Comparison of profile-likelihood-based confidence intervals with other rank-based methods for the two-sample problem in ordered categorical data

For ordered categorical data from randomized clinical trials, the relative effect, the probability that observations in one group tend to be larger, has been considered appropriate for a measure of an effect size. Although the Wilcoxon-Mann-Whitney test is widely used to compare two groups, the null hypothesis is not just the relative effect of 50%, but the identical distribution between groups. The null hypothesis of the Brunner-Munzel test, another rank-based method used for arbitrary types of data, is just the relative effect of 50%. In this study, we compared actual type I error rates (or 1 - coverage probability) of the profile-likelihood-based confidence intervals for the relative effect and other rank-based methods in simulation studies at the relative effect of 50%. The profile-likelihood method, as with the Brunner- Munzel test, does not require any assumptions on distributions. Actual type I error rates of the profile-likelihood method and the Brunner-Munzel test were close to the nominal level in large or medium samples, even under unequal distributions. Those of the Wilcoxon-Mann-Whitney test largely differed from the nominal level under unequal distributions, especially under unequal sample sizes. In small samples, the actual type I error rates of Brunner-Munzel test were slightly larger than the nominal level and those of the profile-likelihood method were even larger. We provide a paradoxical numerical example: only the Wilcoxon-Mann-Whitney test was significant under equal sample sizes, but by changing only the allocation ratio, it was not significant but the profile-likelihood method and the Brunner-Munzel test were significant. This phenomenon might reflect the nature of the Wilcoxon-Mann-Whitney test in the simulation study, that is, the actual type I error rates become over and under the nominal level depending on the allocation ratio.

Longitudinal analysis of pre- and post-treatment measurements with equal baseline assumptions in randomized trials

For continuous variables of randomized controlled trials, recently, longitudinal analysis of pre‐ and posttreatment measurements as bivariate responses is one of analytical methods to compare two treatment groups. Under random allocation, means and variances of pretreatment measurements are expected to be equal between groups, but covariances and posttreatment variances are not. Under random allocation with unequal covariances and posttreatment variances, we compared asymptotic variances of the treatment effect estimators in three longitudinal models. The data‐generating model has equal baseline means and variances, and unequal covariances and posttreatment variances. The model with equal baseline means and unequal variance–covariance matrices has a redundant parameter. In large sample sizes, these two models keep a nominal type I error rate and have high efficiency. The model with equal baseline means and equal variance–covariance matrices wrongly assumes equal covariances and posttreatment variances. Only under equal sample sizes, this model keeps a nominal type I error rate. This model has the same high efficiency with the data‐generating model under equal sample sizes. In conclusion, longitudinal analysis with equal baseline means performed well in large sample sizes. We also compared asymptotic properties of longitudinal models with those of the analysis of covariance (ANCOVA) and t‐test.

Trends in smoking and lung cancer mortality in Japan, by birth cohort, 1949-2010

OBJECTIVE

To determine smoking trends in Japan in comparison with lung cancer mortality.

METHODS

Age-specific smoking prevalence among cohorts born between 1897 and 1985 were determined for the period 1949-2010. The percentages of the cohorts born between 1893 and 1979 who initiated smoking early (e.g. before the age of 20 years) were determined. The results were compared against lung cancer mortality rates in people aged 40-84 years belonging to cohorts born between 1868 and 1968.

FINDINGS

In males, smoking prevalence was generally high, particularly among those born before the late 1950s, and early initiation was fairly uncommon. Early initiation was most common among recent birth cohorts of males, who showed relatively low prevalences of smoking. In females, the prevalence of smoking was generally low and early initiation was very uncommon, particularly among those born in the late 1930s and before the late 1940s, respectively. Recent cohorts of females showed relatively high prevalences of smoking and relatively high percentages of early initiation. In both sexes, lung cancer mortality was generally low but increased over the study period.

CONCLUSION

Lung cancer mortality in Japanese males was relatively low given the high prevalence of smoking, perhaps because early initiation was fairly uncommon. Over the last four decades, however, early initiation of smoking has become more common in both sexes. The adverse effect this is likely to have on lung cancer mortality rates has probably not been observed because of the long time lag between smoking initiation and death from lung cancer.

