Familywise error for multiple time-to-event endpoints in a group sequential design.

We investigate the familywise error rate (FWER) for time-to-event endpoints evaluated using a group sequential design with a hierarchical testing procedure for secondary endpoints. We show that, in this setup, the correlation between the log-rank test statistics at interim and at end of study is not congruent with the canonical correlation derived for normal-distributed endpoints. We show, both theoretically and by simulation, that the correlation also depends on the level of censoring, the hazard rates of the endpoints, and the hazard ratio. To optimize operating characteristics in this complex scenario, we propose a simulation-based method to assess the FWER which, better than the alpha-spending approach, can inform the choice of critical values for testing secondary endpoints.

Simulation-based sample size calculations of marginal proportional means models for recurrent events with competing risks.

In randomised controlled trials, the outcome of interest could be recurrent events, such as hospitalisations for heart failure. If mortality rates are non-negligible, both recurrent events and competing terminal events need to be addressed when formulating the estimand and statistical analysis is no longer trivial. In order to design future trials with primary recurrent event endpoints with competing risks, it is necessary to be able to perform power calculations to determine sample sizes. This paper introduces a simulation-based approach for power estimation based on a proportional means model for recurrent events and a proportional hazards model for terminal events. The simulation procedure is presented along with a discussion of what the user needs to specify to use the approach. The method is flexible and based on marginal quantities which are easy to specify. However, the method introduces a lack of a certain type of dependence. This is explored in a sensitivity analysis which suggests that the power is robust in spite of that. Data from a randomised controlled trial, LEADER, is used as the basis for generating data for a future trial. Finally, potential power gains of recurrent event methods as opposed to first event methods are discussed.

Bivariate pseudo-observations for recurrent event analysis with terminal events.

The analysis of recurrent events in the presence of terminal events requires special attention. Several approaches have been suggested for such analyses either using intensity models or marginal models. When analysing treatment effects on recurrent events in controlled trials, special attention should be paid to competing deaths and their impact on interpretation. This paper proposes a method that formulates a marginal model for recurrent events and terminal events simultaneously. Estimation is based on pseudo-observations for both the expected number of events and survival probabilities. Various relevant hypothesis tests in the framework are explored. Theoretical derivations and simulation studies are conducted to investigate the behaviour of the method. The method is applied to two real data examples. The bivariate marginal pseudo-observation model carries the strength of a two-dimensional modelling procedure and performs well in comparison with available models. Finally, an extension to a three-dimensional model, which decomposes the terminal event per death cause, is proposed and exemplified.

Methodological challenges in the analysis of recurrent events for randomised controlled trials with application to cardiovascular events in LEADER.

Analysis of recurrent events is becoming increasingly popular for understanding treatment effects in randomised controlled trials. The analysis of recurrent events can improve efficiency and capture disease burden compared to standard time-to-first event analyses. However, the added knowledge about the multi-state process comes at the cost of modelling complexity. High mortality rates can complicate matters even more. A case study using data from a randomised controlled trial, LEADER, is presented to highlight interpretation of common methods as well as potential pitfalls when analysing recurrent events in the presence of a competing risk. The presented methods either target features of the underlying intensity functions or marginal traits of a multi-state process which includes terminal events or not. In particular, approaches to handle death as a part of an event and as a competing risk are discussed. A new method targeting the marginal mean function for a composite endpoint, which includes both death as a component and as a competing risk, will be introduced. Finally, recommendations for how to capture meaningful treatment effects in randomised controlled trials when analysing recurrent and terminal events will be made.

Semaglutide Effects on Cardiovascular Outcomes in People With Overweight or Obesity (SELECT) rationale and design.

