A new statistical test for age-of-onset anticipation: application to bipolar disorder

The Contribution of Somatic Expansion of the CAG Repeat to Symptomatic Development in Huntington's Disease: A Historical Perspective

The discovery in the early 1990s of the expansion of unstable simple sequence repeats as the causative mutation for a number of inherited human disorders, including Huntington’s disease (HD), opened up a new era of human genetics and provided explanations for some old problems. In particular, an inverse association between the number of repeats inherited and age at onset, and unprecedented levels of germline instability, biased toward further expansion, provided an explanation for the wide symptomatic variability and anticipation observed in HD and many of these disorders. The repeats were also revealed to be somatically unstable in a process that is expansion-biased, age-dependent and tissue-specific, features that are now increasingly recognised as contributory to the age-dependence, progressive nature and tissue specificity of the symptoms of HD, and at least some related disorders. With much of the data deriving from affected individuals, and model systems, somatic expansions have been revealed to arise in a cell division-independent manner in critical target tissues via a mechanism involving key components of the DNA mismatch repair pathway. These insights have opened new approaches to thinking about how the disease could be treated by suppressing somatic expansion and revealed novel protein targets for intervention. Exciting times lie ahead in turning these insights into novel therapies for HD and related disorders.

Telomere shortening is associated with genetic anticipation in Chinese Von Hippel-Lindau disease families

Von Hippel-Lindau (VHL) disease is a rare autosomal dominant cancer syndrome. A phenomenon known as genetic anticipation has been documented in some hereditary cancer syndromes, where it was proved to relate to telomere shortening. Because studies of this phenomenon in VHL disease have been relatively scarce, we investigated anticipation in 18 Chinese VHL disease families. We recruited 34 parent-child patient pairs (57 patients) from 18 families with VHL disease. Onset age was defined as the age when any symptom or sign of VHL disease first appeared. Anticipation of onset age was analyzed by paired t test and the other two special tests (HV and RY2). Relative telomere length of peripheral leukocytes was measured in 29 patients and 325 healthy controls. Onset age was younger in child than in parent in 31 of the 34 parent-child pairs. Patients in the first generation had older onset age with longer age-adjusted relative telomere length, and those in the next generation had younger onset age with shorter age-adjusted relative telomere length (P < 0.001) in the 10 parent-child pairs from eight families with VHL disease. In addition, relative telomere length was shorter in the 29 patients with VHL disease than in the normal controls (P = 0.003). The anticipation may relate to the shortening of telomere length in patients with VHL in successive generations. These findings indicate that anticipation is present in families with VHL disease and may be helpful for genetic counseling for families with VHL disease families and for further understanding the pathogenesis of VHL disease.

Anticipation in lynch syndrome: where we are where we go

Lynch syndrome (LS) is the most common form of inherited predisposition to develop cancer mainly in the colon and endometrium but also in other organ sites. Germline mutations in DNA mismatch repair (MMR) gene cause the transmission of the syndrome in an autosomal dominant manner. The management of LS patients is complicated by the large variation in age at cancer diagnosis which requires these patients to be enrolled in surveillance protocol starting as early as in their second decade of life. Several environmental and genetic factors have been proposed to explain this phenotypic heterogeneity, but the molecular mechanisms remain unknown. Although the presence of genetic anticipation in Lynch syndrome has been suspected since 15 years, only recently the phenomenon has been increasingly reported to be present in different cancer genetic syndromes including LS. While the biological basis of earlier cancer onset in successive generations remains poorly known, recent findings point to telomere dynamics as a mechanism significantly contributing to genetic anticipation in Lynch syndrome and in other familial cancers. In this review, we summarize the clinical and molecular features of Lynch syndrome, with a particular focus on the latest studies that have investigated the molecular mechanisms of genetic anticipation.

