The stati sti cs of suicide

Robert D. GIBBONS

·Biostatistics in psychiatry (14】·

The stati sti cs of suicide

Robert D. GIBBONS

1. Why is suicide so important to study?

Worldwide， there are about one million suicides annually. In the United States （USA） approximately 750，000 people died by suicide over the last 25 years.Suicides outnumber homicides by at least a 3:2 rati o in the USA. Deaths from suicide exceeded deaths from AIDS by 200 000 in the past 20 years. Four ti mes as many Americans died by suicide during the Vietnam War than from warti me fatalities.[1]Nore deaths by suicide were recorded among American military during the recent Iraq and Afghanistan wars than were recorded for military related casualti es.[2]Nonetheless， suicide is a rare event with an annual rate in the US of 12 per 100 000， making it an extremely difficult phenomenon to study using conventional approaches. Suicide is the third leading cause of death in adolescents 10 to 14 years of age in the US and the leading cause of death in this age group in several other countries including China， Sweden， Ireland， Australia and New Zealand.[1]

The enormous human cost of suicide in youth makes research and preventi on a national priority.Over 90% of youth suicides in the USA are associated with psychiatric illness；[1，3，4]however， only 2% of youth suicides were on medication at the ti me of their suicide.[5，6]In a study of 49 adolescent suicides in Utah State， 24% had been prescribed anti depressants but none of them tested positive for anti depressants at the ti me of their death.[7]In a post-mortem study conducted on 66 youth suicides in New York City，[5]only four had measurable levels of anti depressants （2 with imipramine and 2 with fl uoxeti ne）.

Suicide is rare in younger children （less than 1/100 000 per year in 5- to 14- year-olds[1]）， but it is more common aft er mid-adolescence. The annual rates in the US of 15- to 19-year-olds are 3 per 100 000 for girls and 15 per 100 000 for boys.[8]In contrast to suicide mortality， suicidal thinking and suicide attempts are relatively common: every year， 19% of teenagers 15 to 19 years of age in the general USA populati on have suicidal ideation and nearly 9% make a suicide attempt.[9]The rate of suicidal behavior is even more frequent in youth receiving care for depression； 35 to 50% have made， or will make， a suicide attempt[10-12]and between 2 and 8% will die by suicide over the decade following their fi rst treatment.[10，11，13]

2. Why is suicide diffi cult to study?

For many reasons， suicide is one of the more diffi cult adverse events to study. First， suicide is a rare event so it is generally not possible to study completed suicide in RCTs or even in reasonably large pharmacoepidemiologic studies. Consequently， the suicidal events that form the basis for preventi on measures （such as the FDA black-box warnings）are usually suicidal thoughts， which are far more prevalent than suicide completi ons or suicide att empts（parti cularly in psychiatric populati ons） but may be of limited value in predicting completed suicide.

Large scale pharmacoepidemiologic studies generally focus on suicide att emptsor acts of deliberate self-harm，though in some cases they also include a small number of completed suicides， particularly in countries where national death registries are linkable to health services uti lizati on data， which is generally not true in the USA.These observational studies oft en suffer from selection bias that can result in ‘confounding by indicati on’ and other problems which limit our ability to draw causal inferences. For example， patients with depression have both an increased risk of suicidal behavior and an increased likelihood of taking anti depressant medications； hence the appearance of an association between taking anti depressants and suicidal events that is invariably found is confounded by the indication for the use of anti depressants， namely depression.While anti depressants may increase risk of suicidal events， suicidal events def i nitely increase thelikelihood of anti depressant treatment. As shown by Simon and colleagues，[14]the greatest risk of suicidal behavior is in the month prior to treatment initiation.The same confounding by indication problem exists for the purported role of anti -smoking medicati ons and anti -epilepti c medicati ons in suicidal behavior: pati ents with psychiatric illness have elevated rates of smoking so they are more likely to use anti -smoking medications and several anti -epileptic medications are oft en prescribed as adjunctive treatment of bipolar disorder.

Selection effects are generally eliminated in RCTs，but RCTs are not without their own set of problems which limit inferences. As discussed above， given their limited size， RCTs are generally only able to examine suicidal ideati on， which may tell us litt le about suicide risk. Traditi onally， RCTs have not been designed to examine suicide risk； they are usually focused on retrospecti ve spontaneous reports of suicidal thoughts and behaviors of study participants. Such data are subject to ascertainment bias[15]in which the method of eliciting the suicidal informati on can result in apparent differences in the rates of these events between treated subjects and untreated controls. For example，pati ents randomized to active medication will have more side-effects in general than patients randomized to placebo； this will result in greater contact with study staff and more opportunity to report suicidal thoughts and behavior. Similarly， suicide attempts in which the individual ingests the study medicati on will result in increased likelihood of detection among actively treated subjects because overdose of active medication（e.g.， an anti depressant） will have a greater likelihood of emergency room contact than overdose of an inert placebo.