Cardiovascular disease (CVD) is a major cause of morbidity and mortality. Although it has been widely appreciated that obesity is a major risk factor for CVD, treatments that produce effective, durable weight loss and the impact of weight reduction in reducing cardiovascular risk have been elusive. Instead, progress in CVD risk reduction has been achieved through medications indicated for controlling lipids, hyperglycemia, blood pressure, heart failure, inflammation, and/or thrombosis. Obesity has been implicated as promoting all these issues, suggesting that sustained, effective weight loss may have independent cardiovascular benefit. GLP-1 receptor agonists (RAs) reduce weight, improve glycemia, decrease cardiovascular events in those with diabetes, and may have additional cardioprotective effects. The GLP-1 RA semaglutide is in phase 3 studies as a medication for obesity treatment at a dose of 2.4 mg subcutaneously (s.c.) once weekly. Semaglutide Effects on Heart Disease and Stroke in Patients with Overweight or Obesity (SELECT) is a randomized, double-blind, parallel-group trial testing if semaglutide 2.4 mg subcutaneously once weekly is superior to placebo when added to standard of care for preventing major adverse cardiovascular events in patients with established CVD and overweight or obesity but without diabetes. SELECT is the first cardiovascular outcomes trial to evaluate superiority in major adverse cardiovascular events reduction for an antiobesity medication in such a population. As such, SELECT has the potential for advancing new approaches to CVD risk reduction while targeting obesity.

Complete and on-time routine childhood immunisation: determinants and association with severe morbidity in urban informal settlements, Nairobi, Kenya.

Background: Completion of the full series of childhood vaccines on-time is crucial to ensuring greater protection against vaccine-preventable diseases.Aim: To examine determinants of complete and on-time vaccination and evaluate the relationship between vaccination patterns and severe morbidity outcomes.Subjects and methods: Vaccination information from infants in Nairobi Urban Health and Demographic Surveillance System was used to evaluate full and on-time vaccination coverage of routine immunisation. Logistic regression was used to identify determinants of full and on-time vaccination coverage. Cox regression model was used to evaluate the relationship between vaccination status and subsequent severe morbidity. A shared frailty cox model was fitted to account for the heterogeneity in hospitalisation episodes.Results: Maternal age, post-natal care, parity, ethnicity, and residence place were identified as determinants of vaccination completion. Institutional deliveries and residence place were identified as the determinants of on-time vaccination. A significant 58% (confidence interval [CI]: 15-79%) (p = .017) lower mortality was observed among fully immunised children compared with not fully immunised. Lower mortality was observed among on-time immunised children, 64% (CI: 20-84%) compared to those with delays.Conclusions: Improving vaccination timeliness and completion schedule is critical for protection against vaccine preventable diseases and may potentially provide protection beyond these targets.

Modeling marginal features in studies of recurrent events in the presence of a terminal event.

We study models for recurrent events with special emphasis on the situation where a terminal event acts as a competing risk for the recurrent events process and where there may be gaps between periods during which subjects are at risk for the recurrent event. We focus on marginal analysis of the expected number of events and show that an Aalen-Johansen type estimator proposed by Cook and Lawless is applicable in this situation. A motivating example deals with psychiatric hospital admissions where we supplement with analyses of the marginal distribution of time to the competing event and the marginal distribution of the time spent in hospital. Pseudo-observations are used for the latter purpose.

Rapid Protective Effects of Early BCG on Neonatal Mortality Among Low Birth Weight Boys: Observations From Randomized Trials.

Background: Three randomized trials (RCTs) in low-weight (<2.5 kg) infants have shown that Bacille Calmette-Guérin (BCG) vaccine nonspecifically reduces all-cause mortality in the neonatal period. Methods: Using data from 3 RCTs of early BCG (n = 6583) we examined potential sex differences in the timing of the mortality reduction in the neonatal period, presenting metaestimates of the main outcome mortality rate ratios (MRR) for BCG-vaccinated and controls. Results: Among controls, boys had a particularly high mortality during the first week after randomization: male-female MRR 2.71 (95% CI, 1.70-4.50). During the first week, BCG had a marked beneficial effect for boys, reducing mortality 3-fold (MRR [BCG/no BCG] = 0.36 [0.20-0.67]). In weeks 2-4 the effect waned for boys (MRR = 0.91 [0.51-1.69]). In girls, the pattern was opposite with a limited effect in the first week (MRR = 0.85 [0.46-1.54]), but a significant reduction in weeks 2-4 (MRR = 0.56 [0.31-1.00]). This was consistent in all 3 trials. Verbal autopsies linked early benefit to fewer sepsis-related deaths among BCG-vaccinated boys. Discussion: The marked reduction in mortality in the days after BCG vaccination in boys emphasizes the importance of providing BCG soon after birth. Trial registration numbers: ClinicalTrials.gov (NCT00146302) and ClinicalTrials.gov (NCT00625482).