Bayesian modeling for genetic anticipation in presence of mutational heterogeneity: a case study in Lynch syndrome

Genetic anticipation, described by earlier age of onset (AOO) and more aggressive symptoms in successive generations, is a phenomenon noted in certain hereditary diseases. Its extent may vary between families and/or between mutation subtypes known to be associated with the disease phenotype. In this article, we posit a Bayesian approach to infer genetic anticipation under flexible random effects models for censored data that capture the effect of successive generations on AOO. Primary interest lies in the random effects. Misspecifying the distribution of random effects may result in incorrect inferential conclusions. We compare the fit of four-candidate random effects distributions via Bayesian model fit diagnostics. A related statistical issue here is isolating the confounding effect of changes in secular trends, screening, and medical practices that may affect time to disease detection across birth cohorts. Using historic cancer registry data, we borrow from relative survival analysis methods to adjust for changes in age-specific incidence across birth cohorts. Our motivating case study comes from a Danish cancer register of 124 families with mutations in mismatch repair (MMR) genes known to cause hereditary nonpolyposis colorectal cancer, also called Lynch syndrome (LS). We find evidence for a decrease in AOO between generations in this article. Our model predicts family-level anticipation effects that are potentially useful in genetic counseling clinics for high-risk families.

A review of statistical methods for testing genetic anticipation: looking for an answer in Lynch syndrome

Anticipation, manifested through decreasing age of onset or increased severity in successive generations, has been noted in several genetic diseases. Statistical methods for genetic anticipation range from a simple use of the paired t-test for age of onset restricted to affected parent-child pairs to a recently proposed random effects model which includes extended pedigree data and unaffected family members [Larsen et al., 2009]. A naive use of the paired t-test is biased for the simple reason that age of onset has to be less than the age at ascertainment (interview) for both affected parent and child, and this right truncation effect is more pronounced in children than in parents. In this study, we first review different statistical methods for testing genetic anticipation in affected parent-child pairs that address the issue of bias due to right truncation. Using affected parent-child pair data, we compare the paired t-test with the parametric conditional maximum likelihood approach of Huang and Vieland [1997] and the nonparametric approach of Rabinowitz and Yang [1999] in terms of Type I error and power under various simulation settings and departures from the modeling assumptions. We especially investigate the issue of multiplex ascertainment and its effect on the different methods. We then focus on exploring genetic anticipation in Lynch syndrome and analyze new data on the age of onset in affected parent-child pairs from families seen at the University of Michigan Cancer Genetics clinic with a mutation in one of the three main mismatch repair (MMR) genes. In contrast to the clinic-based population, we re-analyze data on a population-based Lynch syndrome cohort, derived from the Danish HNPCC-register. Both datasets indicate evidence of genetic anticipation in Lynch syndrome. We then expand our review to incorporate recently proposed statistical methods that consider family instead of affected pairs as the sampling unit. These prospective censored regression models offer additional flexibility to incorporate unaffected family members, familial correlation and other covariates into the analysis. An expanded dataset from the Danish HNPCC-register is analyzed by this alternative set of methods.

An effect from anticipation also in hereditary nonpolyposis colorectal cancer families without identified mutations

Optimal prevention of hereditary cancer is central and requires initiation of surveillance programmes and/or prophylactic measures at a safe age. Anticipation, expressed as an earlier age at onset in successive generations, has been demonstrated in hereditary nonpolyposis colorectal cancer (HNPCC). We specifically addressed anticipation in phenotypic HNPCC families without disease-predisposing mismatch repair (MMR) defects since risk estimates and age at onset are particularly difficult to determine in this cohort. The national Danish HNPCC register was used to identify families who fulfilled the Amsterdam criteria for HNPCC and showed normal MMR function and/or lack of disease-predisposing MMR gene mutation. In total, 319 cancers from 212 parent-child pairs in 99 families were identified. A paired t-test and a bivariate statistical model were used to assess anticipation. Both methods demonstrated an effect from anticipation with cancer diagnosed mean 11.4 years (t-test, p<0.0001) and mean 5.9 (bivariate model, p=0.02) years earlier in children than in parents. This observation suggests that anticipation may apply also to families without identified mutations and serves as a reminder to initiate surveillance programmes at young age also in HNPCC families with undefined genetic causes.

Role for genetic anticipation in Lynch syndrome

PURPOSE

Anticipation (ie, an earlier age at onset in successive generations) is linked to repeat expansion in neurodegenerative syndromes, whereas its role in hereditary cancer is unclear. We assessed anticipation in Lynch syndrome (hereditary nonpolyposis colorectal cancer [HNPCC]), in which DNA mismatch repair (MMR) defects cause early and accelerated tumor development with a broad tumor spectrum.

