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Partial imputation approach to analysis of repeated measurements with dependent drop-outs.

In clinical trials repeated measurements of a response variable are usually taken at prespecified time-points to compare the treatment effects. However, the comparison of treatment effects is often complicated by missing data caused by the withdrawal of some patients before the end of the study (that is, drop-outs). When the drop-out process depends on the response variable of interest, ignoring missing data may lead to biased comparison of the treatment effect. In this paper, conditions for ignoring the dependent missingness are investigated and a new approach using the usual testing procedure based on data with partial carrying-forward imputation is proposed. The proposed approach is conceptually and practically simple, and is motivated by making incremental improvement on the familiar 'all available data' (AAD) approach and the 'last value carrying forward' (LVCF) approach, which are commonly used in data analysis with drop-outs by practitioners. It is also compared favourably to the mixed-effect model approach with dependent drop-outs. Simulations and real data are used to evaluate and illustrate statistical properties of the proposed approach. The principle of the proposed approach can also be extended to using other imputation methods such as the multiple imputation.

Analysis of Variance↗

Design and analysis of trials with rare outcomes: examples from trials in herpes transmission and influenza prophylaxis.

For trials with rare outcomes, the number of events to be observed drives the power of the study rather than the proportions of subjects with the event and this is an important consideration when determining sample size. The stratified version of Fisher's exact test was described by Cox as long ago as 1966, but it is only recently that computing power has allowed this to be performed routinely. The issue of stratified analysis can also be addressed through permutation tests and their implementation for multicentre trials where randomisation is stratified by site has potential value. Where the time to event is available, analysis using a proportional hazards model has a potentially valuable role but estimates of differences in proportions are often required particularly for non-inferiority studies and typical software employed for these analyses uses an asymptotic approximation rather than an exact analysis. It is important to assess the impact of missing data on such trials. This can be approached through examination of the pattern of missing data and the covariates predicting discontinuation as well as through sensitivity analysis. Sensitivity analyses need to be done carefully using realistic alternative assumptions and an appealing approach is to impute events for subjects with missing data using the observed placebo rate. Issues of design and analysis for trials with rare outcomes are discussed in the context of two examples-one from a trial designed to investigate transmission of herpes and one that studied prophylaxis of influenza.

Chemoprevention↗

Prediction of survival and opportunistic infections in HIV-infected patients: a comparison of imputation methods of incomplete CD4 counts.

In evaluating the risk of mortality or development of opportunistic infections in HIV-infected patients, the number of CD4 lymphocyte cells per cubic millimetre of blood is widely recognized as one of the best available predictors of such future events. However, its usefulness is limited by the incompleteness and variability of such CD4 measurements during follow-up. Because of these limitations, analysis of such data requires the missing measurements to be 'filled in' or the patients without them to be excluded. We consider multiple imputation of CD4 values based partly on information from other health status measures such as haemoglobin, as well as on the event status of interest. These alternative health status measures are also considered as possible independent predictors of survival endpoints. Our work is motivated by a cohort of 1530 patients enrolled in two AIDS clinical trials. We compare our approach to other strategies such as basing evaluation of risk on baseline CD4, the last measured CD4 before an event, or a time-dependent covariate based on carrying the last CD4 value forward; we conclude with a strong recommendation for multiple imputation.

AIDS-Related Opportunistic Infections↗

Assessing research outcomes by postal questionnaire with telephone follow-up. TOTAL Study Group. Trial of Occupational Therapy and Leisure.

BACKGROUND: Face-to-face assessment of research outcomes is expensive and may introduce bias. Postal questionnaires offer a cheaper alternative which avoids observer bias, but non-response and incomplete response reduce the effective sample size and may be equally serious sources of bias. This study examines the extent and potential effects of missing data in the postal collection of outcomes for a large rehabilitation trial. METHODS: Questionnaires containing a number of established scales were posted to participants in a trial of occupational therapy after stroke. Response was maximized by telephone and postal reminders, and incomplete questionnaires were followed up by telephone. Scale scores obtained by imputing values to questionnaire items missing on return were compared with those achieved by telephone follow-up. FINDINGS: Response to the initial posting was 60%, rising to 85% after reminders. Participants receiving the experimental treatment were more likely to respond without a reminder. There were no significant differences on any known factors between eventual responders and non-responders. Of the questionnaires, 43% were incomplete on return: partial responders were significantly different to complete responders on baseline disability and home circumstances. Of the incomplete questionnaires, 71% were resolved by telephone follow-up. In these, the scale scores achieved by telephone were generally higher than those derived by conventional imputation. CONCLUSION: Postal outcome assessment achieved a good response rate, but considerable effort was needed to minimize non-response and incomplete response, both of which could have been serious sources of bias.

Bias↗

[Meta-analysis of the Italian studies on short-term effects of air pollution--MISA 1996-2002].