Analysis of covariance with pre-treatment measurements in randomized trials under the cases that covariances and post-treatment variances differ between groups

When primary endpoints of randomized trials are continuous variables, the analysis of covariance (ANCOVA) with pre-treatment measurements as a covariate is often used to compare two treatment groups. In the ANCOVA, equal slopes (coefficients of pre-treatment measurements) and equal residual variances are commonly assumed. However, random allocation guarantees only equal variances of pre-treatment measurements. Unequal covariances and variances of post-treatment measurements indicate unequal slopes and, usually, unequal residual variances. For non-normal data with unequal covariances and variances of post-treatment measurements, it is known that the ANCOVA with equal slopes and equal variances using an ordinary least-squares method provides an asymptotically normal estimator for the treatment effect. However, the asymptotic variance of the estimator differs from the variance estimated from a standard formula, and its property is unclear. Furthermore, the asymptotic properties of the ANCOVA with equal slopes and unequal variances using a generalized least-squares method are unclear. In this paper, we consider non-normal data with unequal covariances and variances of post-treatment measurements, and examine the asymptotic properties of the ANCOVA with equal slopes using the variance estimated from a standard formula. Analytically, we show that the actual type I error rate, thus the coverage, of the ANCOVA with equal variances is asymptotically at a nominal level under equal sample sizes. That of the ANCOVA with unequal variances using a generalized least-squares method is asymptotically at a nominal level, even under unequal sample sizes. In conclusion, the ANCOVA with equal slopes can be asymptotically justified under random allocation.

Impacts of early smoking initiation: long-term trends of lung cancer mortality and smoking initiation from repeated cross-sectional surveys in Great Britain

OBJECTIVE

To show long-term trends of smoking initiation in Great Britain including unanalysed data and assess the impact of early smoking initiation on the lung cancer mortality in later ages focusing on birth cohorts.

DESIGN

Reanalysis of repeated cross-sectional surveys conducted 13 times during 1965-1987.

SETTING

Great Britain.

PARTICIPANTS

Men and women aged 16 years and over in each survey.

PRIMARY OUTCOME MEASURES

Smoking initiation for 1898-1969 birth cohorts and lung cancer mortality in 1950-2009.

RESULTS

In men, 1900-1925 birth cohorts showed high smoking initiation (>32%, >50% and >80% at 15, 17 and 29 years old, respectively). Correspondingly, the lung cancer mortality in these cohorts exceeded 1 per 1000 at a young age (50-54 years old). In women, smoking initiation increased clearly from the 1898 cohort to the 1925 cohort (2% to 12%, 4% to 24%, and 13% to 54% at 15, 17 and 29 years old, respectively). Correspondingly, the age at which the mortality exceeded 1 per 1000 became younger (75-79 to 60-64 years old). In both men and women, short-term decreases in initiation were seen from the late-1920s cohorts. Correspondingly, lung cancer mortality decreased. In women, initiation increased again after the mid-1930s cohorts, and mortality increased after they became 60-64 years old.

CONCLUSIONS

Clear relationships between smoking initiation and lung cancer mortality across birth cohorts were observed. Countries with rapid increases in initiation in teens should not underestimate the risk in the distant future. Because of the long time lags within cohorts compared with rapid changes in smoking habits across cohorts, age-specific measures focusing on birth cohorts should be monitored.

An estimation method of the clearance for a one-compartment model of a single bolus intravenous injection by a single sampling

In clinical trials, sometimes only a single drug concentration can be measured from a patient, because of the burden on the patient. From a single concentration, we cannot generally obtain point estimates of each pharmacokinetic parameter in a patient. In this article, we propose a method to estimate the clearance using a one-compartment model of a single-bolus intravenous injection from a single concentration at a sampling point between 1.5 and 2.5 half-lives. This method requires an assumed value for the volume of distribution but is robust to misspecification. This approach is illustrated by simulated concentration data and cadralazine concentration data.

The NADH-ubiquinone oxidoreductase 1 alpha subcomplex 5 (NDUFA5) gene variants are associated with autism

OBJECTIVE

Autism appears to have a strong genetic component. The product of the NADH-ubiquinone oxidoreductase 1 alpha subcomplex 5 (NDUFA5) gene is included in the mitochondrial electron transport chain.

