Simulation study of joint transition and Weibull survival model with shared parameters

This study investigates a theoretical model where a longitudinal process, that is a stationary Markov-Chain, and a Weibull survival process share a bivariate random effect. Furthermore, a Quality-of-Life adjusted survival is calculated as the weighted sum of survival time. Theoretical values of population mean adjusted survival of the described model are computed numerically. The parameters of the bivariate random effect do significantly affect theoretical values of population mean. Maximum-Likelihood and Bayesian methods are applied on simulated data to estimate the model parameters. Based on the parameter estimates, predicated population mean adjusted survival can then be calculated numerically and compared with the theoretical values. Bayesian method and Maximum-Likelihood method provide parameter estimations and population mean prediction with comparable accuracy; however Bayesian method suffers from poor convergence due to autocorrelation and inter-variable correlation. ^

Prognosis of amyotrophic lateral sclerosis

Two cohorts of amyotrophic lateral sclerosis (ALS) patients were identified. One incidence-based cohort from Harris County, Texas with 97 cases, and the other a clinic referral series from an ALS clinic in Houston, Texas with 439 cases were followed-up to evaluate the prognosis of ALS. The overall Kaplan-Meier 3-year survival after diagnosis was similar, 0.287 for the incidence cohort and 0.313 for the referral cohort. However, the 5-year survival was much lower for the incidence cohort than the referral cohort (0.037 vs. 0.206). The large difference in 5-year survival was thought to be the results of a stronger unfavorable effect of the prognostic factors in the incidence cohort than in the referral cohort.^ Cohort-specific Weibull regression models were derived to evaluate the cohort-specific prognostic factors and survival probability with adjustment of certain prognostic factors.^ The major prognostic factors were: age at diagnosis, bulbar onset, black ethnicity, and positive family history of ALS in both cohorts. Female gender, simultaneous upper and lower extremities onset were specifically unfavorable factors in the incidence cohort. In the incidence cohort the prognosis was relatively favorable for cases with duration from onset to diagnosis longer than 4 months, however in the referral cohort the relatively favorable prognosis only occurred in cases with duration from onset to diagnosis 1 year or longer and was strongest in cases with duration 5 years and longer. Age at diagnosis modified the effect of bulbar onset in the incidence cohort but not in the referral cohort. The estimated survival with presence of an unfavorable prognostic factor identified in the incidence cohort was higher for the referral cohort than for the incidence cohort. Future studies are indicated to investigate the disease heterogeneity issue of ALS based on survival distribution of ALS. ^

The assumptions and effects of conservative procedures in low -dose risk assessment for setting safety standards

Conservative procedures in low-dose risk assessment are used to set safety standards for known or suspected carcinogens. However, the assumptions upon which the methods are based and the effects of these methods are not well understood.^ To minimize the number of false-negatives and to reduce the cost of bioassays, animals are given very high doses of potential carcinogens. Results must then be extrapolated to much smaller doses to set safety standards for risks such as one per million. There are a number of competing methods that add a conservative safety factor into these calculations.^ A method of quantifying the conservatism of these methods was described and tested on eight procedures used in setting low-dose safety standards. The results using these procedures were compared by computer simulation and by the use of data from a large scale animal study.^ The method consisted of determining a "true safe dose" (tsd) according to an assumed underlying model. If one assumed that Y = the probability of cancer = P(d), a known mathematical function of the dose, then by setting Y to some predetermined acceptable risk, one can solve for d, the model's "true safe dose".^ Simulations were generated, assuming a binomial distribution, for an artificial bioassay. The eight procedures were then used to determine a "virtual safe dose" (vsd) that estimates the tsd, assuming a risk of one per million. A ratio R = ((tsd-vsd)/vsd) was calculated for each "experiment" (simulation). The mean R of 500 simulations and the probability R $<$ 0 was used to measure the over and under conservatism of each procedure.^ The eight procedures included Weil's method, Hoel's method, the Mantel-Byran method, the improved Mantel-Byran, Gross's method, fitting a one-hit model, Crump's procedure, and applying Rai and Van Ryzin's method to a Weibull model.^ None of the procedures performed uniformly well for all types of dose-response curves. When the data were linear, the one-hit model, Hoel's method, or the Gross-Mantel method worked reasonably well. However, when the data were non-linear, these same methods were overly conservative. Crump's procedure and the Weibull model performed better in these situations. ^