INTRODUCTION: the Italian Meta-analysis of short-term effects of air pollution for the period 1996-2002 (MISA-2) is a planned study on 15 Italian cities, among the larger country towns summing up 9 millions and one hundred thousand inhabitants at 2001 census. HEALTH OUTCOMES DATA: mortality for all natural causes (362254 deaths), for respiratory causes (22317) and cardiovascular causes (146830), and hospital admissions for acute conditions, respiratory (278028 admissions), cardiac (455540) and cerebrovascular (60960), have been considered. Mortality data came from Regional or Local Health Unit Registries, while hospital admissions data have been selected from Regional or Hospital Archives (exclusion percentages range for all admissions between 45% and 82%). For each participating city daily series averaged about 4.3 years, with a minimum of three consecutive years. AIR POLLUTANTS DATA: daily pollutants concentration series (SO2, NO2, CO, PM10, O3) came from air quality monitoring networks of Regional Environmental Protection Agencies, of Environmental Offices of Provinces or Municipalities. Monitors' selection has been done by a working group composed by representatives of monitoring network Agencies. The selection criteria are the representativeness of general population exposure for each specific pollutant, avoiding as possible monitors close to high traffic roads; and the number, quality and location of monitors, selecting around 3-4 monitors with continuous data flow in the period (at least 75% of valid hourly data). The final series has been created averaging over monitors and imputing missing values under proportionality assumptions. Median of Pearson correlation coefficients between pairs of monitors of the each city was 0.62, interquartile range 0.42-0.77. STATISTICAL METHODS: A generalized linear model on daily counts of health events has been fitted for each city. Linear pollutant effect has been specified and bi-pollutant models have been fitted for PM10+NO2 and PMO+O3. Temperature has been modelled parametrically using a change point at 21 degrees C and lagged effects. Humidity, day of the week, national holidays and influenza epidemics (using data from the National Surveillance Programs from 1999) are the other considered confounders. An age-specific natural cubic spline on season has been specified with 5 degree of freedom (on average) per year for mortality and 7 degree of freedom per year for hospital admission data. The base model is age-stratified (0-64, 65-74, 75+ years). Gender, age, season specific models have been fitted, too. Five sensitivity analyses have been done, varying the degree of freedom for the seasonality spline and specifying non parametric functions on temperature. Constrained distributed lag models have been fitted on mortality data to study potential harvesting effects. City-specific results have been meta-analyzed by random effects hierarchical Bayesian model. Four different models have been fitted in the sensitivity analyses, assuming different priors on heterogeneity variance and outlier-resistant prior on city-specific effects. Bayesian meta-regressions have been fitted on base model, bi-pollutant and season-specific city-specific results. Attributable deaths have been estimated by Monte Carlo methods using effect, pollutant, baseline rate distributions. Fourteen different scenarios have been considered for PM10 and ten for NO2 and CO, using meta-analitic and posterior city-specific effect estimates RESULTS: Pollutants effects are reported as percent increase on mortality or hospital admissions for an increase of 10 microg/m3 of SO2, NO2 and PM10, and 1 mg/m3 of CO. We found an increase on mortality for all natural causes associated to increase of air pollutants concentration (for NO2 0.6% 95%CrI 0.3,0.9; CO 1.2% 0.6,1.7; PM10 0.31% -0.2,0.7). Similar findings were found for cardiorespiratory mortality and hospital admissions for respiratory and cardiac diseases. We found no difference by gender. There was a weak evidence of greater effect size in extreme age groups (0-24 months and over 85 years where we found a percent increase in mortality for all natural causes for PM10 of 0.39% CrI95% 0.0,0.8). There was a strong evidence for each pollutant of greater effects in the warm season (1st May-30th September) on mortality and hospital admissions (we found a percent increase in mortality for all natural causes for PM10 in the warm season of 1.95% CrI95% 0.6,3.3). The associations between pollutants concentration and health events were present at different time lags, depending on outcome and exposure. For mortality, the excess risk peaked within few days from the exposure increase (two days for PM10, up to four days for NO2 and CO). Mortality displacement was minor and ended within two weeks. Cumulative effects at fifteen days showed higher risks for respiratory diseases (PM10 1.65% CI95% 0.3,3.0). The results of meta-regressions showed associations between PM10 effects on mortality and hospital admissions, and mortality for all causes (SMR) and PM10/NO2 ratio. The effect modification of temperature was very consistent, and also using bi-pollutant models. Such effect modification was greater during the cold season. We found and overall impact on mortality for all natural causes in the period 1996-2002 between 1.4% and 4.1% of all deaths for gaseous pollutants (NO2 and CO). The estimates were more imprecise for PM10, due to the variability among cities of the effect estimates (0.1%; 3.3%). The limits stated in the European Union directives for 2010 would have been saved about 900 deaths (1.4%) for PM10 or 1400 deaths for NO2 (1.7%) among all the MISA cities, applying posterior city-specific effect estimates.

Adolescent↗

Growth and fatness at three to six years of age of children born small- or large-for-gestational age.

