Todd Mackenzie

Time-Dependent Hazard Ratio: Modeling and Hypothesis Testing with Application in Lupus Nephritis

Abstract We investigate the association between duration of untreated disease and survival in lupus nephritis, a rare rheumatologic disease. In this case, as in many other studies of survival, a priori considerations suggest that the effect of the predictor on hazard may change with increasing follow-up time. To accommodate such situations, we use regression splines to model the hazard ratio as a flexible function of time. We propose model-based tests of the hypotheses of hazards proportionality and of no association. We evaluate the accuracy of estimation and inference in simulations and also present analysis of a larger medical data set.

The pathogenesis and prognosis of lupus nephritis: Information from repeat renal biopsy

Of an inception cohort of 87 patients with lupus nephritis who underwent a renal biopsy, 42 underwent second biopsies a median of 25 months later. From first to second biopsy, focal and diffuse proliferative nephritis (World Health Organization classes III and IV) became less frequent, and mesangial hypercellularity (class II) and a membranous pattern (class V) increased. The National Institutes of Health activity index and mesangial and subendothelial deposits declined while the chronicity index, a tubulointerstitial index, and subepithelial deposits increased. The biopsy improvement in urinary protein excretion was best explained by decreases in the activity index score and the amount of subendothelial deposits. A decrease in the amount of subendothelial deposits tended to predict an improvement in the serum creatinine level from first to second biopsy. With follow-up from second biopsy in excess of 7 years, the best predictors of long-term outcome were the ultrastructural variables mesangial, subendothelial and subepithelial deposits. When the change in biopsy predictors from first to second biopsy was evaluated, a decrease in the amount of mesangial or subendothelial deposits was best at predicting a lower risk of renal impairment, renal insufficiency, and mortality. The results confirm the importance of immune complex deposition as measured by electron microscopy in the pathogenesis of lupus nephritis and suggest that control of this process may alter renal function and prognosis.

Comparing the psychometric properties of preference-based and nonpreference-based health-related quality of life in coronary heart disease

A cross-sectional survey (n = 878) was conducted to compare the psychometric properties of three preference-based and one nonpreference-based health-related quality of life measures among healthy subjects with and without treatment for dyslipidemia and/or hypertension and patients with coronary heart disease (CHD). All measures were stable over a 3 to 6 week period. Compared to the Time Trade-off (TTO) and the Standard Gamble (SG), the Rating Scale (RS) correlated with the SF-36 Health Survey most highly. In contrast to the SF-36 General Health Perception (GHP), the SF-36 Physical Component scale and the RS, the TTO and SG were less able to discriminate CHD patients with various levels of physical disability. Only the SF-36 GHP subscale and the RS were able to differentiate healthy participants from participants receiving dyslipidemia and/or hypertension treatment. Neither the SF-36 Physical or Mental Component scales were able to discriminate these two groups. Overall, these results suggest that unlike the RS, the TTO and the SG, as administered in this study, may not be sufficiently sensitive to measure the impact of primary cardiovascular disease prevention strategies on the health-related quality of life of the participants.

Health-related quality of life with coronary heart disease prevention and treatment

Estimating the net benefits of dyslipidemia treatment is limited by the lack of comprehensive and standardized information on the preference for dyslipidemia and coronary heart disease. In a hospital-based study, we measured the health-related quality of life (HRQOL) of healthy participants without dyslipidemia (n = 307) and with dyslipidemia (n = 251) and patients with coronary heart disease (n = 320). Compared to the healthy participants without dyslipidemia, those with dyslipidemia reported lower adjusted mean scores on the Rating Scale (-2.8 points, P = 0.02) and the SF-36 General Health Scale (-3.3 points, P = 0.02). No differences were observed on the Time Trade-off and the Standard Gamble Scales. Coronary patients reported lower scores on all preference scales and most SF-36 scales. The causes of the small but real reduction in HRQOL reported by dyslipidemic individuals should be identified in order to optimize the net benefits of lipid therapy.

A nonlinear allocation problem

We consider the problem of deploying work force to tasks in a project network for which the time required to perform each task depends on the assignment of work force to the task, for the purpose of minimizing the time to complete the project. The rules governing the deployment of work force and the resulting changes in task times of our problem are discussed in the contexts of a) related work on project networks and b) more general allocation problems on polytopes. We prove that, for these problems, the obvious lower bound for project completion time is attainable.