METHOD

We performed a case-control study of 235 patients with autism and 214 controls and examined three single-nucleotide polymorphisms (SNPs) within this gene in a Japanese population. We then conducted a transmission disequilibrium test (TDT) analysis in 148 autistic trios.

RESULTS

In the case-control study, two SNPs (rs12666974 and rs3779262) showed a significant association with autism (P=0.00064 and 0.00046 respectively). Furthermore, a haplotype containing these two SNPs showed a significant association (P-global=0.0013, individual haplotype A-A: P=0.010). In TDT analysis, the global and A-A haplotype P-values also indicated significant associations. Minor allele and genotype frequencies were decreased in the autistic subjects.

CONCLUSION

We found significant association between the NDFA5 gene and autism.

An autoregressive linear mixed effects model for the analysis of longitudinal data which include dropouts and show profiles approaching asymptotes

We are interested in longitudinal data of a continuous response that show profiles with an initial sharp change and approaching asymptotes for each patient, and many patients drop out with a reason related to the response. In this paper, we focus on a model that assumes a dropout process is missing at random (MAR). In this dropout process, we can obtain consistent maximum likelihood estimators as long as both the mean and covariance structures are correctly specified. However, parsimonious covariance structures for the profiles approaching asymptotes are unclear. An autoregressive linear mixed effects model can express the profile with random individual asymptotes. We show that this model provides a new parsimonious covariance structure. The covariance structure at steady state is compound symmetry and the other elements of the covariance depend on the measurement points. In simulation studies, the estimate of the asymptote is unbiased in MAR dropouts, but biased in non-ignorable dropouts. We also applied this model to actual schizophrenia trial data.

A bivariate autoregressive linear mixed effects model for the analysis of longitudinal data

In clinical studies, dependent bivariate continuous responses may approach equilibrium over time. We propose an autoregressive linear mixed effects model for bivariate longitudinal data in which the current responses are regressed on the previous responses of both variables, fixed effects, and random effects. The equilibria are modeled using fixed and random effects. This model is a bivariate extension of the model for univariate longitudinal data given by Funatogawa et al. (Statist. Med. 2007; 26:2113-2130). As an illustration of the approach we analyze parathyroid hormone and serum calcium measurements in the treatment of secondary hyperparathyroidism in chronic hemodialysis patients.

Screening method for severe sleep-disordered breathing in hypertensive patients without daytime sleepiness

The high prevalence of sleep-disordered breathing (SDB) in hypertensive patients has been well studied. However, regular screening of SDB in these patients is not performed routinely as the diagnostic procedures are both time-consuming and labour-intensive. Overnight portable device screening is useful, but is sometimes not acceptable for asymptomatic SDB patients. We evaluated the usefulness of daytime 30-min recording with a portable recording device during pulse wave velocity (PWV) measurement sessions as a screening method for detection of asymptomatic SDB in hypertensive patients. Eighty-one hypertensive patients underwent 30-min daytime screening session using a Type III portable recording device during PWV measurement. Each screening session was followed by full overnight Level I polysomnography (PSG). The screening session included recordings of airflow (mouth-nose), chest movement, oximetry, and electrocardiography. The correlation coefficient between respiratory disturbance index (RDI) by screening session and apnea-hypopnea index (AHI) by PSG was 0.64. Using AHI ≥ 30 as diagnostic of severe SDB, 47 of 80 patients had the disorder based on PSG results. Using an RDI cut-off value of 22, the sensitivity and specificity for detection of severe SDB were 86.1% and 64.5%, respectively. Daytime 30-min recording with a portable device for apnea detection during PWV recording is useful for screening of asymptomatic severe SDB in hypertensive patients.

Changes in body mass index by birth cohort in Japanese adults: results from the National Nutrition Survey of Japan 1956-2005

Background The National Nutrition Survey, Japan (NNS-J) provides annual anthropometric information for a whole nation over 50 years. Based on this survey, the mean body mass index (BMI) of Japanese men and elderly women has increased in recent decades, but that of young women has decreased. We examined the effect of birth cohort on this phenomenon.

Methods We analysed data from the NNS-J for subjects aged 20–69 years. BMI during 1956–2005 and the prevalence of overweight and obesity (BMI ≥ 25 kg/m²) during 1976–2005 were estimated.