OBJECTIVE: To compare young children 3 to 6 years of age who were born small-for-gestational age (SGA; <10th percentile for gestational age) or large-for-gestational age (LGA; >/=90th percentile) with those who were born appropriate-for-gestational age (10th-89th percentile) to determine whether there are differences in growth and fatness in early childhood associated with birth weight status. DESIGN AND METHODS: National sample of 3192 US-born non-Hispanic white, non-Hispanic black, and Mexican-American children 3 to 6 years of age (36-83 months) examined in the third National Health and Nutrition Examination Survey and for whom birth certificates were obtained. On the birth certificates, length of gestation from the mother's last menstrual period was examined for completeness, validity, and whether the pattern of missing (n = 141) and invalid data (n = 147) on gestation was random. Gestation was considered invalid when >44 weeks, or when at gestations of </=35 weeks, birth weight was inconsistent with gestation. To reclaim cases with missing or invalid data on gestation for analysis, a multiple imputation (MI) procedure was used. MI procedures are recommended when, as in this case, a critical covariate (length of gestation) is not missing at random, and complete-subject analysis may be biased. Using the results of the MI procedure, children were categorized, and growth outcome was assessed by birth weight-for-gestational age status. The growth outcomes considered in these analyses were body weight (kg), height (cm), head circumference (cm), mid-upper arm circumference (MUAC; cm), and triceps and subscapular skinfold thicknesses (mm). The anthropometric outcomes first were transformed to approximate normal distributions and converted into z scores (standard deviation units [SDU]) to scale the data for comparison across ages. Outcomes at each age then were estimated using regression procedures. SUDAAN software that adjusts variance estimates to account for the sample design was used in analysis for prevalence estimates and to calculate regression coefficients (in SDU). RESULTS: Over these ages, children born SGA remained significantly shorter and weighed less (-0.70 to -0.60 SDU). Children born LGA remained taller and weighed more (0.40-0.60 SDU). For weight and height among LGA children, there was a divergence from the mean with age compared with those born appropriate-for-gestational age (10th-89th percentile). Head circumference and MUAC followed these same patterns. The coefficients for MUAC show values for SGA children fairly consistently at about -0.50 SDU and children born LGA show increasing MUAC from +0.40 to +0.50 SDU from 36 to 83 months of age. As with weight, there is a trend toward increased MUAC coefficients with age. Measures of fatness (triceps and subscapular skinfolds), which are more prone to environmental influences, showed less association with birth weight-for-gestational age status. Only a single age group, the oldest (6 years of age) group showed a significant deficit in fatness for children born SGA. For children born LGA, there was an increase in fatness at both the triceps and subscapular sites after 3 years of age. CONCLUSION: These findings on a national sample of US-born non-Hispanic white, non-Hispanic black, and Mexican-American children show that children born SGA remain significantly shorter and lighter throughout early childhood and do not seem to catch up from 36 to 83 months of age. LGA infants remain longer and heavier through 83 months of age, but unlike children born SGA, children born LGA may be prone to an increasing accumulation of fat in early childhood. Thus, early childhood may be a particularly sensitive period in which there is increase in variation in levels of fatness associated with size at birth. These findings have implications for the evaluation of the growth of young children. The results indicate that intrauterine growth is associated with size in early childhood. (ABSTR

Adipose Tissue↗

Probability imputation revisited for prognostic factor studies.

The analysis of prognostic factor studies by Cox or logistic regression models is often impeded by missing covariate values. In 1990 Schemper and Smith recommended a conditional probability imputation technique (PIT) for the analysis of treatment studies which can be easily applied using standard software and which has been demonstrated to outperform the complete case and omission of covariates strategies. Recent research, however, showed that PIT cannot universally be recommended and it was concluded that model-based methods should be preferred. We agree with these conclusions but also think that there is enough empirical evidence to judge the performance of PIT to be satisfactory in typical prognostic factor studies. Furthermore, comparisons of PIT with multiple imputation in the same context did not indicate an advantage of the latter more involved technique. By means of an analysis of a prostate cancer data set various aspects of application of PIT are discussed, in particular that PIT permits direct comparability of marginal and partial effects analyses. We conclude that PIT continues to be an appropriate and attractive choice for analyses of prognostic factor studies.

Data Interpretation, Statistical↗

Calcitonin for metastatic bone pain.

