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GEE estimation of a misspecified time-varying covariate: an example with the effect of alcoholism treatment on medical utilization.

The generalized estimation equation (GEE) method is widely used in longitudinal data analysis, particularly when the outcome variable is non-Gaussian distributed. Under mild regulatory conditions, the parameter estimates are consistent and their asymptotic variances are efficient. In an observational study focusing on alcoholism patients, we applied the GEE method to longitudinal count data from medical utilization records from a large national managed care organization. The health services research question was whether there was a change in medical utilization for patients after engaging in alcoholism treatment as compared to before treatment. Thus, the main effect of interest was a time-varying covariate indicating whether the patient had undergone treatment yet or not. GEE under five different working correlations was employed and mixed results regarding the significance of the treatment effect were found. Because of the large sample size, i.e. 8485 patients with an average of 46 repeated measurements per patient, differences across the estimates produced by the different working correlation structures was suspicious. It is shown that these differences are maybe caused by the fact that the time-varying covariate in the marginal mean model is misspecified. A simulation study is performed to demonstrate that misspecification of the time-varying covariate in the marginal mean structure can cause differences in GEE results across various choices of working correlation structure.

Adult↗

Investigating heterogeneity in an individual patient data meta-analysis of time to event outcomes.

Differences across studies in terms of design features and methodology, clinical procedures, and patient characteristics, are factors that can contribute to variability in the treatment effect between studies in a meta-analysis (statistical heterogeneity). Regression modelling can be used to examine relationships between treatment effect and covariates with the aim of explaining the variability in terms of clinical, methodological, or other factors. Such an investigation can be undertaken using aggregate data or individual patient data. An aggregate data approach can be problematic as sufficient data are rarely available and translating aggregate effects to individual patients can often be misleading. An individual patient data approach, although usually more resource demanding, allows a more thorough investigation of potential sources of heterogeneity and enables a fuller analysis of time to event outcomes in meta-analysis. Hierarchical Cox regression models are used to identify and explore the evidence for heterogeneity in meta-analysis and examine the relationship between covariates and censored failure time data in this context. Alternative formulations of the model are possible and illustrated using individual patient data from a meta-analysis of five randomized controlled trials which compare two drugs for the treatment of epilepsy. The models are further applied to simulated data examples in which the degree of heterogeneity and magnitude of treatment effect are varied. The behaviour of each model in each situation is explored and compared.

Anticonvulsants↗

Death after marital bereavement--is the risk increased?

Previous studies on the effect of marital bereavement on mortality have suggested various time periods during which the risk of mortality is increased. As many of the studies compared the widowed group with national mortality statistics for the married, there has been no opportunity to adjust for confounders which might themselves be responsible for this increased risk after bereavement. In this paper the various hypotheses proposed are reviewed and then modelled on a dataset of 344 elderly persons who were living with a spouse and who were part of a survey of a population of people aged 75 years and over. The 344 index-cases and their spouses were followed up for seven years and the times of death (for those who died) of the index-case and spouse were noted. The data were analysed by fitting a proportional hazards model to the subject's survival time after adjustment for other factors such as mental and physical health which had already been shown to be associated with mortality. The bereavement effects were fitted as time-dependent covariates. The best fitting model for females and males indicated an increased relative risk of mortality which lasted for approximately six months after bereavement. In the case of widows this relative risk was significantly increased, being 3.8 with 95 per cent confidence interval (1.4, 10.3) while for widowers the risk was 0.03 with 95 per cent confidence interval (0.00, 37.3).

Aged↗

Birth-weight-adjusted infant mortality in evaluations of perinatal care: towards a useful summary measure.

Since birth-weight-specific infant mortality rates are widely considered to be measures of the effects of perinatal medical care, birth-weight-adjusted and birth-weight-specific infant mortality rates have often been used in comparisons across hospitals and geographic areas. Wilcox and Russell have provided a model which leads to the conclusion that birth weight adjustment is biased against populations with heavier birth weights and that birth-weight-specific infant mortality rates can yield misleading results. Nevertheless, evaluators and health planners still need a summary measure of the infant mortality rate in which some sort of birth weight adjustment is used to generate an (appropriately) weighted mean of birth-weight-specific relative risks. We used the 1983-85 national linked files of live births and infant deaths to investigate two new methods that extend the Wilcox-Russell approach, 'mean adjustment' and 'Z-adjustment', to compare birth-weight-specific infant mortality rates among the white populations of the states. Colorado was used as the reference population in logistic regression analyses. Statistical interactions between state and birth weight on the conventional kilogram scale, the mean-adjusted scale, and the Z scale were examined. There were substantial interactions with birth weight on all three scales. In addition, when Colorado was used as the reference population, mean adjustment shifted the odds ratios downward to implausibly low values, especially at lower weights. The Z-adjustment method incorporating the Wilcox-Russell approach appears to be a useful alternative to birth weight adjustment. However, because birth-weight-specific mortality rates do not differ uniformly across all birth weight groups, multiple summary measures are needed.