A marginal structural model for recurrent events in the presence of time-dependent confounding: non-specific effects of vaccines on child hospitalisations.

Using a Danish register-based study on childhood vaccination and hospitalisation as motivation, a marginal structural model for recurrent events is studied. The model addresses a number of challenges which may be seen more generally in large register-based cohort studies. One is to adjust for a time-dependent confounder when studying the effect of a time-varying exposure on a recurrent event based on an analysis in continuous time. Another is to report results via a measure which is easy to interpret and communicate even though quite elaborate treatment regimes are considered. Lastly, the implementation of continuously updated weights implies a substantial computationally demanding workload. Copyright © 2016 John Wiley & Sons, Ltd.

Development of BCG Scar and Subsequent Morbidity and Mortality in Rural Guinea-Bissau.

BACKGROUND: Previous studies have found that BCG vaccination has nonspecific beneficial effects on child survival, especially among children who developed a BCG scar. These studies have mostly been done in settings with a high scar frequency. In rural Guinea-Bissau, many children do not develop a scar; we tested the hypothesis that among BCG-vaccinated children, a vaccination scar was associated with lower mortality and fewer hospital admissions. METHODS: During 2009-2011, children <5 years of age in villages followed by Bandim Health Project's demographic surveillance system had their scar status assessed at semiannual visits. We compared mortality and hospital admission rates of scar-positive and scar-negative BCG-vaccinated children during 6 months of follow-up in Cox proportional hazards models. RESULTS: Among 15 911 BCG-vaccinated children, only 52% had a scar. There were 106 non-injury-related deaths among scar-positive children and 137 among scar-negative children. The mortality rate ratio (MRR) was 0.74 (95% confidence interval [CI], .56-.96) overall; 0.48 (95% CI, .26-.90) in infancy, 0.69 (95% CI, .45-1.05) in the second year of life, and 0.89 (95% CI, .61-1.31) in the third-fifth year of life. The association between scar positivity and lower mortality differed significantly by cause of death and was strongest for respiratory infections (MRR, 0.20 [95% CI, .07-.55]). There were 99 hospital admissions among scar-positive children and 125 admissions among scar-negative children, resulting in an incidence rate ratio of 0.74 (95% CI, .60-.92). CONCLUSIONS: Among BCG-vaccinated children in a setting with low scar prevalence, having a scar is associated with lower mortality and morbidity. BCG scar prevalence may be an important marker of vaccination program quality.

The Effect of Oral Polio Vaccine at Birth on Infant Mortality: A Randomized Trial.

BACKGROUND: Routine vaccines may have nonspecific effects on mortality. An observational study found that OPV given at birth (OPV0) was associated with increased male infant mortality. We investigated the effect of OPV0 on infant mortality in a randomized trial in Guinea-Bissau. METHODS: A total of 7012 healthy normal-birth-weight neonates were randomized to BCG only (intervention group) or OPV0 with BCG (usual practice). All children were to receive OPV with pentavalent vaccine (diphtheria, tetanus, pertussis, Haemophilus influenzae type b, and hepatitis B) at 6, 10, and 14 weeks of age. Seven national OPV campaigns were also conducted during the trial period. Children were followed to age 12 months. We used Cox regression to calculate hazard ratios (HRs) for mortality. RESULTS: The trial contradicted the original hypothesis about OPV0 increasing male infant mortality. Within 12 months, 73 children in the BCG + OPV group and 87 children in the BCG-only group died, all from infectious diseases. Comparing BCG + OPV0 vs BCG only, the HR was 0.83 (95% confidence interval [CI], .61-1.13): 0.72 (95% CI, .47-1.10) in boys and 0.97 (95% CI, .61-1.54) in girls. For children enrolled within the first 2 days of life, the HR for BCG + OPV0 vs BCG only was 0.58 (95% CI, .38-.90). From enrollment until the time of OPV campaigns, the HR was 0.68 (95% CI, .45-1.00), the beneficial effect being separately significant for males (0.55 [95% CI, .32-.95]). CONCLUSIONS: This is the only randomized trial of the effect of OPV0 on mortality. OPV0 may be associated with nonspecific protection against infectious disease mortality, particularly when given early in life. There are reasons to monitor mortality when OPV is being phased out. CLINICAL TRIALS REGISTRATION: NCT00710983.