3. What do we know about suicide and anti depressants?

One of the greatest recent controversies in the safety of pharmaceuti cals is the question of whether certain classes of medicati ons （e.g.， anti depressants） increase the risk of suicidal thoughts， behavior， and completion. In 2004， the US Food and Drug Administration （FDA） placed a black-box warning on all anti depressants because of concern that such medications increased risk of suicidal thoughts and behavior in children and， in 2006， extended the warning to young adults. These warnings are not limited to anti depressants， but have also been placed on anti -epilepti cs， smoking cessati on drugs （varenicline），acne medicati ons such as isotreti noin， beta blockers，reserpine and drugs for weight loss.[16]This topic was discussed in a recent paper in the Shanghai Archives of Psychiatry.[17]A recent review by Gibbons and Nann[18]provides a detailed summary of the recent research about the relati onship between medicati on use and suicide.

Questi ons regarding a possible relati onship between anti depressants and suicide emerged in 1990 with the publicati on of a series of case reports in which the then newly introduced selecti ve serotonin reuptake inhibitors（SSRIs） were associated with the apparent emergence of suicidal thoughts and behavior.[19]These early observati ons led to US FDA hearings in 1991 that did not fi nd evidence of an increased risk of suicidal acts associated with anti depressants. These early case studies set the stage for the development of new approaches to the analysis of pharmacovigilance data in general and with respect to suicide in parti cular. Att enti on to the potenti al relati onship between anti depressants and suicide led to a US black-box warning for children under 18 years of age in October 2004. The evidence supporti ng the warning was a meta-analysis conducted by the FDA，[20]which combined spontaneous reports of suicidal thoughts and behaviors from 25 placebocontrolled pediatric RCTs of newer anti depressant medications. The conclusion was that higher rates of self-reported suicidal ideati on and behavior occurred in children treated with anti depressants than in those receiving placebo （OR=1.78； 95% CI=1.14， 2.77）. The FDA also presented results of an analysis of prospecti ve data （based on a suicidal ideation or behavior rati ngscale item）， which showed no effect of anti depressant use on the emergence or worsening of suicidal thoughts and behaviors （OR=0.92； CI=0.76， 1.11）. The difference between prospective clinician ratings and spontaneous patient reports of suicidal ideation and behavior has never been adequately explained； it may be due to ascertainment bias between active treatment and placebo groups.

In January 2006， the FDA conducted a second metaanalysis[21]of 372 RCTs of newer anti depressants in adults with a pooled sample of approximately 100 000 individuals. The analysis was based solely on spontaneous adverse event reports from these RCTs； no data on prospecti ve clinician rati ngs were provided in the studies.While the overall analysis revealed no evidence of an associati on， strati fi cati on by age revealed that for the primary endpoint of suicidal ideation or behavior， 18- to 24-year-olds taking anti depressants had an increased risk compared to those taking placebo that approached statistical significance （OR=1.62； CI=0.97， 2.71）. Fowever，adults aged 25 to 64 years had a significantly decreased risk （OR=0.79； CI=0.64， 0.98）， and geriatric patients had a markedly significantly decreased risk （OR=0.37； CI=0.18，0.76）. On the basis of these results， the FDA extended the black-box warning to include 18- to 24-year-olds.

Since the FDA warnings， several studies have raised serious questi ons regarding the results of the FDA analyses. Bridge and colleagues[22]analyzed an expanded set （27 studies） of pediatric RCTs of anti depressant treatment and suicidality； they found that the associati on between anti depressant treatment and suicidality was much weaker than reported in the FDA’s original fi ndings. Gibbons and colleagues[23]studied a cohort of 226 866 veterans with a new episode of major depressive disorder and found a signif i cantly lower rate of suicide att empt in those treated with monotherapy SSRIs compared with those treated without anti depressant medicati on （123/100 000 for SSRIs versus 335/100 000 for no anti depressant； OR 0.37； p＜0.0001）. Noreover，among veterans treated with monotherapy SSRIs the rate of suicide att empts aft er treatment （123/100 000） was signif i cantly lower than the rate before treatment （221/100 000； relati ve risk 0.56； p＜0.0001）. Analyses stratified by age did not confirm the FDA’s findings of increased suicidality for 18- to 24-year-olds. The veterans data have also been re-analyzed using person-ti me logistic regression.[24]This analysis found a significant decrease in suicide att empt rate during monotherapy SSRI treatment （hazard rati o [FR]， 0.17； CI=0.10， 0.28；p=0.0001）； the suicide attempt rate decreased withti me from the index episode and the hazard rate is much lower for patients treated with monotherapy SSRIs （versus non-pharmacological treatments） during the first few months following treatment initiati on， but the difference between the different treatment groups becomes indistinguishable by 9 months following the index episode.