BACKGROUND: Pain is the most frequent symptom experienced by cancer patients, its intensity dependent on the site of the tumour. Tumours that compromise bone or nervous structures due to the bone destruction process are the most painful. There are several treatments to deal with pain (and other symptoms) caused by bone metastasis. The hormone, calcitonin, has the potential to relieve pain, and also retain bone density, thus reducing the risk of fractures. OBJECTIVES: To assess the effectiveness of calcitonin in controlling metastatic bone pain and reducing bone complications (hypercalcemia, fractures and nervous compression) in patients with bone metastases. SEARCH STRATEGY: Electronic searches were performed in MEDLINE (1966-2001), EMBASE (1974-2001), the Cochrane Central Register of Controlled Trials (Issue 2, 2001), specialised registers of the Cochrane Cancer Network and of the Cochrane Pain, Palliative and Supportive Care Group. Registers of clinical trials in progress were also searched. SELECTION CRITERIA: Studies were included if they were randomised, double-blind clinical trials of patients with metastatic bone pain, treated with calcitonin, where the major outcome measure was pain, assessed at four weeks or longer. DATA COLLECTION AND ANALYSIS: Study selection and data extraction were performed by two independent reviewers. Only two studies (90 patients) were eligible for inclusion in the review and therefore meta-analysis of the data was not possible. Intention-to-treat analysis was performed by imputing all missing values as adverse outcomes. MAIN RESULTS: Of the two small studies included in the review, one study showed a non-significant effect of calcitonin in the number of patients with total pain reduction (RR 2.50; CI 95%, 0.55 to 11.41). The second study provided no evidence that calcitonin reduced analgesia consumption (RR 1.05; CI 95%, 0.90 to 1.21) in patients with painful bone metastases. There was no evidence that calcitonin was effective in controlling complications due to bone metastases; for improving quality of life; or patients' survival. Although not statistically significant, a greater number of adverse effects were observed in the groups given calcitonin in the two included studies (RR 3.35, CI 95%, 0.72 to 15.66). REVIEWER'S CONCLUSIONS: The limited evidence currently available for systematic review does not support the use of calcitonin to control pain from bone metastases. Until new studies provide additional information on this treatment, other therapeutic approaches should be considered.

Bone Neoplasms↗

Calcitonin for metastatic bone pain.

BACKGROUND: Pain is the most frequent symptom experienced by cancer patients, its intensity dependent on the site of the tumour. Tumours that compromise bone or nervous structures due to the bone destruction process are the most painful. There are several treatments to deal with pain (and other symptoms) caused by bone metastases. The hormone, calcitonin, has the potential to relieve pain, and also retain bone density, thus reducing the risk of fractures. This review is an update of a previously published review in The Cochrane Library (Issue 3, 2003) on this topic. OBJECTIVES: To assess the effectiveness of calcitonin in controlling metastatic bone pain and reducing bone complications (hypercalcemia, fractures and nerve compression) in patients with bone metastases. SEARCH STRATEGY: Electronic searches were performed in MEDLINE (1966 to 2005), EMBASE (1974 to 2005), the Cochrane Central Register of Controlled Trials (Issue 2, 2005), specialised registers of the Cochrane Cancer Network and of the Cochrane Pain, Palliative and Supportive Care Group. Registers of clinical trials in progress were also searched. SELECTION CRITERIA: Studies were included if they were randomised, double-blind clinical trials of patients with metastatic bone pain, treated with calcitonin, where the major outcome measure was pain, assessed at four weeks or longer. DATA COLLECTION AND ANALYSIS: Study selection and data extraction were performed by two independent review authors. Only two studies (90 patients) were eligible for inclusion in the review and therefore meta-analysis of the data was not possible. Intention-to-treat analysis was performed by imputing all missing values as adverse outcomes. MAIN RESULTS: Of the two small studies included in the review, one study showed a non-significant effect of calcitonin in the number of patients with total pain reduction (RR 2.50; CI 95%, 0.55 to 11.41). The second study provided no evidence that calcitonin reduced analgesia consumption (RR 1.05; CI 95%, 0.90 to 1.21) in patients with painful bone metastases. There was no evidence that calcitonin was effective in controlling complications due to bone metastases; for improving quality of life; or patients' survival. Although not statistically significant, a greater number of adverse effects were observed in the groups given calcitonin in the two included studies (RR 3.35, CI 95%, 0.72 to 15.66). AUTHORS' CONCLUSIONS: The limited evidence currently available does not support the use of calcitonin to control pain from bone metastases. Since the last version of this review, none of the new relevant studies have provided additional information on this treatment, in contrast to other therapeutic approaches that should be considered.

Bone Neoplasms↗

Intention-to-treat: methods for dealing with missing values in clinical trials of progressively deteriorating diseases.

Since it came up in the 1960s, the principle of intention-to-treat (ITT) has become widely accepted for the analysis of controlled clinical trials. In this context the question of how to perform such an analysis in the presence of missing information about the main endpoint is of major importance. Uncritical use of several ad hoc strategies for dealing with missing values is common in the practice of clinical trials. On the other hand, little is known about possible dangers and problems of applying these strategies. We therefore performed a detailed investigation of different methods for dealing with missing values in order to develop recommendations for their practical use. A simulation study was performed investigating possible consequences on type I error and power of applying different methods for dealing with missing values. The simulations were based on a clinical trial of osteoporosis, a progressively deteriorating disease. The strategies examined can be roughly classified into numerical imputation strategies (last observation carried forward, mean and regression based methods) and non-parametric strategies (rank and dichotomization based methods). Different drop-out mechanisms and different types of progression of disease are considered. The type I error increases drastically for the different strategies, especially if the courses of disease vary between treatment groups. The loss in power can be substantial. There is no strategy which is adequate for all different combinations of drop-out mechanisms, drop-out rates and courses of disease over time. For drop-out rates less than 20 per cent and similar courses of disease in the treatment groups, missing values might be replaced by the mean of the other group, or counted as treatment failures after dichotomization of the endpoint. For larger drop-out rates or less similar courses of disease, no adequate recommendations can be given. Because of the drastic consequences of increasing drop-out rates, it has to be a primary goal in clinical trials to keep missing values to a minimum. Unobserved information cannot be reliably regained by any methodological resources. As there are no strategies for universal use, reasons for the choice of a certain method have to be provided when designing and analysing clinical trials.