Alabama↗

Differences in morbidity measures and risk factor identification using multiple data sources: the case of coronary heart disease.

The NHANES I Epidemiologic Followup Study contains several sources of information that can be used to define case status. Incidence rates and relative risks associated with selected, documented risk factors for heart disease were estimated using nine different case definitions. Despite wide variation in the estimates of incidence, the characteristics of the cases were remarkably similar as were the risks associated with heart disease incidence. The main difference occurred when cases were defined on the basis of death certificate information. Cases defined this way are more severe and models based on this definition result in relative risks of greater magnitude.

Aged↗

The price and purity of cocaine: the relationship to emergency room visits and death, and to drug use among arrestees.

This paper examines the relationship of the price and purity of cocaine to emergency room visits and deaths associated with cocaine use and to cocaine use among arrestees. A model is developed for the trend in cocaine prices at the retail level during the period January 1986 to December 1991. This trend is then compared to information on emergency room visits, medical examiner reports, and the percentage of arrestees testing positive for cocaine use over the same period. The principal conclusion is that there is a significant negative relationship between the estimated street price of cocaine and the level of related medical emergencies and deaths and the number of arrestees who test positive for cocaine.

Cocaine↗

Mercury contamination in fish from Santarém, Pará, brazil.

This paper reports on total mercury concentrations in edible tissue from 11 fish species caught in the Municipality of Santarém, Tapajós River Basin, Pará State, which are most consumed by the local population and investigates the influence of the distance between the goldmining areas and Santarém city on fish contamination by mercury. It was found that the carnivorous species reached an average of 222.1 ng.g(-1) (n=69), higher than the herbivorous species with 31.9 ng.g(-1) (n=30) and the omnivorous species with 68.7 ng.g(-1) (n=10). Significant relationships are found between fish weight and total mercury concentrations by using descriptive statistical and regression analysis for the two species, the carnivorous Pellona sp. (Sarda, r=0.73) and Pseudoplatystoma sp. (Surubim, r=0.63).

Animals↗

Quantitative structure-activity relationships by neural networks and inductive logic programming. II. The inhibition of dihydrofolate reductase by triazines.

One of the largest available data sets for developing a quantitative structure-activity relationship (QSAR)--the inhibition of dihydrofolate reductase (DHFR) by 2,4-diamino-6,6-dimethyl-5-phenyl-dihydrotriazine derivatives--has been used for a sixfold cross-validation trial of neural networks, inductive logic programming (ILP) and linear regression. No statistically significant difference was found between the predictive capabilities of the methods. However, the representation of molecules by attributes, which is integral to the ILP approach, provides understandable rules about drug-receptor interactions.

Animals↗

Control of remembered reaching sequences in monkey. I. Activity during movement in motor and premotor cortex.

Motor and premotor cortex firing patterns from 307 single neurons were recorded while monkeys made rapid sequences of three reaching movements to remembered target buttons arrayed in two-dimensional space. A primary goal was to study and compare directionally tuned responses for each of three movement periods during 12 movement sequences that uniformly sampled the directional space in front of the monkey. The majority of neurons showed maximal responses during movements in a preferred direction with smaller increases during movements close to the preferred direction. These responses showed a statistically significant regression fit to a cosine function for 72% of the neurons examined. Comparisons among tuning directions computed separately for the first, second, and third movement periods suggested the near constancy of preferred direction across a rapidly executed series of movements even though these movements began at different starting points in space. Although directionally tuned neurons were only broadly tuned for a specific direction of movement, the neuronal ensemble carried accurate directional information. A population vector computed by summing vector contributions from the entire population of tuned neurons predicted movement direction with a mean accuracy of 20 degrees. This population code made consistent predictions for each of the 36 movements that were studied using a single set of population parameters. Most of the remaining neurons (24%) that were not tuned during movement did show significant changes in activity during other aspects of task performance. Some nontuned neurons had nondirectional increases that were sustained during movement, while others showed identical phasic bursts during the three movement periods. These nontuned neurons may control stabilizations of the shoulder, trunk, and forearm during movement, or forearm movements during button pushing.

