socio‐emotional and cognitive development. Maternal depression is a well‐known risk factor for disrupting mother–infant interactions, but findings regarding gaze behavior in infants of depressed versus nondepressed mothers have been ambiguous. In this study, we examined gaze duration and activity in a sample of 27 infants of mothers with postpartum depression (PPD) and 49 infants of nondepressed mothers. Maternal depressive symptoms were assessed with the Edinburgh Postnatal Depression Scale, and diagnoses were confirmed in clinical interview. Infant gaze was assessed during 4‐month face‐to‐face interactions using continuous timed‐event coding with high temporal resolution. Although we found no differences in gaze duration, infants of PPD mothers had both significantly less Gaze On and also less Gaze Off events. Findings suggest that PPD is related to reduced gaze activity during mother–infant interaction in 4‐month‐olds. This reduced activity may have long‐term negative consequences for child development.