Computer Simulation↗

Prospective prediction in the presence of missing data.

A variety of methods and algorithms are available for estimating parameters in the class of a generalized linear model in the presence of missing values. However, there is little information on how this already built model can be used for prediction in new observations with missing data in the covariates. Dropping the observations with missing values is a widespread practice with serious statistical and non-statistical implications. One solution is to fit separate regression models, or submodels, to each pattern of missing covariates. In practice, for any iterative regression method, this approach is computationally intensive. We propose a simple methodology to predict outcomes for individuals with incomplete information based on the estimated coefficients and covariance from the already built model. This method does not require revisiting the original data set used to build the original model and works by generating a first-order approximation of any submodel coefficient estimates. This is achieved by using the SWEEP operator on an augmented covariance matrix obtained from the original model. We refer to this approach as the one-step sweep (OSS) method. The methodology is demonstrated using data from the Department of Veterans Affairs Continuous Improvement in Cardiac Surgery Program (CICSP). These data contain 30 day mortality, the outcome of interest, and risk information for over 14,000 patients who underwent coronary artery bypass grafting (CABG) surgery over a four-year period. Using complete data from the first 3.5 years of this study period, a logistic regression model was built. This model was then used to predict mortality for patients undergoing CABG in the most recent 6-months. In order to evaluate the performance of the OSS method we randomly generated observations with missing covariates in the 6-month prediction database. We use this simulation to demonstrate that the computationally efficient OSS substantially reduces the error in risk-adjusted mortality created when cases with incomplete information are eliminated. Lastly, we derive the relationship between the OSS method and data imputation.

Computer Simulation↗

Handling missing data in patient-level cost-effectiveness analysis alongside randomised clinical trials.

BACKGROUND: Missing data are potentially an extensive problem in cost-effectiveness analyses conducted alongside randomised clinical trials, where prospective collection of both resource use and health outcome information is required. There are several possible reasons for the presence of incomplete records, and the validity of the analysis in the presence of data with missing values is dependent upon the mechanism generating the missing data phenomenon. In the past, the most commonly used methods for analysing datasets with incomplete observations were relatively ad hoc (e.g. case deletion, mean imputation) and suffered from potential limitations. Recently, several alternative and more sophisticated approaches (e.g. multiple imputation) have been proposed that attempt to correct the flaws of the simple imputation methods. OBJECTIVES: The objectives are to provide a concise and accessible description of the quantitative methods most commonly used in trial-based cost-effectiveness analysis for handling missing data, and also to demonstrate the potential impact of these alternative approaches on the cost-effectiveness results reported in two case studies. METHODS: Data from two recently conducted, trial-based economic evaluations are used to explore the sensitivity of the study results to the technique used to deal with incomplete observations. A statistical framework for representing the uncertainty in the alternative methods is outlined using an approach based on net benefits and cost-effectiveness acceptability curves. RESULTS: The case studies demonstrate the potential importance of the approach used to handle missing data. Although the analytical strategy did not appear to alter the results of one of the studies, the other case study showed that that the results of the cost-effectiveness analysis were sensitive to both the decision to impute and also the imputation strategy adopted. CONCLUSIONS: Analysts should be more explicit in reporting the analytical strategies applied in the presence of missing data. The use of a multiple imputation approach is recommended in the majority of cases, so as to adequately reflect the uncertainty in the study results due to the presence of missing data.

Bias↗

[Meta-analysis of the Italian studies on short-term effects of air pollution].