Animals↗

[Relationship between lead concentration in the air and blood lead levels of people living and working in the centre of a city (Frankfurt blood lead study). II. Correlations and conclusions (author's transl)].

The correlation analysis of the relationship between blood lead levels and lead-in-air concentrations measured in three winter periods showed a highly significant association despite a generally loose dependence of the variables. The regression equations clearly show that there would be a finite residual blood lead value even with completely lead-free air. In the case of the populations exposed to motor traffic in this study, this residual blood lead value is 80--90% of the initial value prior to the decrease in immission. The regression equations, statistically yield results which compare convincingly with ones obtained from model calculations based on studies of metabolism and respiratory physiology. The correlation between the observed changes in blood lead and the initial absolute values of blood lead concentration demonstrates with high statistical certainty that the higher the initial level, the greater was the observed change. This type of association also implies that there is a lower limit value of blood lead below which the decrease in blood lead changes to an increase despite reduction of lead-in-air.

Air Pollutants↗

An assessment of a urinary biomarker for total human environmental exposure to benzo[a]pyrene.

Urinary banzo[a]pyrene (BaP) metabolite levels were compared to human environmental exposure to BaP through inhalation and dietary ingestion to assess the predictive validity of the exposure biomarker. These measurements were made for 14 adult volunteers over 14 consecutive days, once during summer/fall, again during winter periods. Based on personal air monitoring, median potential inhalation doses of 11.0 and 2.3 ng/day were estimated for the winter and summer/fall studies, respectively. A median potential ingested dose of 176 ng/day, estimated from "duplicate plate" sampling, exceeded inhalation by 6- and 122-fold for the winter and summer/fall studies, respectively. "Total" urinary BaP metabolites were measured using a published "reverse metabolism" (BaP) method of analysis. Median rates of urinary BaP metabolite elimination for the winter and summer/fall studies were 121 and 129 ng/day, respectively. The changes in inhaled and ingested potential doses were regressed on the change in urinary metabolite elimination from week 1 to week 2 to test the predictive validity of the biomarker measurement. The regression was statistically significant (r = 0.620, p = 0.015, n = 25) when body weight was included and two extreme values were removed. Consistent with the exposure measurements showing diet as the dominant route of exposure, most of the variation in urinary metabolite elimination was explained by the ingested dose. It is concluded that the measurement of urinary BaP by "reverse metabolism" is qualitative and of marginal predictive validity as an exposure biomarker due to the method's low recoveries and the large unexplained variance.

Adult↗

Experimental subarachnoid hemorrhage: events related to anti-oxidant enzymatic systems and eicosanoid peroxide enhancement.

Experimental and clinical studies have emphasized the role of free radicals in the pathogenesis of vasospasm and neurological dysfunction after subarachnoid hemorrhage (SAH). Increases in both enzymatic (arachidonic acid cascade and eicosanoid peroxide production) and non-enzymatic (thiobarbituric acid reactive substances production) lipid peroxidation were found, pointing out the key role of arachidonic acid cascade in impairing membrane functionality in the post-hemorrhage brain. The aim of this work is to investigate whether a correlation exists between time-dependent modifications of eicosanoid peroxide production ("ex vivo" release of leukotriene C4 = LTC4) and antioxidant enzymatic systems in the brain after experimental subarachnoid hemorrhage in the rat. The release of the LTC4 is significantly enhanced at 1, 6 and 48 hours after SAH induction. Cu-Zn superoxide dismutase (SOD) activity is significantly reduced at 6 and 48 hours after SAH induction; Mn-SOD activity is significantly affected at 1, 6 and 48 hours after the hemorrhage. GSH-Px activity is significantly reduced only in the late phase (48 hours) after SAH. The linear regression of statistical analysis, performed to investigate any possible relationship among time-dependent modifications shows that the "ex vivo" release of LTC4 is significantly related to the decreasing trend of MnSOD activity (p < 0.001). The present results suggest that after SAH, a deficit in endogenous anti-oxidant defenses may play a role in making the brain more susceptible to lipid peroxidative events.

Animals↗

Martingales without tears.

This pedagogical paper presents a casual introduction to martingales, or fair gambling processes. Our objective is to describe the concept of a martingale and its application to common statistical tests used in the analysis of survival data, but without the mathematical rigor required for formal proofs. We use heuristic arguments to demonstrate that the logrank statistic evaluated over followup time is a fair gambling process, and introduce some mathematical notation and terminology along the way. We then employ the counting process approach to show that the logrank statistic computed over followup time can be expressed as the difference of two martingale transforms, and thus is a martingale. These ideas are first time introduced in the context of a discrete time process, and are then generalized to a continuous time process. With slight modifications, the same idea extends from the logrank to other weighted Mantel-Haenszel statistics computed over time.