PATIENTS AND METHODS

In the population-based Danish HNPCC registry, 407 MMR gene mutation carriers who had developed cancer associated with Lynch syndrome, were identified. These individuals formed 290 parent-child pairs in which age at the first cancer diagnosis was assessed. A paired t-test and a specifically developed bivariate model were used to assess a possible role of anticipation.

RESULTS

Both methods revealed anticipation with children developing cancer mean 9.8 years (P < .001) earlier than parents using the paired t-test and 5.5 years (P < .001) earlier using the bivariate model. Birth cohort effects were excluded since anticipation with 7.2 years earlier age at onset was identified also in the oldest cohort, in which the children were observed until they were older than 80 years. The effect remained when cancers diagnosed at surveillance were excluded, applied to maternal as well as paternal inheritance, and was independent of the MMR gene mutated.

CONCLUSION

The effect from anticipation demonstrated in this large, population-based Lynch syndrome cohort underscores the need to initiate surveillance programs at young age. It should also stimulate research into the genetic mechanisms that determine age at onset and whether the genetic instability that characterizes Lynch syndrome can be linked to anticipation.

New simple tests for age-at-onset anticipation: application to panic disorder

Recently, testing for anticipation has received renewed interest. It is well known that standard statistical methods are inappropriate for this purpose due to problems of sampling bias. Few statistical tests have been proposed for comparing mean age of onset in affected parents with mean age of onset in affected children. All of them are difficult to compute and lack software to perform the tests. In this report, we formulate the problem in terms of symmetry tests. We propose a simple generalized paired t-test and a Wilcoxon signed rank test to adjust for the bias caused by the right truncation of both the parent's and child's ages at onset. We also extend the generalized paired t-test to a random effects model that enables analysis of correlated data from nuclear families, and could be further extended to larger family structures. We illustrate the approaches with an example of panic disorder.

Perspectives on familial chronic lymphocytic leukemia: genes and the environment

Chronic lymphocytic leukemia (CLL) comprises a substantial proportion of leukemias in adults in the western hemisphere. Male gender, increasing age, ethnicity (high in Caucasians, lowest in Asians), and family history are risk factors. Although no specific extrinsic etiologic factors have been established, farming and pesticide exposure are associated with increased risk. Migration studies confirm that ethnic groups retain the risk associated with their origin rather than their new location, favoring a role for heredity. Kindreds with multiple cases of CLL have been well described in the literature and studies in large populations confirm that lymphoproliferative malignancies and especially CLL occur together at a rate that cannot be attributed to chance. Since environmental factors cannot readily explain the familial aggregations, a hereditary factor that affects susceptibility to CLL is likely. The identification of clones that are immunophenotypically identical to CLL in healthy individuals from CLL kindreds (14% to 18%) as well as in the general population (3.5% in age bracket >65 years) suggests a possible precursor condition, but longitudinal studies will be necessary to establish significance in the general population. Family (linkage) and population (candidate gene) studies to date have been too small to identify the specific genes that account for increased susceptibility; larger studies including planned consortia to identify additional high-risk kindreds for genetic studies, as well as the application of advanced technologies such as genomics, cytogenetic, expression, and proteomics, are widely expected to advance understanding over the next few years.

Familial risk of lymphoproliferative tumors in families of patients with chronic lymphocytic leukemia: results from the Swedish Family-Cancer Database

The importance of genetic factors in etiology of chronic lymphocytic leukemia (CLL) is suggested by family and population studies. However, the spectrum of malignancies sharing common genetic factors with CLL and the effects of sex and age on familial risk are unknown. We used the Swedish Family-Cancer Database to test for increased familial risks of CLL and other lymphoproliferative tumors. Cancer diagnoses from 1958 to 1998 were assessed in 14 336 first-degree relatives of 5918 CLL cases and in 28 876 first-degree relatives of 11 778 controls. Cancer risks in relatives of cases were compared with those in relatives of controls using marginal survival models. Relatives of cases were at significantly increased risk for CLL (relative risk [RR] = 7.52; 95% confidence interval [CI], 3.63-15.56), for non-Hodgkin lymphoma (RR = 1.45; 95% CI, 0.98-2.16), and for Hodgkin lymphoma (RR = 2.35; 95% CI, 1.08-5.08). CLL risks were similar in parents, siblings, and offspring of cases, in male and female relatives, and were not affected by the case's age at diagnosis. Anticipation was not significant when analyzed using life table methods. We conclude that the familial component of CLL is shared with other lymphoproliferative malignances, suggesting common genetic pathways. However, because clinically diagnosed CLL is uncommon, absolute excess risk to relatives is small.

