Summary. The maximum likelihood approach to jointly model the survival time and its longitudinal covariates has been successful to model both processes in longitudinal studies. Random effects in the longitudinal process are often used to model the survival times through a proportional hazards model, and this invokes an EM algorithm to search for the maximum likelihood estimates (MLEs). Several intriguing issues are examined here, including the robustness of the MLEs against departure from the normal random effects assumption, and difficulties with the profile likelihood approach to provide reliable estimates for the standard error of the MLEs. We provide insights into the robustness property and suggest to overcome the difficulty of reliable estimates for the standard errors by using bootstrap procedures. Numerical studies and data analysis illustrate our points.

SummaryAlthough it is widely known that dietary restriction (DR) not only extends the longevity of a wide range of species but also reduces their reproductive output, the interrelationship of DR, longevity extension and reproduction is not well understood in any organism. Here we address the question: 'Under what nutritional conditions do the longevity-enhancing effects resulting from food restriction either counteract, complement or reinforce the mortality costs of reproduction? To answer this question we designed a fine-grained DR study involving 4800 individuals of the tephritid fruit fly, Anastrepha ludens , in which we measured sex-specific survival and daily reproduction in females in each of 20 different treatments (sugar : yeast ratios) plus 4 starvation controls. The database generated from this 3-year study consisted of approximately 100 000 life-days for each sex and 750 000 eggs distributed over the reproductive lives of 2400 females. The fertility and longevity-extending responses were used to create contour maps (X-Y grid) that show the demographic responses (Z-axis) across dietary gradients that range from complete starvation to both ad libitum sugar-only and ad libitum standard diet (3 : 1 sugar : yeast). The topographic perspectives reveal demographic equivalencies along nutritional gradients, differences in the graded responses of males and females, egg production costs that are sensitive to the interaction of food amounts and constituents, and orthogonal contours (equivalencies in longevity or reproduction) representing demographic thresholds related to both caloric content and sugar : yeast ratios. In general, the finding that lifespan and reproductive maxima occur at much different nutritional coordinates poses a major challenge for the use of food restriction (or a mimetic) in humans to improve health and extend longevity in humans.

The results of our nationwide, population-based study suggest that patients who undergo anaesthesia and surgery may be at increased risk of dementia.

The pre-LASIK refraction can be used theoretically to determine an accurate IOL power.