Results The BMI increased with age in every birth cohort, with similar increments, and did not peak until 60–69 years of age. However, with cross-sectional age, the BMI usually peaked before 60–69 years of age. The differences among cohorts already existed at 20–29 years of age, and slightly increased in men between 20–29 and 30–39 years of age. The BMI in all male age groups increased from the 1891–1900 through 1971–80 cohorts. However, in women, the figure increased until the 1931–40 cohorts, but later decreased. Changes in prevalence were generally consistent with changes in BMI. The recent increase (decrease in young women) in the mean BMI is attributable to birth cohort, indicating that thinner (fatter) and less recent birth cohorts have been replaced by fatter (thinner) ones.

Conclusions A cohort effect was quantitatively demonstrated based on a repeated annual survey. In Japan, the differences in BMI among cohorts were already established by young adulthood.

Do overweight children necessarily make overweight adults? Repeated cross sectional annual nationwide survey of Japanese girls and women over nearly six decades

OBJECTIVE

To compare growth curves of body mass index from children to adolescents, and then to young adults, in Japanese girls and women in birth cohorts born from 1930 to 1999.

DESIGN

Retrospective repeated cross sectional annual nationwide surveys (national nutrition survey, Japan) carried out from 1948 to 2005.

SETTING

Japan.

PARTICIPANTS

76,635 females from 1 to 25 years of age.

MAIN OUTCOME MEASURE

Body mass index.

RESULTS

Generally, body mass index decreased in preschool children (2-5 years), increased in children (6-12 years) and adolescents (13-18 years), and slightly decreased in young adults (19-25 years) in these Japanese females. However, the curves differed among birth cohorts. More recent cohorts were more overweight as children but thinner as young women. The increments in body mass index in early childhood were larger in more recent cohorts than in older cohorts. However, the increments in body mass index in adolescents were smaller and the decrease in body mass index in young adults started earlier, with lower peak values in more recent cohorts than in older cohorts. The decrements in body mass index in young adults were similar in all birth cohorts.

CONCLUSIONS

An overweight birth cohort in childhood does not necessarily continue to be overweight in young adulthood. Not only secular trends in body mass index at fixed ages but also growth curves for wide age ranges by birth cohorts should be considered to study obesity and thinness. Growth curves by birth cohorts were produced by a repeated cross sectional annual survey over nearly six decades.

An estimation method of the half-life for a one-compartment model of a single bolus intravenous injection by a single sampling

In clinical trials, sometimes only a single drug concentration can be measured from a patient because of the patient's burden. In this case, the sampling point is usually identical for all patients. From a single concentration, we cannot generally obtain point-estimates of each pharmacokinetic parameter. In this paper, we propose a method to estimate the half-life of a one-compartment model of a single bolus intravenous injection from a single concentration at a sampling point of or after three half-lives. We analytically show that the later the sampling point is the better estimate of the half-life we can get. This approach is illustrated by simulated concentration-data and nicorandil concentration-data. Therefore, we compared the performance of the proposed method with that of the Bayesian approach.

Tachykinin 1 (TAC1) gene SNPs and haplotypes with autism: a case-control study

Autism (MIM 209850) is a severe neurodevelopmental disorder characterized by disturbances in social interaction and communication, by repetitive body movements and restricted interests, and by atypical language development. Several twin and family studies have shown strong evidence for genetic factors in the etiology of autism. Glutamate is a major excitatory neurotransmitter in the human brain. Glutamate systems are involved in the pathophysiology of autism. There are many similarities between the symptoms evoked by glutamate antagonist treatment and symptoms of autism found in several human and animal studies. To elucidate the genetic background of autism, we analyzed the relationship between three single nucleotide polymorphisms (SNPs) of the Tachykinin 1 gene (TAC1) and autism, because TAC1 is located in the candidate region for autism and produces substance P and neurokinins. These products modulate glutamatergic excitatory synaptic transmission and are also involved in inflammation. Many different inflammation-related mechanisms could be involved in the autistic brain. Therefore, TAC1 may have some functions associated with the presumable pathophysiology of autism. We compared the allele and haplotype frequencies between autistic patients (n=170) and normal controls (n=214) in the Japanese population, but no significant difference was observed. Thus, the TAC1 locus is not likely to play a major role in the development of autism.