Anticipation and repeat expansion in bipolar disorder

Anticipation is the phenomenon whereby a disease becomes more severe and/or presents with earlier onset as it is transmitted down through generations of a family. The only known mechanism for true anticipation is a class of mutations containing repetitive sequences exemplified by the pathogenic trinucleotide repeat. Studies of bipolar disorder (BPD) are consistent with the presence of anticipation and, by inference, the possibility that trinucleotide repeats contribute to this disorder, although it is possible that these data are the result of methodological problems. On the assumption that anticipation in BPD may be real, several surveys of the genome of BPD probands for large trinucleotide repeats have been conducted, as have studies of many repeat-containing candidate genes. No pathogenic triplet repeat has yet been unambiguously implicated.

The unstable trinucleotide repeat story of major psychosis

New hopes for cloning susceptibility genes for schizophrenia and bipolar affective disorder followed the discovery of a novel type of DNA mutation, namely unstable DNA. One class of unstable DNA, trinucleotide repeat expansion, is the causal mutation in myotonic dystrophy, fragile X mental retardation, Huntington disease and a number of other rare Mendelian neurological disorders. This finding has led researchers in psychiatric genetics to search for unstable DNA sites as susceptibility factors for schizophrenia and bipolar affective disorder. Increased severity and decreased age at onset of disease in successive generations, known as genetic anticipation, was reported for undifferentiated psychiatric diseases and for myotonic dystrophy early in the twentieth century, but was initially dismissed as the consequence of ascertainment bias. Because unstable DNA was demonstrated to be a molecular substrate for genetic anticipation in the majority of trinucleotide repeat diseases including myotonic dystrophy, many recent studies looking for genetic anticipation have been performed for schizophrenia and bipolar affective disorder with surprisingly consistent positive results. These studies are reviewed, with particular emphasis placed on relevant sampling and statistical considerations, and concerns are raised regarding the interpretation of such studies. In parallel, molecular genetic investigations looking for evidence of trinucleotide repeat expansion in both schizophrenia and bipolar disorder are reviewed. Initial studies of genome-wide trinucleotide repeats using the repeat expansion detection technique suggested possible association of large CAG/CTG repeat tracts with schizophrenia and bipolar affective disorder. More recently, three loci have been identified that contain large, unstable CAG/CTG repeats that occur frequently in the population and seem to account for the majority of large products identified using the repeat expansion detection method. These repeats localize to an intron in transcription factor gene SEF2-1B at 18q21, a site named ERDA1 on 17q21 with no associated coding region, and the 3' end of a gene on 13q21, SCA8, that is believed to be responsible for a form of spinocerebellar ataxia. At present no strong evidence exists that large repeat alleles at either SEF2-1B or ERDA1 are involved in the etiology of schizophrenia or bipolar disorder. Preliminary evidence suggests that large repeat alleles at SCA8 that are non-penetrant for ataxia may be a susceptibility factor for major psychosis. A fourth, but much more infrequently unstable CAG/CTG repeat has been identified within the 5' untranslated region of the gene, MAB21L1, on 13q13. A fifth CAG/CTG repeat locus has been identified within the coding region of an ion transporter, KCNN3 (hSKCa3), on 1q21. Although neither large alleles nor instability have been observed at KCNN3, this repeat locus has been extensively analyzed in association and family studies of major psychosis, with conflicting findings. Studies of polyglutamine containing genes in major psychosis have also shown some intriguing results. These findings, reviewed here, suggest that, although a major role for unstable trinucleotides in psychosis is unlikely, involvement at a more modest level in a minority of cases cannot be excluded, and warrants further investigation.

Triplet repeats and bipolar disorder

Anticipation, the phenomenon of a disease becoming more severe or having earlier onset as it is transmitted down the generations, was originally described in families with psychiatric illness but was thought due to ascertainment bias and became forgotten. Interest was rekindled when a number of neurodegenerative disorders that show this phenomenon, were found to be due to a novel form of mutation--unstable triplet repeats showing intergenerational expansion. Some recent studies of anticipation are consistent with its occurrence in bipolar disorder but are still associated with methodological problems making interpretation difficult. A number of case-control studies employing the repeat expansion detection (RED) technique have found longer repeats in bipolar probands but other studies have found no such association. Despite a large number of studies examining the role of various repeat containing candidate genes, a pathogenic triplet repeat has yet to be found for bipolar disorder. It is likely that the controversy surrounding anticipation and the existence of triplet repeats will only finally be resolved with the demonstration of such a mutation in the aetiology of bipolar disorder.