Ecological studies conducted following the FDA’s black-box warning revealed that there may have been unintended consequences of the warning. Several authors[25-28]have now shown that anti depressant prescripti on rates precipitously dropped following the warning. Both Gibbons and colleagues[26]and the US Centers for Disease Control and Preventi on[29]documented a 14% increase in child and adolescent suicide rates following the decrease in anti depressant prescripti ons. Libby and colleagues[30，31]found a 44% reducti on in the diagnosis of new cases of child depression among general practitioners following the black-box warning and a 37% reducti on in the diagnosis of new cases among young adults.

Recently， Gibbons and colleagues[32，33]synthesized all the longitudinal data from 40 drug company sponsored and one large Nati onal Insti tute of Nental Fealth placebo-controlled RCTs of fluoxetine for youth，adults and the elderly， and of venlafaxine in adults. Both drugs were shown to be efficacious in all age cohorts although the maximum benefit was observed for children and only marginal benefit was observed for the elderly following six weeks of treatment. With respect to suicidal thoughts and behavior， significant benefits of anti depressant treatment were observed in adults and the elderly， and these benefits were mediated by larger decreases in depressive severity observed in treated pati ents relati ve to placebo controls. In children，despite statistically and clinically significant benefits in terms of depression observed with acti ve treatment，no signif i cant difference between treated and control pati ents was observed in the rates of suicidal ideati on and behavior. These results indicate that suicidal thoughts and behavior are driven by depression in adults but this does not appear to be the case for children. This fi nding is consistent with a recent finding by Kessler and colleagues[34]who found that over 80%of suicidal adolescents received some form of mental health treatment， but the treatment failed to prevent suicidal behavior.

4. Are there more effective methods for measuring suicide risk?

As noted， the use of spontaneously reported retrospective accounts of suicidal thoughts and behavior even in the context of RCTs can lead to invalid statisti cal inferences.Previously， prospective measurements of suicidality were usually based on ratings of a single symptom item that has response categories ranging from suicidal thoughts to planning to behavior. Recently， the US FDA[16]has endorsed use of the Columbia-Suicide Severity Rati ng Scale （C-SSRS）[35]for routi ne prospecti ve assessment of suicidal risk in RCTs involving any central nervous system related drug. The C-SSRS provides direct classificati on of suicidal events into 11 categories， 5 of which concern suicidal ideati on （ranging from passive thoughts to acti ve ideati on including method， intent and planning），5 suicidal behaviors （ranging from preparatory acti ons to completed suicide）， and self-injurious behavior with no suicidal intent. The advantage of the C-SSRS is that it standardizes what we mean by suicidal events and eliminates the ascertainment bias that can be produced by spontaneous reports when comparing patients receiving an active treatment versus a pharmacologically inactive control. This is an important advance for RCTs in which suicide is an adverse event of concern， and it will be of considerable interest to examine the associati on between anti depressant treatment and suicidal events in youth as more data using the C-SSRS become available.

