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Statistical considerations regarding the use of ratios to adjust data.

OBJECTIVE: The use of ratios to adjust data (i.e. 'index' variables) is common in obesity and related research. The rationale for the use of ratios often seems to be the desire to control or eliminate the influence of the variable in the denominator. The purpose of this paper is to gain a greater appreciation of the statistical assumptions underlying ratios and their impact on data interpretation. RESULTS: We demonstrate the limitations of the indiscriminant use of ratios to adjust data. Specifically, we show that: (1) given linearity, a zero intercept between the numerator and denominator are necessary and sufficient conditions for a ratio to remove the confounding effects of the denominator; (2) seemingly minor departures from a zero intercept can have major consequences on the ratio's ability to control for the denominator; (3) the ratio of two normally distributed variables cannot be normally distributed, and this may violate the assumptions of subsequent parametric statistical analyses; (4) the use of ratios affects the error distribution of the data which may also violate the assumptions of subsequent parametric statistical analyses; (5) the use of ratios cannot easily take nonlinear effects between the numerator and denominator into account; (6) the use of ratios can introduce spurious correlations among the ratios and other variables; (7) the use of ratios can create interpretive difficulties. We also clarify that the mean of ratios is not necessarily equivalent to the ratio of the means of the numerator and denominator. Finally, we present and discuss formulae for the reliability of ratios and residuals. CONCLUSION: Because of the above issues, we question the indiscriminant use of ratios and advocate that investigators consider regression-based approaches as alternatives.

Body Constitution

Study duration for group sequential clinical trials with censored survival data adjusting for stratification.

The study duration in a clinical trial with censored survival data is the sum of the accrual duration, which determines the sample size in a traditional sense, and the follow-up duration, which more or less controls the number of events to be observed. We propose a design procedure for determining the study duration or for calculating the power in a group sequential clinical trial with censored survival data and possibly unequal patient allocation between treatments, adjusting for stratified randomization. The group sequential method is based on the use function approach. We describe a clinical trial recently activated by the Eastern Cooperative Oncology Group for an illustration of the proposed procedure.

Carcinoma, Non-Small-Cell Lung

A comparison of methods for organ-weight data adjustment in chicks.

An experiment was conducted with 168 Arbor Acre X Peterson unsexed, crossbred broiler chicks to compare methods of expressing organ-weight data and to assess changes in organ weights and physiological parameters as body weight (97 to 791 g) and age (5 to 26 days) increased. Actual wet weight of liver, heart, intestine, spleen, and pancreas and percent bone ash increased (P less than .01) as age and body weight increased. Tibia length-to-width ratio decreased (P less than .01) as age and body weight increased. Blood hemoglobin, hematocrit, and plasma protein were not affected (P greater than .1) by age or by body weight. Liver, heart, and intestinal weight decreased (P less than .01) and spleen weight increased (P less than .01) as body weight and age increased when these tissue weights were expressed as percent of body weight. Liver weight adjusted for body weight by covariance analysis, however, remained constant; adjusted heart and intestinal weights decreased (P less than .01), and adjusted spleen weights increased (P less than .01) with increasing age and body weight. The covariate, body weight, was not significant (P greater than .1) for pancreas weight, tibia length-to-width ratio, and percent bone ash. Except for spleen, adjustment by covariance analysis more effectively reduced variation due to body weight than did expression as percent of body weight.(ABSTRACT TRUNCATED AT 250 WORDS)

Aging

A suggestion for improving intelligibility in multivariate confounder adjustment using alcohol intake and birth weight as an example. A 'confounder score' approach in analyzing continuous data.

Adjustment for multiple confounding is usually done by applying some kind of regression model. This requires assumptions about the type of relationship between the exposure of interest and outcome. It has been suggested to use confounder scores within strata of which the relationship can be scrutinised without such assumptions. Adjusting continuous outcomes for confounding factors, like birth weight for gestational age and lung function measures for age, is sometimes done by using the ratio of the observed outcome to an outcome expected from a reference series external to the study, with a concomitant risk of introducing new confounding. In some cases, the ideas from both these approaches can, slightly modified, be successfully combined. By using an internal rather than an external reference series, i.e. a group within the data with constant exposure, expected values for outcome can be derived as the fitted values from some model, appropriate for the purpose, depicting outcome conditional on all the potential confounders that are registered and for which control is desired. The relationship between the exposure of interest and the outcome, now represented by the fractional departure for each individual from the value expected conditional on her/his confounder status, can be scrutinised without any assumptions about the form of this relationship but, contrary to the confounder score approach, on the basis of the entire data set. This method also provides a way of presenting the relationship of interest, adjusted for confounding, that is easier to understand than the traditional regression approach. The impact of alcohol intake during pregnancy on birth weight will be given as an example.