Studies of anticipation in bipolar affective disorder

Anticipation refers to the increase in disease severity or decrease in age of onset in successive generations. The concept evolved from the theories and dogma of degeneration that were pervasive in psychiatry and medicine in the late 19th century and into the early 20th century. The term was set aside with the criticism of geneticist Lionel Penrose, who argued that anticipation was the result of ascertainment biases. The renewed interest in anticipation followed the identification of its molecular genetic basis in the form of unstable trinucleotide repeats. Subsequently, several diseases have been studied clinically for the presence of anticipation. Although anticipation has been identified in many diseases, including bipolar disorder, only diseases showing a pattern of progressive neurodegeneration have been associated with unstable trinucleotide repeats. This review summarizes the research on anticipation in bipolar disorder and other secular trends in the patterns of the illness such as the cohort effect. The changing nature of bipolar disorder is likely to be a result of combined influences from several genes, some of which are likely to be in a state of flux, as well as environmental or cultural forces that converge to give the clinical picture of anticipation.

Trinucleotide repeat expansions: do they contribute to bipolar disorder?

It has long been known that bipolar disorder has a true but complex genetic background. Reports on genetic anticipation in bipolar disorder opened the way to a new approach for genetic studies. Indeed, anticipation, a decreasing age at onset, and/or increasing disease severity in successive generations, were recently explained by an expansion of trinucleotide repeats in monogenic diseases like Huntington's disease and Fragile X syndrome. The involvement of trinucleotide repeat expansions in bipolar disorder received even more support when studies reported association of large CAG/CTG repeats with bipolar disorder. Even though a large number of studies have been conducted, this association is still unexplained. Here, we review the studies investigating the trinucleotide repeat expansion hypothesis in bipolar disorder. Studies on anticipation, on association of anonymous large CAG/CTG repeats and on specific trinucleotide repeats are critically analysed and discussed, showing a field with precipitate conclusions or inconclusive results. The analysis suggests that there are indications, though disputable, supporting the trinucleotide repeat expansion hypothesis in bipolar disorder, but no conclusive evidence has been hitherto provided.

Genetic survival analysis of age-at-onset of bipolar disorder: evidence for anticipation or cohort effect in families

Age-at-onset (AAO) in a number of extended families ascertained for bipolar disorder was analysed using survival analysis techniques, fitting proportional hazards models to estimate the fixed effects of sex, year of birth, and generation, and a random polygenic genetic effect. Data comprised the AAO (for 171 affecteds) or age when last seen (ALS) for 327 unaffecteds, on 498 individuals in 27 families. ALS was treated as the censored time in the statistical analyses. The majority of individuals classified as affected were diagnosed with bipolar I and II (n = 103) or recurrent major depressive disorder (n = 68). In addition to the significant effects of sex and year of birth, a fitted 'generation' effect was highly significant, which could be interpreted as evidence for an anticipation effect. The risk of developing bipolar or unipolar disorder increased twofold with each generation descended from the oldest founder. However, although information from both affected and unaffected individuals was used to estimate the relative risk of subsequent generations, it is possible that the results are biased because of the 'Penrose effect'. Females had a twofold increased risk in developing depressive disorder relative to males. The risk of developing bipolar or unipolar disorder increased by approximately 4% per year of birth. A polygenic component of variance was estimated, resulting in a 'heritability' of AAO of approximately 0.52. In a family showing strong evidence of linkage to chromosome 4p (family 22), the 'affected haplotype' increased the relative risk of being affected by a factor of 46. In this family, there was strong evidence of a time trend in the AAO. When either year of birth or generation was fitted in the model, these effects were highly significant, but neither was significant in the presence of the other. For this family, there was no increase in trinucleotide repeats measured by the repeat expansion detection method in affected individuals compared with control subjects. Proportional hazard models appear appropriate to analyse AAO data, and the methodology will be extended to map quantitative trait loci (QTL) for AAO.

