Juni Palmgren

Maximum likelihood inference for multivariate frailty models using an automated Monte Carlo EM algorithm.

We present a maximum likelihood estimation procedure for the multivariate frailty model. The estimation is based on a Monte Carlo EM algorithm. The expectation step is approximated by averaging over random samples drawn from the posterior distribution of the frailties using rejection sampling. The maximization step reduces to a standard partial likelihood maximization. We also propose a simple rule based on the relative change in the parameter estimates to decide on sample size in each iteration and a stopping time for the algorithm. An important new concept is acquiring absolute convergence of the algorithm through sample size determination and an efficient sampling technique. The method is illustrated using a rat carcinogenesis dataset and data on vase lifetimes of cut roses. The estimation results are compared with approximate inference based on penalized partial likelihood using these two examples. Unlike the penalized partial likelihood estimation, the proposed full maximum likelihood estimation method accounts for all the uncertainty while estimating standard errors for the parameters.

Correcting for non-compliance in randomized trials: an application to the ATBC study

Different methods for estimating the effect of treatment actually received in a longitudinal placebo-controlled trial with non-compliance are discussed. Total mortality from the ATBC Study is used as an illustrative example. In the ATBC Study some 25 per cent of the participants dropped out from active follow-up prior to the scheduled end of the study. The intention-to-treat analysis showed an increased death risk in the beta-carotene arm when compared with the no beta-carotene arm. Owing to considerable non-compliance it is also of interest to estimate the effect of beta-carotene actually received. We use a simple model for the treatment action and discuss three methods for estimation of the treatment effect under the model - the intention-to-treat approach, the as-treated approach and the g-estimation approach. These approaches are compared in a simulation study under different settings for non-compliance. Finally, the data from the ATBC Study are analysed using the proposed methods.

Vitamin A and Infant Mortality: Beyond Intention-to-Treat in a Randomized Trial

This paper investigates the effect of one dose of vitamin A on subsequent 4 month mortality in children under 6 months of age in a randomized, double-blind placebo-controlled community trial in Nepal. An earlier published intention-to-treat analysis showed no benefit, but ignored the information on actual receipt of treatment. Structural failure time models (Robins and Tsiatis, 91) use randomization based inference and incorporate compliance information which is possibly selective. The data presented here offer some new challenges for this approach: ward-based randomization induces correlation between survival outcomes; and the actual receipt of vitamin A dose is not always recorded. To tackle the problem of the clustered survival data we consider a robust version of the structural parameter vector estimator. A sensitivity analysis captures boundaries for the estimated structural parameters reflecting a range of potential values of children whose true receipt of treatment is unknown. The analysis suggests that the effect of vitamin A was beneficial in the beginning of the trial but towards the end of the trial there was a reversal of this effect.

Serum epidermal growth factor receptor and p53 as predictors of lung cancer risk in the ATBC study.

Serum samples from the Alpha-Tocopherol, Beta-Carotene Cancer Prevention Study were used in a nested case control study to identify the possible association between the serum level of epidermal growth factor receptor and p53 in respect to lung cancer. The proteins were assayed for by commercial immunoassays that showed uneven, often unacceptable, quality. For EGFR there was no relationship to lung cancer. Two physiological variables appeared to modify the serum level of EGFR, age by decreasing it annually by about 4 fmolml-1, and stroke by increasing it by 150 fmolml-1. For p53, myocardial infarction appeared to cause an increase in serum levels of this protein. While the serum levels of p53 were only moderately increased in lung cancer patients, particularly those with squamous cell carcinoma, the intriguing findings related to the high frequency of p53-positive patients among those belonging to the group of patients being treated by surgery and those belonging to clinical stages 1 and 2 as compared with higher clinical stages. An untested rationalization of these results was that patients with advanced lung cancer, stages 3 and higher, develop autoantibodies against the mutant p53 and thus mask the serum levels of the mutant p53 protein.

Fitting exponential family mixed models

The generalized linear model (McCullagh and Nelder, 1972) and the semiparametric multiplicative hazard model (Cox, 1972) have significantly influenced the way in which statistical modelling is taught and practiced. Common for the two model families is the assumption that conditionally on covariate information (including time) the observations are independent. The obvious difficulty in identifying and measuring all relevant covariates has pushed for methods that can jointly handle both mean and dependence structures. The early 1990s saw a myriad of approaches for dealing with multivariate generalized linear models. More recently, the hazard models have been extended to multivariate settings. Here we review (i) penalized likelihood, (ii) Monte Carlo EM, and (iii) Bayesian Markov chain Monte Carlo methods for fitting the generalized linear mixed models and the frailty models, and we discuss the rationale for choosing between the methods. The similarities of the toolboxes for these two multivariate model families open up for a new level of generality both in teaching and applied research. Two examples are used for illustration, involving censored failure time responses and Poisson responses, respectively.