Alcohol Drinking

A note on the grouping of surveillance data when adjusting for reporting delays.

Analyses that adjust disease incidence data for reporting delays are often based on grouped data. A way of grouping data based on the quarter in which a case is reported, using all cases reported by a given cutoff date, is compared with the usual method of categorization based on a time-delay between diagnosis and reporting. The two methods of tabulation are illustrated using cases of the acquired immunodeficiency syndrome (AIDS) diagnosed and reported in Australia. A simple simulation study confirms that estimates of adjusted quarterly AIDS counts based on the quarter of report grouping are less variable than those based on the time-delay grouping.

Acquired Immunodeficiency Syndrome

Sex-specific causal factors and effects of common environment for symptoms of anxiety and depression in twins.

Two thousand five hundred seventy intact pairs and 724 single responders from Norwegian twins aged 18-25 years completed questionnaires with information about anxiety and depression and perceived cotwin closeness. The aim of the study was the univariate estimation of sex-specific genetic and environmental effects on an index tapping symptoms of anxiety and depression. An index of social closeness between cotwins was significantly related to the cotwin correlation for anxiety/depression scores. MZ pairs were reported to be closer than DZ pairs, and like-sexed DZ pairs were closer than unlike-sexed pairs. The symptom data were adjusted for this apparent violation of the "equal-environment" assumption in twin studies, but the adjustment did not dramatically affect the parameter estimates of genetic and environmental effects on anxiety/depression. A model specifying male (aM) and female (aF) genetic additive effects, shared environment for males (cM), and individual environmental effects (eM and eF) fitted the adjusted data very well. An alternative model, specifying aM = aF, cM = cF, and eM = eF, and no correlation between those environmental factors shared by brothers and those shared by sisters, fitted equally well. Estimated proportions of total variance from the first model were aM2 = .30, aF2 = .52, and cM2 = .21. The estimates from the second model were aM2 = aF2 = .43 and cM2 = cF2 = .11.

Adolescent

Family functions and children's postdivorce adjustment.

Data on school-age children of divorced parents were examined to determine which dimensions of family dynamics were most associated with the children's socioemotional adjustment. Those factors found to be most significant were family roles, behavior control, and affective involvement, as well as children's reaction to and insight into the divorce, and conflict in the home after the divorce. Implications for parent education and early intervention are discussed.

Adaptation, Psychological

Meta-analysis of failure-time data with adjustment for covariates.

The objective of this study was to present and illustrate a technique for combining failure-time data from various sources, adjusting for differences in case-mix among studies. Based on the proportional-hazards model and the actuarial life-table approach, the method used assumes that the variation across studies is in part due to heterogeneity of the case-mix and adjusts for the case-mix before pooling results. As an example, the technique is applied to life-table data from six selected papers reporting patency of affected arteries following femoropopliteal angioplasty. Published 4- and 5-year patency results ranged from 25% to 58%, with a pooled five-year cumulative patency rate (without adjustment for case-mix) of 45% (+/- 2%). The populations in these studies, however, differed markedly in the prevalence of factors with prognostic value: type of lesion and distal runoff vessels. After adjustment for these differences in case-mix, the pooled five-year patency rates ranged from 60% (+/- 2%) for patients with stenotic lesions and good runoff to 24% (+/- 9%) for those with occlusion and poor runoff. The authors conclude that pooling studies without considering the effect of case-mix yields an average result with inappropriately narrow confidence intervals that does not reflect the variability across subgroups. The presented technique provides a method for combining failure-time data, adjusting for case-mix.

Analysis of Variance

Socioeconomic factors and cancer incidence among blacks and whites.