BACKGROUND: In recent years, much attention has been given to review reports on the early effects of air pollution on health, measured through daily series of deaths and/or hospital admissions. A number of large planned meta-analyses (in which methods for data retrieval and processing are commonly planned a priori for all participating centers) are on going both in the US and in Europe. The National Mortality, Morbidity and Air Pollution Study included data from 90 US cities, whereas APHEA (Air Pollution and Health, a European Approach) considers data from about 30 european cities. The present paper summarizes methods and findings of MISA, a meta-analysis of data from 8 Italian cities. It belongs to an ad hoc supplement of Epidemiologia & Prevenzione (Epidemiol Prev 2001; 25 (2) Suppl: 1-72), the official Journal of the Italian Association of Epidemiology, which contains a full description of the study. MISA was launched on March 2000, within the project "Statistics, Environment and Health" (GRASPA), funded by the Italian Ministry of Education. Additional support was given by the Authorities of the 8 participating cities (from North to South: Turin, Milan, Verona, Ravenna, Bologna, Florence, Rome and Palermo). DAILY HEALTH DATA: Deaths certificate and hospital admission data have been collected respectively from the Local Health Authority and regional files. The same programme for retrieval of data on selected hospital admissions for acute conditions was used in the 8 cities. Main data are summarized in Table 1. DAILY CONCENTRATION OF POLLUTANTS: Most data were obtained from Regional Environmental Protection Agencies, which are responsible for environmental monitoring since 1993. Verona, Palermo and Milan (1990-94) data were obtained from local sources. Monitors with more than 25% of missing data were excluded. Meteorological data were collected by the same monitors and completed with data from monitors situated in the suburbs or (in Milan and Bologna) in the airport. The monitors were selected by a group of experts to ensure comparability. For SO2 and NO2 daily averages of hourly measurements were used, whereas concentrations of ozone and CO were estimated as the maximum 8 hours moving average. Total suspended particulate or PM10 were measured as 24 hours deposition. All analyses used the whole range of observed values (Table 2). Daily data were considered as missing when more than 25% of hourly data were not available. Missing data in one monitor were imputed as average of data from the remaining monitors weighted by the ratio between the specific monitor's year average and the general year average of all the selected city monitors. Missing data in one day were imputed as average of four days (preceding and following day, the same day of the previous and following weeks). In the city of Florence and Palermo PM10 concentrations were available. For the other cities we applied a conversion factor from PTS to PM10 (0.6 for Turin and 0.8 for all the others) estimated through validation studies. Ozone concentrations were used only where background monitors were available (Turin, Verona, Bologna and Florence) and limited to the warm season (May through September). METHODS: A common protocol for the city-specific analyses was defined on the basis of a structured exploratory analysis. The adopted basic model was a Generalized Additive Model for Poisson data. Effect estimates were age-adjusted (0-64, 65-74, 75+) and formal tests of interaction pollutant-age were conducted. In the first two age groups, indicator variables for seasonality were specified, and cubic splines with fixed number of degree of freedom were specified for the last age group and for all age groups for the morbidity data. Model adequacy was checked by residual analysis and inspection of the partial autocorrelation function. In a sensitivity analysis non linear pollutant effects were considered and overdispersed [table: see text] transitional models were fitted; the analysis was conducted for all lags 0-3 and some distributed lags (0-1, 1-2, 0-3); no multipollutant models were fitted. The same model was fitted to the city data. No model selection was done: Table 3 describes the steps in model building. In the meta-analysis, for each outcome, the estimates for each pollutant and for each city were combined using fixed and random effects models. Heterogeneity of effects was tested according to DerSimonian and Laird. Results were checked using a hierarchical bayesian model, which was used to investigate heterogeneity across cities in a meta-regression phase. Non informative priors were used. Posterior distributions of parameters of interest have been obtained with WinBUGS. 10,000 iterations (excluding [table: see text] the first 2000) were retained, while for the meta-regression 100,000 iterations (excluding the first 4000) were stored. To approximate the marginal posteriors only one sample out of five were used. Achieved convergence was assessed using the Gelman and Rubin approach. In the meta-regression the models specified were the following: [formula: see text] i denotes city, j calendar period (1990-1994; 1995-1999). The first model includes only period as effect modifier, while the second model other potential variables. The ui terms (which do not vary with j) represent city specific random effects. RESULTS: For each pollutant, the meta-analysis detected a statistically significant association with mortality for natural causes. But for ozone, positive associations were commonly found for death and hospital admissions for both cardiovascular and respiratory diseases. Indeed, the only estimates whose lower 95% confidence limit bore a negative sign regarded the association between PM10 and mortality from respiratory diseases. Ozone in the warm season was positively and significantly associated with daily mortality and mortality for cardiovascular diseases whereas other estimates did not reach statistical significance and some were negative (only lag 0-1 for external comparability are reported in Table 4). Risks were highest (up to 4%) for respiratory conditions (Table 4). They were more pronounced at lag 1-2 for mortality, and at lag 0-3 for hospital admissions. Age was an effect modifier for mortality, the elderly being more susceptible. In the random effect meta-analysis, at lag 1-2, excess risks for unit increase of the pollutants at age 75+ and at age 0-64 were respectively: 4.9% and -0.4% for SO2, 1.7% and 0.6% for NO2; 2.3% and 0.2% for CO. Corresponding figures for PM10 at lag 0-1 were 1.1% and 0.2%. The effect of PM10 on mortality [table: see text] was greater during the warm season (2.8% vs 0.8%). A complete analysis is reported in the Italian text. Here we provide some details on the effects of PM10, about which the residual heterogeneity across cities was highest (Table 4). In addition, the epidemiological evidence on the hazards from this fraction of particulate matter is more controversial. Table 5 reports the excess risk estimated through the meta-analysis in 1995-99 for a 10 micrograms/m3 increase of PM10 for some outcomes. Proper prior distributions (overdispersed normal and inverse gamma) were adopted in the final bayesian analyses. The sensitivity of results to the choice of the priors were investigated (we defined proper and improper uniform, student's t), obtaining comparable results. Total natural mortality was significantly heterogeneous across cities (Q = 18.96, 5 df, p < 0.001). City-specific estimates are represented graphically in Fig. 1. As expected, the confidence (credibility) intervals are widest [table: see text] for bayesian estimates, intermediate for those obtained under a random effects model, and narrowest for those found under a fixed effects model. Nevertheless, differences in point estimates are negligible. A North-South gradient in risk is obvious. Table 6 shows, for the cities for which mortality data were available, the improvement in precision and the shrinkage of effect estimates toward the overall mean introduced by the bayesian modelling. In the meta-regression, total mortality and a deprivation score were associated with greater effects. The excess risks on hospital admission were modified by the deprivation score and by the NO2/PM10 ratio. Overall, the risk estimates were greater in the calendar period 1995-99 and there was a North-South gradient, with larger effects in cities located in Central and Southern Italy (Florence, Rome, Palermo). CONCLUSIONS: The meta-analysis of the Italian studies on short-term effects of air pollution in 8 cities, MISA, exhibits the following features: With the exception of Naples, all greatest Italian cities were included; overall a population of 7 million was enrolled. The study protocol was accurate with regard to the selection of hospital admissions for acute conditions. Monitored data of concentration of pollutant were carefully evaluated before their inclusion in the meta-analysis. City specific analyses were carried out according to a common protocol controlling for seasonality, influenza epidemics, age and meterological variables; [table: see text] the protocol derived from a structured exploratory analysis. The meta-analysis was done using fixed and random effects models; a hierarchical bayesian model was fitted in a sensitivity analysis. The heterogeneity of effects across cities was investigated using a hierarchical bayesian model for meta-regression. While mortality data are of good quality, hospital admission data are more problematic. Since the filing criteria for the latter changed around 1995, comparability of results before and after such date is limited. Moreover, hospital admissions rely on availability of beds, the offer of which may be restricted during the warm season. Comparability of pollutant concentration estimates among cities may have been influenced by differences in monitor characteristics. (ABSTRACT TRUNCATED)