Tuberculin reaction and BCG scar: association with infant mortality.

OBJECTIVE: To test the hypothesis that having a scar and a positive tuberculin skin test (TST) response after vaccination with Bacille Calmette-Guérin (BCG) is associated with reduced infant mortality. METHODS: We studied cohorts of 2709 normal-birthweight (NBW) and 1102 low-birthweight (LBW) infants in Guinea-Bissau. Children were enrolled in randomised trials between year 2002 and 2008 and received BCG vaccination at birth. BCG scars and TST responses were assessed at 2 and 6 months of age. The infants were followed for mortality to 12 months of age, and survival was analysed using Cox regression. RESULTS: At age 2 months, 88% of NBW children and 91% of LBW children had a BCG scar, and 36% and 17% had a TST response, respectively. The LBW infants had nearly twofold higher mortality (4.5%) than the NBW infants (2.8%) between 2 and 12 months of age. In the LBW cohort, the adjusted mortality rate ratio (MRR) comparing children with a BCG scar with those without was 0.42 (95% CI = 0.19; 0.93). There was a similar tendency for TST positivity: MRR = 0.47 (95% CI = 0.14; 1.54). For LBW children who had both a positive TST reaction and a scar, the MRR was 0.22 (95% CI = 0.05; 0.87). For NBW children, a scar and a positive TST were associated with 20% reductions in mortality, which did not reach statistical significance. CONCLUSION: We confirmed previous observations that having a scar and a TST response after BCG vaccination is associated with lower mortality risk. The possibility of revaccinating scar-negative children should be considered.

Effects of low birth weight on time to BCG vaccination in an urban poor settlement in Nairobi, Kenya: an observational cohort study.

BACKGROUND: The World Health Organization recommends Bacillus Calmette-Guérin (BCG) vaccination against tuberculosis be given at birth. However, in many developing countries, pre-term and low birth weight infants get vaccinated only after they gain the desired weight. In Kenya, the ministry of health recommends pre-term and low birth weight infants to be immunized at the time of discharge from hospital irrespective of their weight. This paper seeks to understand the effects of birth weight on timing of BCG vaccine. METHODS: The study was conducted in two Nairobi urban informal settlements, Korogocho and Viwandani which hosts the Nairobi Urban Health and Demographic Surveillance system. All infants born in the study area since September 2006 were included in the study. Data on immunization history and birth weight of the infant were recorded from child's clinic card. Follow up visits were done every four months to update immunization status of the child. A total of 3,602 infants were included in this analysis. Log normal accelerated failure time parametric model was used to assess the association between low birth weight infants and time to BCG immunization. RESULTS: In total, 229 (6.4%) infants were low birth weight. About 16.6% of the low birth weight infants weighed less than 2000 grams and 83.4% weighed between 2000 and 2490 grams. Results showed that, 60% of the low birth weight infants received BCG vaccine after more than five weeks of life. Private health facilities were less likely to administer a BCG vaccine on time compared to public health facilities. The effects of low birth weight on females was 0.60 and 0.97-times that of males for infants weighing 2000-2499 grams and for infants weighing <2000 grams respectively. The effect of low birth weight among infants born in public health facilities was 1.52 and 3.94-times that of infants delivered in private health facilities for infants weighing 2000-2499 grams and those weighing < 2000 grams respectively. CONCLUSION: Low birth weight infants received BCG immunization late compared to normal birth weight infants. Low birth weight infants delivered in public health facilities were more likely to be immunized much later compared to private health facilities.

Early BCG vaccine to low-birth-weight infants and the effects on growth in the first year of life: a randomised controlled trial.