Findings from previous studies suggest that differences in socioeconomic status may be responsible for some, if not all, of the elevated incidence of cancer among blacks as compared with whites. Using incidence data from the National Cancer Institute's Surveillance, Epidemiology, and End Results (SEER) Program, we tested this hypothesis by correlating black and white cancer incidence rates in three US metropolitan areas between 1978 and 1982 with data from the 1980 census on socioeconomic status within individual census tracts. The study analyzed data on the incidence of cancer at all sites combined (greater than 100 cancer sites) and at seven major sites separately. As in other studies, income and educational levels served as surrogates for socioeconomic status. The present study also used census-tract data on population density as a surrogate factor. Each of these measures of socioeconomic status was analyzed independently. Before correlation with census-tract data, age-adjusted data on cancer incidence showed statistically significant elevated risks among blacks for cancer at all sites combined and at four of the seven separate sites; whites showed an elevated risk for cancer at two sites. Cancer at only one site, the colon, showed no significant association with race. When age-adjusted incidence data were correlated with socioeconomic status, the comparative black-white risks changed: Whites showed an elevated risk of cancer at all sites combined and at three of the seven separate sites; blacks maintained their elevated risk at three sites. These findings suggest that the disproportionate distribution of blacks at lower socioeconomic levels accounts for much of the excess cancer burden among blacks. They also suggest that for both blacks and whites unidentified racial factors, which may be either cultural or genetic and which are not closely linked to socioeconomic status, may play a role in the incidence of some cancers.

Black or African American

Estimating age incidence from survey data with adjustments for recall errors.

In this paper we propose a method and discuss the type of data required to estimate age incidence rates from population survey data. While surveys are typically designed to estimate the prevalence of a disease or medical condition, they can also be used to estimate incidence rates. A limitation of survey data, however, is that recall is prone to errors. Three types of errors are common: telescopic, false negative, and false positive reports. Telescopic reports are thought to be the most common. We propose a method to adjust for recall errors by modeling the reported age of onset (ONST) and the time interval since the reported first occurrence of the medical condition (LAG). A number of models were examined using migraine headache data from over 10,000 subjects in Washington County, Maryland. Population surveys should be considered as a relatively inexpensive means for estimating the age incidence of medical conditions, especially for symptom based problems like back pain, asthma, mental illness, and serious headache. We recommend that data be collected on variables which can be used as surrogates for the different types of recall errors. Specifically, the age at interview, the date when the condition was cured or in remission, the severity of the condition, and possibly a specific inquiry as to how certain the respondent is in reporting the date of medical events, should be considered for this purpose.

Adolescent

Surviving hematological malignancies: stress responses and predicting psychological adjustment.

Within the adolescent survivor sample, the psychosocial response of having been diagnosed and successfully treated for cancer is not universal as evidenced by the variability in psychosocial adjustment. Data from the MHI suggests that adolescent cancer survivors do experience more global psychological distress than a comparison group of healthy adolescents. In addition, the majority of these patients reported persistent, intrusive thoughts about their illness and its treatment. Conversely, the adolescent cancer survivors did not differ from a normative sample on social competence, manifestation of problems behaviors, or school achievement. Thus, our data suggest that adjustment in this population is multi-dimensional with variability. While they are functioning quite adequately at school and in social situation, they continue to experience heightened and persistent distress of both a global and illness-specific quality. A number of factors that are conducive to psychosocial intervention appear to be related to adjustment. Family communication and family cohesion were significantly related to the mental health of the adolescent survivors, suggesting a need to further explore the family context of adolescent adjustment. The present work also represents the first attempt to directly examine the psychosocial functioning of young adult, acute leukemia survivors. When compared with normative samples of nonpatients, these survivors (taken as a whole group), reported heightened levels on several indicators of psychological distress. While not entirely consistent across different psychological measures, these young people were generally one standard deviation above the mean for psychological distress. But when compared to normative samples of psychiatric outpatients, our survivors reported significantly less psychological distress. For instance, leukemia survivors reported less intrusive and avoidant cognitions associated with the stressor of being diagnosed and treated for cancer than those associated with patients experiencing traumatic stress disorders. In aggregate, these findings again suggest that the psychosocial adjustment of leukemia survivors is quite variable. Finally, while group comparisons shed light on the psychosocial functioning of leukemia survivors, in general, wide variability in psychosocial adjustment may mask identification of a cohort of cancer survivors most at-risk for psychosocial dysfunction. Sociodemographic, disease/treatment and psychological distress variables only partially explain this variability. The findings from our data suggest several clinical recommendations. First, the prevalence of persistent, psychiatric comorbidity is quite low among long-term survivors of hematologic malignancies survivors. Second, if survivors do experience some psychological distress, usually, it is of non-psychopathological proportions.(ABSTRACT TRUNCATED AT 400 WORDS)

Adaptation, Psychological

Statistical approaches to experimental design and data analysis of in vivo studies.