Female↗

Evaluating selection out of health plans for Medicaid beneficiaries with substance abuse.

In the absence of adequate risk adjustment, capitation for enrollees creates incentives for health plans to enroll and retain good risks and to avoid bad risks. This article examines whether Maryland Medicaid beneficiaries with histories of substance abuse disenroll from health plans more frequently than those without such histories. The findings indicate that enrollees with a history of substance abuse were more likely to switch plans than other enrollees, regardless of whether they chose the health plan or were randomly assigned to the plan. These results suggest that current risk-adjustment systems may fail to offset selection incentives in modern capitated health plans.

Adult↗

A relation between the Akaike criterion and reliability of parameter estimates, with application to nonlinear autoregressive modelling of ictal EEG.

The Akaike minimum information criterion provides a means to determine the appropriate number of lags in a linear autoregressive model of a time series. We show that the Akaike criterion is closely related to the reliability estimates of successively determined parameters of a linear autoregressive (LAR) model. A similar criterion may be applied to determine whether the addition of a nonlinear term to an LAR model provides a statistically significant improvement in the description of the time series. As an example, we use this method to identify quadratic contributions to a nonlinear autoregressive characterization of a typical 3/s spike and wave seizure discharge.

Data Interpretation, Statistical↗

Bone mineral density measured by dual-energy X-ray absorptiometry in healthy Finnish women.

A cross-sectional study of 351 healthy Finnish women aged 20-76 years was done to establish reference values of bone mineral density (BMD) using dual-energy X-ray absorptiometry (DEXA). The effects of age and of several physical and lifestyle factors on BMD of the lumbar spine and proximal femur (femoral neck, trochanter, and Ward's triangle area) were investigated. Altogether 58 women were excluded from the final analysis due to significant spinal osteoarthritis or other diseases or drugs known to influence calcium or bone metabolism. The precision of the method was 0.9, 1.2, 2.7, and 2.4% in the lumbar, femoral neck, Ward's triangle and trochanter area, respectively. Lumbar BMD was increased by 30% (P less than 0.001) in 15 patients with osteoarthritis (21% of women 50 years or older), but it was apparently unaffected in 5 cases with aortic calcification. Except for the trochanter area, BMD diminished along with age, and this was significant after the menopause. The peak of mean BMD was observed at the age of 31-35 years in the spine and at the age of 20-25 years in the femoral neck and Ward's triangle. BMD was in a positive relationship to weight both in premenopausal and postmenopausal women and to the use of oral contraceptives in premenopausal women and to that of estrogen replacement therapy in postmenopausal women. Labors and pregnancies had a weak positive effect on BMD in premenopausal women. As compared with nonusers premenopausal women who had used alcohol showed a slightly decreased BMD of Ward's triangle. In postmenopausal women there was a positive correlation between alcohol intake and BMD.

Adult↗

Continued increase in the incidence of childhood Type 1 diabetes in a population-based Australian sample (1985-2002).

AIMS/HYPOTHESIS: Our aim was to determine the incidence of Type 1 diabetes in children who were 0 to 14 years of age in Western Australia from 1985 to 2002, and to analyse the trends in incidence rate over the same period. METHODS: Primary case ascertainment was from a prospective population-based diabetes register that was established in 1987, and secondary case ascertainment was from the Western Australia Hospital Morbidity Data System. Denominator data were obtained from the Australian Bureau of Statistics. Poisson regression was used to analyse the incidence rates by calendar year, sex and age at diagnosis. RESULTS: There was a total of 1144 cases (560 boys, 584 girls). Using the capture-recapture method, case ascertainment was estimated to be 99.8% complete. The mean age standardised incidence from 1985 to 2002 was 16.5 per 100,000 person years (95% CI 14.7-18.2), ranging from 11.3 per 100,000 in 1985 to 23.2 per 100,000 in 2002. The incidence increased on average by 3.1% (95% CI 1.9%-4.2%) a year over the period ( p<0.001). No significant difference was found between boys and girls. A significant increase in incidence was found in all age groups, with no disproportionate increase found in the 0 to 4-year-olds. CONCLUSIONS/INTERPRETATION: The incidence of childhood-onset Type 1 diabetes in Western Australia has increased significantly over the past 18 years and shows no signs of abating. In contrast to other studies, a higher rate of increase was not found in the youngest children.

Adolescent↗