BACKGROUND: Randomised trials have shown that early Bacille Calmette-Guérin (BCG) vaccine reduces overall neonatal and infant mortality. However, no study has examined how BCG affects growth. We investigated the effect on infant growth of early BCG vaccine given to low-birth-weight (LBW) infants. METHODS: Two-thousand three hundred forty-three LBW infants were randomly allocated 1:1 to "early BCG" (intervention group) or "late BCG" (current practice). Furthermore, a subgroup (N = 1717) were included in a two-by-two randomised trial in which they were additionally randomised 1:1 to vitamin A supplementation (VAS) or placebo. Anthropometric measurements were obtained 2, 6, and 12 months after enrolment. RESULTS: Overall there was no effect of early BCG on growth in the first year of life. The effect of early BCG on weight and mid-upper-arm circumference at 2 months tended to be beneficial among girls but not among boys (interaction between "early BCG" and sex: weight p = 0.03 and MUAC p = 0.04). This beneficial effect among girls was particularly seen among the largest infants weighing 2.0 kg or more at inclusion. CONCLUSION: Though BCG vaccination is not recommended to be given to LBW infants at birth in Guinea-Bissau, early BCG had no negative effect on infant growth and may have had a beneficial effect for girls. TRIAL REGISTRATION NUMBER: ClinicalTrials.gov (NCT00146302).

A randomized trial of a standard dose of Edmonston-Zagreb measles vaccine given at 4.5 months of age: effect on total hospital admissions.

Observational studies and trials from low-income countries indicate that measles vaccine has beneficial nonspecific effects, protecting against non-measles-related mortality. It is not known whether measles vaccine protects against hospital admissions. Between 2003 and 2007, 6417 children who had received the third dose of diphtheria, tetanus, and pertussis vaccine were randomly assigned to receive measles vaccine at 4.5 months or no measles vaccine; all children were offered measles vaccine at 9 months of age. Using hospital admission data from the national pediatric ward in Bissau, Guinea-Bissau, we compared admission rates between enrollment and the 9-month vaccination in Cox models, providing admission hazard rate ratios (HRRs) for measles vaccine versus no measles vaccine. All analyses were conducted stratified by sex and reception of neonatal vitamin A supplementation (NVAS). Before enrollment the 2 groups had similar admission rates. Following enrollment, the measles vaccine group had an admission HRR of 0.70 (95% confidence interval [CI], .52-.95), with a ratio of 0.53 (95% CI, .32-.86) for girls and 0.86 (95% CI, .58-1.26) for boys. For children who had not received NVAS, the admission HRR was 0.53 (95% CI, .34-.84), with an effect of 0.30 (95% CI, .13-.70) for girls and 0.73 (95% CI, .42-1.28) for boys (P = .08, interaction test). The reduction in admissions was separately significant for measles infection (admission HRR, 0 [95% CI, 0-.24]) and respiratory infections (admission HRR, 0.37 [95% CI, .16-.89]). Early measles vaccine may have major benefits for infant morbidity patterns and healthcare costs. Clinical trials registration NCT00168558.

Measles vaccination in the presence or absence of maternal measles antibody: impact on child survival.

BACKGROUND: Measles vaccine (MV) has a greater effect on child survival when administered in early infancy, when maternal antibody may still be present. METHODS: To test whether MV has a greater effect on overall survival if given in the presence of maternal measles antibody, we reanalyzed data from 2 previously published randomized trials of a 2-dose schedule with MV given at 4-6 months and at 9 months of age. In both trials antibody levels had been measured before early measles vaccination. RESULTS: In trial I (1993-1995), the mortality rate was 0.0 per 1000 person-years among children vaccinated with MV in the presence of maternal antibody and 32.3 per 1000 person-years without maternal antibody (mortality rate ratio [MRR], 0.0; 95% confidence interval [CI], 0-.52). In trial II (2003-2007), the mortality rate was 4.2 per 1000 person-years among children vaccinated in presence of maternal measles antibody and 14.5 per 1000 person-years without measles antibody (MRR, 0.29; 95% CI, .09-.91). Possible confounding factors did not explain the difference. In a combined analysis, children who had measles antibody detected when they received their first dose of MV at 4-6 months of age had lower mortality than children with no maternal antibody, the MRR being 0.22 (95% CI, .07-.64) between 4-6 months and 5 years. CONCLUSIONS: Child mortality in low-income countries may be reduced by vaccinating against measles in the presence of maternal antibody, using a 2-dose schedule with the first dose at 4-6 months (earlier than currently recommended) and a booster dose at 9-12 months of age. CLINICAL TRIALS REGISTRATION: NCT00168558.