The objective of any experiment is to obtain an unbiased and precise estimate of a treatment effect in an efficient manner. Statistical aspects of the design, conduct, and analysis of the experiment play a major role in determining whether this goal is met. We highlight some of the more important statistical issues that pertain to in vivo studies. Particular emphasis is placed on the role of randomization, the number of animals, the utilization of repeated measures data, adjustments for missing data, and dealing with multiple causes of death or treatment failure. The discussion is not intended to be a comprehensive guide to all the statistical issues that can occur in animal experiments. Rather, the objective is to acquaint researchers with components of the experiment that will require careful statistical thought.

Animals

Use of risk-adjusted outcome data for quality improvement by public hospitals.

In 1993 the California Office of Statewide Health Planning and Development (OSHPD) began public release of risk-adjusted monitoring of outcomes (RAMO) under the California Hospital Outcomes Project. We studied how 17 acute are public hospitals in California used these RAMO data for quality improvement purposes following their initial distribution, first by analyzing the outcome data for San Francisco General Hospital Medical Center as recommended by OSHPD and, second, by querying the departments at the other 16 public hospitals to determine how their own analyses compared. We found that the hospitals generally did minimal analyses of the OSHPD RAMO data and considered the data of little value to them. Only 3 hospitals initiated quality improvement activities based on their data review. The major reasons given by the hospitals for not using the RAMO data were that their outcomes were adequate, as verified by a comparison of their observed outcomes and those expected after risk-adjustment; that the hospitals had too few patients in the diagnostic categories; that they had too few resources; and that they were not concerned with the data's public release. Other possible explanations were that awareness of the California Hospital Outcomes Project was not widespread at the time of the study, that the RAMO data were not distributed in a way that encouraged their use, and that public hospitals were not inclined to use the outcome data because the project was imposed on them. Whatever the explanation, our study suggests that the California Hospital Outcomes Project has had little effect on quality improvement in public hospitals.

California

Coronary heart disease mortality and alcohol consumption in Framingham.

The relationship between ethanol consumption and coronary heart disease was examined in the original Framingham Heart Study cohort (1948) with a 24-year follow-up from exam 2 (2,106 males and 2,639 females). Ethanol consumption shows a strong U-shaped relationship with coronary heart disease mortality for male nonsmokers and heavy smokers both in the raw age-adjusted data and in the Cox regression analyses, where ethanol consumption is modeled quadratically. No ethanol effects were found for female nonsmokers. The age-adjusted data suggest a U-shape curve for female smokers, although this was not confirmed by the Cox analysis. Separate analyses relating alcohol consumption to mortality from all causes showed similar effects except that the reduction in mortality for males was much less. For male coronary heart disease mortality, ethanol consumption was subdivided into beer, wine, and spirits consumption. These beverages were also modeled quadratically in the Cox analyses, and all showed strong U-shaped curves for both nonsmokers and heavy smokers. In nonsmokers, beer and wine show greater reductions in coronary heart disease mortality than spirits.

Adult

Smoothed nonparametric back-projection of AIDS incidence data with adjustment for therapy.

Back-projection is a major tool for assessing the extent of the HIV epidemic. Its application relies on a model for the incubation period of AIDS into which the administration and effect of therapy has been incorporated. We propose a compartmental model with proportional transition rates to describe variation and changes in the duration of the incubation period. The model is easily related to available data and offers fast computation. Its detailed and direct reflection of the administration and effect of therapy makes it relatively easy to ensure that therapy has been accommodated to an appropriate extent. The effect of therapy on back-projection estimates of the HIV epidemic curve is demonstrated with an application to Australian AIDS incidence data.

Acquired Immunodeficiency Syndrome