Adolescent↗

Methods to analyse cost data of patients who withdraw in a clinical trial setting.

BACKGROUND: Missing data resulting from premature study withdrawal are a common problem in the analysis of longitudinal data in clinical trials. To date, this subject has received little attention in the context of economic evaluations and with regard to the analysis of cost data. OBJECTIVES: To (i) demonstrate the impact of patients who drop out during the study on the outcomes of an economic evaluation, and (ii) to compare the mean and variation in costs after applying five different methods to deal with incomplete data: multiple imputation, complete cases analysis, linear extrapolation, predicted mean and hot decking. STUDY DESIGN: The study was performed using cost data collected in two randomised clinical trials comparing patients with chronic obstructive pulmonary disease receiving either tiotropium bromide or ipratropium bromide. The overall dropout rate was 17%, with the daily costs of the dropouts approximately 4 times higher than the costs of the completers. METHODS: Multiple imputation is a principled method that deals with missing observations by replacing each missing observation with a set of multiple plausible values. The variance between the resulting multiple datasets is combined with the variance between the datasets to take account of the extra uncertainty that results from missing data. The outcomes after multiple imputation were compared with the results of four naive methods to deal with missing observations: complete cases analysis, linear extrapolation, predicted mean and hot decking. All costs were expressed in 2001 euros. RESULTS: In the tiotropium bromide group, mean (standard error) costs varied from Euro 955 (137) after complete cases analysis to Euro 1298 (198) after linear extrapolation. The corresponding estimates in the ipratropium bromide group were Euro 970 (125) and Euro 1561 (244), respectively. The difference in costs between treatment groups varied from -Euro 15 (95% CI: -379 to 349) after complete cases analysis to -Euro 402 (95% CI: -883 to 79) after predicted mean, in favour of the tiotropium bromide group. The difference in costs according to the other methods varied from -Euro 263 (95% CI: -878 to 353) after linear extrapolation to -Euro 265 (95% CI: -709 to 180) after multiple imputation to -Euro 359 (95% CI: -771 to 54) after hot decking. CONCLUSION: This study showed that the method of dealing with the data of the dropouts had a large impact on the outcomes of an economic evaluation. Information about the rate of patient withdrawal and the way data of dropouts are treated is of vital importance in assessing the results of economic evaluations and should always be reported. Multiple imputation is a principled method that can be used to deal with the data of these patients.

Bronchodilator Agents↗

Pramipexole and levodopa in early Parkinson's disease: dynamic changes in cost effectiveness.