Assessing changes in ages at onset over successive generation: an application to breast cancer

Decreased age at onset in successive generations has been observed for a number of diseases. Two nonparametric matched and unmatched test statistics are proposed, taking into account not only current age or age at death for unaffected individuals and age at disease onset for affected individuals, but also possible correlations among family members. Both are asymptotically normal with readily estimated variances from the data. A simulation study is conducted to compare the proposed tests with the commonly used paired t-test and log-rank test. It has been shown that the proposed test statistics yield valid conclusions in assessing genetic anticipation under all situations considered. However, the paired t-test is valid only when the censoring distributions are comparable between two generations, whereas the log-rank test is valid when the correlation among family members is weak. As expected, the matched test is most powerful when the data are heterogeneous, and the unmatched and the log-rank tests are most powerful when the data are homogeneous and the correlation is weak. Lastly, a population-based family study of breast cancer conducted at the Fred Hutchinson Cancer Research Center is used for illustration of the proposed and the log-rank tests. The preliminary analysis suggests that there appears a decreased age at onset over the successive generations in breast cancer.

Testing for age-at-onset anticipation with affected parent-child pairs

The tendency for the onset of a genetic disease to occur at progressively earlier ages or with progressively greater severity in successive generations is known as anticipation. Following the discovery of trinucleotide repeat expansion as a plausible genetic mechanism for anticipation, interest in testing for anticipation has increased. Studies of anticipation can be biased when parents with late onset or children with early onset are preferentially ascertained. This paper presents a nonparametric approach to testing for age-at-onset anticipation that adjusts for such preferential ascertainment. The approach is illustrated through application to data on panic disorder.

Genetic anticipation and breast cancer: a prospective follow-up study

Genetic anticipation is characterized by an earlier age of disease onset, increased severity, and a greater proportion of affected individuals in succeeding generations. The discovery of trinucleotide repeat expansion (TRE) mutations as the molecular correlate of anticipation in a number of rare Mendelian neurodegenerative disorders has led to a resurgence of interest in this phenomenon. Because of the difficulties presented to traditional genetics by complex diseases, the testing for genetic anticipation coupled with TRE detection has been proposed as a strategy for expediting the identification of susceptibility genes for complex disorders. In the case of breast cancer, a number of previous studies found evidence consistent with genetic anticipation. It is known that a proportion of such families are linked to either BRCA1 or BRCA2, but no TRE mutations have been identified. It has been shown that the typical ascertainment employed in studies purporting to demonstrate genetic anticipation combined with unadjusted statistical analysis can dramatically elevate the type I error. We re-examine the evidence for anticipation in breast cancer by applying a new statistical approach that appears to have validity in the analysis of anticipation to data ascertained from a recent follow-up of a large prospective cohort family study of breast cancer. Using this approach, we find no statistically significant evidence for genetic anticipation in familial breast cancer. We discuss the limitations of our analysis, including the problem of adequate sample size for this new statistical test.

Statistical evaluation of age-at-onset anticipation: a new test and evaluation of its behavior in realistic applications

The discovery that microsatellite repeat expansions can cause clinical disease has fostered renewed interest in testing for age-at-onset anticipation (AOA). A commonly used procedure is to sample affected parent-child pairs (APCPs) from available data sets and to test for a difference in mean age at onset between the parents and the children. However, standard statistical methods fail to take into account the right truncation of both the parent and child age-at-onset distributions under this design, with the result that type I error rates can be inflated substantially. Previously, we had introduced a new test, based on the correct, bivariate right-truncated, age-at-onset distribution. We showed that this test has the correct type I error rate for random APCPs, even for quite small samples. However, in that paper, we did not consider two key statistical complications that arise when the test is applied to realistic data. First, affected pairs usually are sampled from pedigrees preferentially selected for the presence of multiple affected individuals. In this paper, we show that this will tend to inflate the type I error rate of the test. Second, we consider the appropriate probability model under the alternative hypothesis of true AOA due to an expanding microsatellite mechanism, and we show that there is good reason to believe that the power to detect AOA may be quite small, even for substantial effect sizes. When the type I error rate of the test is high relative to the power, interpretation of test results becomes problematic. We conclude that, in many applications, AOA tests based on APCPs may not yield meaningful results.