Factors associated with thymic size at birth among low and normal birth-weight infants.

OBJECTIVE: To study the effect of gestational and perinatal exposures on thymic size in 366 normal birth weight and 426 low birth weight (LBW) neonates in Guinea-Bissau in West Africa. STUDY DESIGN: In a cross-sectional study, thymic size was measured at birth by the use of ultrasound. Information on possible determinants was collected from pregnancy cards, hospital records, and interviews with the mother. We used the log-transformed thymic index and thymus/weight index as outcome measures. Data were analyzed with adjusted linear regression models providing geometric mean ratios (GMRs) with 95% CI. RESULTS: Determinants of thymic size among normal birth weight infants were pathologic amniotic fluid (adjusted GMR for thymic index: 0.84 [0.74-0.96]) and male sex (GMR: 1.13 [1.06-1.22]). Among LBW infants, birth season (1.11 [1.01-1.22]), maternal body temperature (0.89 [0.79-0.98]), antibiotic treatment at the time of labor (0.84 [0.70-1.00]), number of pregnancy consultations (1.03 [1.00-1.05]), maternal age (0.91 [0.84-0.98]), Apgar score (1.06 [1.03-1.10]), and infant convulsions (0.44 [0.29-0.65]) were all independent determinants of thymic index but not all were determinants of thymus/weight index. Pathologic amniotic fluid and cesarean delivery were associated with thymus/weight index among LBW infants (0.85 [0.75-0.95] and 0.80 [0.67-0.96]) but were only borderline significant for thymic index. CONCLUSION: Exposures mainly related to stress and infections were associated with a smaller thymus, mainly in LBW infants.

BCG coverage and barriers to BCG vaccination in Guinea-Bissau: an observational study.

BACKGROUND: BCG vaccination is recommended at birth in low-income countries, but vaccination is often delayed. Often 20-dose vials of BCG are not opened unless at least ten children are present for vaccination ("restricted vial-opening policy"). BCG coverage is usually reported as 12-month coverage, not disclosing the delay in vaccination. Several studies show that BCG at birth lowers neonatal mortality. We assessed BCG coverage at different ages and explored reasons for delay in BCG vaccination in rural Guinea-Bissau. METHODS: Bandim Health Project (BHP) runs a health and demographic surveillance system covering women and their children in 182 randomly selected village clusters in rural Guinea-Bissau. BCG coverage was assessed for children born in 2010, when the restricted vial-opening policy was universally implemented, and in 2012-2013, where BHP provided BCG to all children at monthly visits in selected intervention regions. Factors associated with delayed BCG vaccination were evaluated using logistic regression models. Coverage between intervention and control regions were evaluated in log-binomial regression models providing prevalence ratios. RESULTS: Among 3951 children born in 2010, vaccination status was assessed for 84%. BCG coverage by 1 week of age was 11%, 38% by 1 month, and 92% by 12 months. If BCG had been given at first contact with the health system, 1-week coverage would have been 35% and 1-month coverage 54%. When monthly visits were introduced in intervention regions, 1-month coverage was higher in intervention regions (88%) than in control regions (51%), the prevalence ratio being 1.74 (1.53-2.00). Several factors, including socioeconomic factors, were associated with delayed BCG vaccination in the 2010-birth cohort. When BCG was available at monthly visits these factors were no longer associated with delayed BCG vaccination, only region of residence was associated with delayed BCG vaccination. CONCLUSION: BCG coverage during the first months of life is low in Guinea-Bissau. Providing BCG at monthly vaccination visits removes the risk factors associated with delayed BCG vaccination.

Live vaccine against measles, mumps, and rubella and the risk of hospital admissions for nontargeted infections.