BACKGROUND AND OBJECTIVE: In chronic disease, treatment effects and costs accumulate over time; hence, the choice of time horizon in cost-effectiveness analysis can be particularly important. In this article we analyse the dynamic changes in cumulative costs, effects and incremental cost effectiveness of two competing drug strategies in patients with early Parkinson's disease (PD). METHODS: Three hundred and one subjects with PD were randomised to initial pramipexole or levodopa and followed every 3 months over a 4-year period. Healthcare resource use was recorded in patient diaries and valued using a variety of sources at year 2002 US dollar values. Health-related quality of life (HRQoL) was measured using the EuroQoL EQ-5D. The study was conducted from a US societal perspective. Missing data were imputed using a multivariate fixed-effects model. Additional quality adjusted life years (QALY) gained by using pramipexole compared with levodopa were estimated as the area between the normalised treatment HRQoL profiles. The QALYs and costs for each treatment arm were calculated for various study horizons.The incremental cost-effectiveness ratio (ICER) and the net monetary benefit (NB) [using 50,000 US dollars, 100,000 US dollars and 150,000 US dollars as the value of a QALY] were estimated, and were bootstrapped to calculate the standard errors. Cost-effectiveness acceptability curves (CEAC) were built to estimate the probability that pramipexole was cost effective given different societal values of QALY, for various study horizons.We conducted sensitivity analyses on the ICER and the NB to test their robustness to various assumptions about missing data, for various subpopulations and under changes in the drug prices. RESULTS: Under the base-case assumptions, the ICER for pramipexole was 42,989 US dollars per QALY. Using the CEAC approach, the probability that pramipexole was cost effective relative to levodopa over the first 4 years was 0.57, 0.77 and 0.82 when a QALY was valued at 50,000 US dollars, 100,000 US dollars, and 150,000 US dollars, respectively. Over time, the ICER for pramipexole improved and uncertainty around the ICER decreased. If, after treatment withdrawal, HRQoL improved in pramipexole subjects and declined in levodopa subjects (best-case scenario for pramipexole), the probability of pramipexole being cost effective increased to 0.88, 0.96 and 0.98, respectively. Factors that improved the ICER of pramipexole were a decrease in the relative price of pramipexole and having low HRQoL or depression at baseline. CONCLUSIONS: The cost effectiveness of pramipexole compared with levodopa in the treatment of early PD increased as the time horizon of the clinical trial extended from 2 to 4 years. Our results suggest that pramipexole is more cost effective for patients with depression and low baseline HRQoL than in other patient subgroups.

Administration, Oral↗

Cost-effectiveness and safety of epidural steroids in the management of sciatica.

OBJECTIVES: To investigate the clinical effectiveness of epidural steroid injections (ESIs) in the treatment of sciatica with an adequately powered study and to identify potential predictors of response to ESIs. Also, to investigate the safety and cost-effectiveness of lumbar ESIs in patients with sciatica. DESIGN: A pragmatic, prospective, multicentre, double-blind, randomised, placebo-controlled trial with 12-month follow-up was performed. Patients were stratified according to acute (<4 months since onset) versus chronic (4-18 months) presentation. All analyses were performed on an intention-to-treat basis with last observation carried forward used to impute missing data. SETTING: Rheumatology, orthopaedic and pain clinics in four participating centres: three district hospitals and one teaching hospital in the south of England. PARTICIPANTS: Total of 228 patients listed for ESI with clinically diagnosed unilateral sciatica, aged between 18 and 70 years, who had a duration of symptoms between 4 weeks and 18 months. INTERVENTIONS: Patients received up to three injections of epidural steroid and local anaesthetic (active), or an injection of normal saline into the interspinous ligament (placebo). MAIN OUTCOME MEASURES: The primary outcome measure was the Oswestry Disability Questionnaire (ODQ); measures of pain relief and psychological and physical function were collected. Health economic data on return to work, analgesia use and other interventions were also measured. Quality-adjusted life-years (QALYs) were calculated using the SF-6D, calculated from the Short Form (SF-36). Costs per patient were derived from figures supplied by the centres' finance departments and a costings exercise performed as part of the study. A cost-utility analysis was performed using the SF-36 to calculate costs per QALY. RESULTS: ESI led to a transient benefit in ODQ and pain relief, compared with placebo at 3 weeks (p = 0.017, number needed to treat = 11.4). There was no benefit over placebo between weeks 6 and 52. Using incremental QALYs, this equates to and additional 2.2 days of full health. Acute sciatica seemed to respond no differently to chronic sciatica. There were no significant differences in any other indices, including objective tests of function, return to work or need for surgery at any time-points. There were no clinical predictors of response, although the trial lacked sufficient power to be confident of this. Adverse events were uncommon, with no difference between groups. Costs per QALY to providers under the trial protocol were 44,701 pounds sterling. Costs to the purchaser per QALY were 354,171 pounds sterling. If only one ESI was provided then costs per QALY fell to 25,745 pounds sterling to the provider and 167,145 pounds sterling to the purchaser. ESIs thus failed the QALY threshold recommended by the National Institute for Health and Clinical Excellence (NICE). CONCLUSIONS: Although ESIs appear relatively safe, it was found that they confer only transient benefit in symptoms and self-reported function in a small group of patients with sciatica at substantial costs. ESIs do not provide good value for money if NICE recommendations are followed. Additional research is suggested into the epidemiology of radicular pain, producing a register of all ESIs, possible subgroups who may benefit from ESIs, the use of radiological imaging, optimal early interventions, analgesic agents and nerve root injections, the use of cognitive behavioural therapy in rehabilitation, improved methods of assessment, a comparative cost-utility analysis between various treatment strategies, and methods to reduce the effect of scarring and inflammation.

Acute Disease↗