An autoregressive linear mixed effects model for the analysis of longitudinal data which show profiles approaching asymptotes

In longitudinal data, a continuous response sometimes shows a profile approaching an asymptote. For such data, we propose a new class of models, autoregressive linear mixed effects models in which the current response is regressed on the previous response, fixed effects, and random effects. Asymptotes can shift depending on treatment groups, individuals, and so on, and can be modelled by fixed and random effects. We also propose error structures that are useful in practice. The estimation methods of linear mixed effects models can be used as long as there is no intermittent missing.

No association between the neuronal pentraxin II gene polymorphism and autism

Autism (MIM 209850) is a neurodevelopmental disorder characterized by difficulties with verbal and non-verbal communication, impairments in reciprocal social interactions, and displays of stereotypic behaviors, interests and activities. Twin and family studies have indicated a robust role of genetic factors in the development of autism. Neuronal Pentraxin II (NPTX2) is located in chromosome 7q21.3-q22.1, where it is a candidate region for autism. NPTX2 promotes neuritic outgrowth and is suggested to mediate uptake of degraded synaptic material during synapse formation and remodeling. NPTX2 is also associated with the clustering of synaptic AMPA receptors. It was reported that glutamate systems including AMPA receptor was associated to the pathophysiology of autism. Thus, the NPTX2 gene is involved in neuritic outgrowth, synapse remodeling and the aggregation of neurotransmitter receptors at synapses. These functions play an important role in the mechanisms of learning and brain development. In the present study, we tested for the presence of the association of four single nucleotide polymorphisms (SNPs) of NPTX2 and haplotypes consisting of the SNPs with autism, between autistic patients (n=170) and normal controls (n=214) in a Japanese population. No significant difference was observed in the allele, genotype or haplotype frequencies between the patients and controls. Thus, the NPTX2 locus is not likely to play a major role in the development of autism. However, further studies with larger sample size and sequencing of NPTX2 gene are needed to exclude a role of NPTX2 gene in autism.

The Bayesian Bias Correction Method of the First-Order Approximation of Nonlinear Mixed-Effects Models for Population Pharmacokinetics

Population pharmacokinetic analysis usually employs nonlinear mixed-effects models. To estimate the parameters, Beal and Sheiner (1982) proposed the first-order method that employs a first-order Taylor series expansion around the means of random individual parameters. Because of the small computational burden and the high convergence proportion of maximization of the log likelihood function, this method is often used in practice. However, it is known that the estimates are biased. This paper proposes a simple procedure to reduce the bias. The proposed method maximizes the nonapproximated log likelihood functions of each individual given estimates of the population parameters derived from the first-order method, and the derived Bayes estimates of the random individual parameters are utilized to improve the estimates of the population mean parameters. We confirmed that the proposed method reduced the bias using simulated data and actual erythropoietin concentration data.

Profile Likelihood-Based Confidence Intervals Using Monte Carlo Integration for Population Pharmacokinetic Parameters

Population pharmacokinetic (PPK) analysis usually employs nonlinear mixed effects models using first-order linearization methods. It is well known that linearization methods do not always perform well in actual situations. To avoid linearization, the Monte Carlo integration method has been proposed. Moreover, we generally utilize asymptotic confidence intervals for PPK parameters based on Fisher information. It is known that likelihood-based confidence intervals are more accurate than those from the usual asymptotic confidence intervals. We propose profile likelihood-based confidence intervals using Monte Carlo integration. We have evaluated the performance of the proposed method through a simulation study, and analyzed the erythropoietin concentration data set by the method.

No association of FOXP2 and PTPRZ1 on 7q31 with autism from the Japanese population

Autism is a child-onset pervasive developmental disorder, with a significant role of genetic factors in its development. Genome-wide linkage studies have suggested a 7q region as a susceptibility locus for autism. We investigated several single nucleotide polymorphisms (SNPs) of Forkhead Box P2 (FOXP2) and Protein-Tyrosine Phosphatase, Receptor-type, Zeta-1 (PTPRZ1) at the 7q region in Japanese patients with autism and healthy controls. No significant difference was observed, after correction for the multiple testing, in allele, genotype or haplotype frequencies of the SNPs of FOXP2 or PTPRZ1 between patients and controls. No evidence was thus obtained for a major role of FOXP2 or PTPRZ1 in the development of autism.