IMPORTANCE: In low-income countries, live measles vaccine reduces mortality from causes other than measles infection. Such nonspecific effects of vaccines might also be important for the health of children in high-income settings. OBJECTIVE: To examine whether the live vaccine against measles, mumps, and rubella (MMR) is associated with lower rates of hospital admissions for infections among children in Denmark. DESIGN, SETTING, AND PARTICIPANTS: Population-based cohort study of Danish children born 1997-2006 and followed up from ages 11 months to 2 years (last follow-up, August 31, 2008). Nationwide Danish registers provided data on vaccinations and hospital admissions. The recommended vaccination schedule was inactivated vaccine against diphtheria, tetanus, pertussis, polio, and Haemophilus influenzae type b (DTaP-IPV-Hib) administered at ages 3, 5, and 12 months and MMR at age 15 months. MAIN OUTCOMES AND MEASURES: Incidence rate ratios (IRRs) of hospital admissions for any infection, comparing receipt of MMR vs DTaP-IPV-Hib as the most recent vaccine. Risks, risk difference, and number needed to vaccinate were calculated for receiving MMR on time. RESULTS: The study included 495,987 children contributing with 56,889 hospital admissions for any type of infection during 509,427 person-years (rate, 11.2 per 100 person-years). For the 456,043 children who followed the recommended schedule and received MMR after the third dose of DTaP-IPV-Hib, MMR (rate, 8.9 per 100 person-years) vs the third dose of DTaP-IPV-Hib (rate, 12.4 per 100 person-years) as the most recent vaccine was associated with an adjusted IRR of 0.86 (95% CI, 0.84-0.88) for any admission for infection. There were 19,219 children immunized out of sequence. The adjusted IRR was 0.87 (95% CI, 0.80-0.95) for those receiving MMR (rate, 9.9 per 100 person-years) after the second dose of DTaP-IPV-Hib (rate, 15.1 per 100 person-years). However, in the 1981 children who subsequently received the third dose of DTaP-IPV-Hib (rate, 12.8 per 100 person-years) after MMR, the IRR for hospital admissions for infection was significantly greater (adjusted IRR, 1.62 [95% CI, 1.28-2.05]). The risk of admission for an infection between ages 16 months and 24 months was 4.6% (95% CI, 4.5%-4.7%) for receiving MMR on time and 5.1% (95% CI, 5.0%-5.2%) for not receiving MMR on time. The risk difference was 0.5 percentage point (95% CI, 0.4-0.6), and the number needed to vaccinate with MMR before age 16 months to prevent 1 admission for any infection was 201 (95% CI, 159-272). CONCLUSIONS AND RELEVANCE: In a cohort of Danish children, receipt of live MMR vs inactivated DTaP-IPV-Hib as the most recent vaccine was associated with a lower rate of hospital admissions for any infections. These findings require replication in other high-income populations.

Censored correlated cytokine concentrations: multivariate Tobit regression using clustered variance estimation.

Interest in cytokines as markers for the function of the immune system is increasing. Methods quantifying cytokine concentrations are often subject to detection limits, which lead to non-detectable observations and censored distributions. When distributions are skewed, geometric mean ratios (GMRs) can be used to describe the relative concentration between two cytokines, and the GMR ratio (GMRR) can be used to compare two groups. The problem is how to estimate GMRRs from censored distributions.We evaluated methods, including simple deletion and substitution, in simulated and real data. One method applies Tobit directly to the censored difference between the two cytokine log-concentrations (Diff). However, censoring is correlated to the outcome and is therefore not independent. The correlation increases as the correlation between the two log-concentrations decreases. We propose a Tobit stacking method that uses clustered variance-covariance estimation allowing homogeneous (Stackc) or inhomogeneous (Stackh) variances. We compare it with direct estimation of the bivariate Tobit likelihood function (Bitobit) and multiple imputation. We assess sensitivity to inhomogeneity and non-normality. Simulations show that deletion and substitution are empirically biased and that Diff has an empirical bias, which increases as the correlation between the log-concentrations decreases. Estimates from multiple imputation, Stackh and Bitobit are almost identical. The estimates exhibit small empirical bias for both homogeneous and inhomogeneous normal distributions. For skewed mixture and heavy-tailed distributions, they perform reasonably well if censoring is less than 30%. We recommend these methods to estimate GMRRs. At least one of the methods is available in Stata, R or SAS.