Identification of individuals with significant suicidal ideation or those who have already made a serious att empt may be too late for the purpose of prevention.[1]In adults and the elderly， we know that depressive severity is an important mediator of suicidal thoughts and behaviors and therefore the ability to more widely and less invasively measure depression and screen for suicidal risk is sti ll sorely needed. This is parti cularly true in high-risk populations such as veterans of military acti ons who in the US are at greater risk of death by suicide than death from a batt le-related injury. Recently Gibbons and colleagues[36]developed a computerized adaptive test of depressive severity （the CAT-Depression Inventory， CAT-DI） that can be self-administered in two minutes， requires an average of 12 items per subject yet maintains a correlati on of 0.95 with the total item bank score based on almost 400 items. Using a simple empirically derived threshold， the test has a sensiti vity of 0.92 and a specif i city of 0.88 for identifying a major depressive disorder （using the diagnosis derived by a clinician using the Structured Clinical Interview for DSN-IV as the gold standard）. The test is based on multi dimensional item response theory （NIRT）[37，38]and one of the subdomains includes 14 suicide items.In the event that a suicide item is not administered as a part of the adapti ve test， 1 to 4 additi onal suicide screening items are administered and if any item is endorsed at a moderate level or above， a suicide alert is sent to the treati ng clinician or managed care provider.The advantage of an adaptive self-report measure of depressive severity and suicidal risk is that it can be administered to large populati ons via the internet from a cloud computing environment. Furthermore， unlike traditi onal brief， fi xed-length instruments such as the PFQ-9 （Pati ent Fealth Questi onnaire）， which involve repeatedly administering the same set of items （which can result in response set bias）， the CAT-DI adapts to changes in depressive severity within individuals and asks different questions depending on the current level of impairment. Reducti on in respondent burden is achieved by initiating the next CAT testing session based on the esti mated depressive severity from the previous session and， thus， reducing the number of items that need to be administered. Another advantage of CAT is that the terminati on criterion （which determines the required level of precision of the esti mate and is inversely proporti onal to the number of items required）can be diff erent for diff erent applicati ons. For example，in an RCT we may want extremely precise esti mates that will enable us to obtain the most accurate esti mate of a treatment eff ect of interest and will， thus， require a larger number of items （e.g.， 20-30）. In primary care，we may require a somewhat less precise esti mate which is suffi cient to detect depression when present and monitor the effectiveness of treatment so it will require an intermediate number of items （e.g.， 10-12）. In psychiatric epidemiology， we may require a less precise estimate based on fewer items （e.g.， 5 or 6） that is sufficient for determining the prevalence of depression within a specif i ed population. All that is required is to change the terminati on criterion （i.e. the required standard error of the severity level esti mate） depending on the requirements of the specif i c applicati on. The paradigm shift is from a traditional fixed-length test that has a small number of items and may result in variable measurement precision， to a variable length test with a small but optimally selected set of items for the specif i c respondent and leads to constant measurement precision across individuals. Additi onal CATs for anxiety， hypomania/mania spectrum and a brief depression diagnostic screening test have also been developed using this methodology.

5. What improvements in stati sti cal methodologies are possible for the study of suicide?

From a statistical perspective， the analysis of suicide and related events are among the most challenging and interesti ng drug safety problems. There is no other area where the indication for treatment is so strongly confounded with the adverse event of interest. Even in well-controlled observational studies， selection effects can lead to severely biased results. Since suicide events are rare， RCTs in and of themselves generally have sample sizes that are too small to draw valid inferences. Furthermore， pati ents enrolled in RCTs may have litt le resemblance to those pati ents who are the ulti mate consumers of the medications of interest. In the following， I provide a brief overview of several areas of promising stati sti cal research.

5.1 Meta-analysis

Nost meta-analyses of rare binary events in medical research （including suicidal events） are based on the fi xed-eff ect model or ‘Nantel-Faenszel Nethod’ or the random-effect model of DerSimonian and Laird.[39]The fi xed-eff ect model assumes that the treatment eff ect is constant over studies and the random-effect model allows the treatment eff ect to vary from study to study.Recently， Bhaumik and colleagues[40]studied these estimators and found that the estimated treatment eff ect can be grossly over-esti mated when there is signif i cant variability in the treatment effect across studies. The bias is smaller for the random-eff ect model than for the fixed-effect model， but still appreciable.These estimators also require a continuity correction to zero cells from a given trial and if the number of events in both arms is zero， then the study must be removed from the computation. Alternative methods based on non-linear mixed-eff ects regression models[41]do not require continuity corrections or removal of zero-event studies and do not suffer from bias due to treatment effect heterogeneity across studies. The disadvantage of these more advanced meta-analysis procedures is that the results are dependent on the particular model specification （random background event rate， random treatment effect， both random effects and their correlation）. While the correct model specif i cation is an empirical question， a model with two correlated random effects （random background incidence and random treatment effect） generally works well in all cases.[42]

While meta-analysis combines effect sizes such as standardized mean differences or odds ratios， ‘research synthesis’ provides a re-analysis of the complete set of person-level longitudinal data from each study. As an example， the previously discussed papers by Gibbons and colleagues[32，33]performed 3-level linear （efficacy） and non-linear （safety） mixed-effects regression analyses[37]of the data from a series of 41 RCTs on the efficacy and safety of anti depressants. In these analyses， the intercept and slope of the temporal trends in effi cacy and safety measures are allowed to vary from individual to individual and the study means of these same effects are allowed to vary from study to study. With proper specif i -cati on of the variance component structure， the overall pooled estimate of the treatment by ti me interaction tests the overall efficacy （or safety） of the medication of interest.

5.2 Person-ti me models

Person-ti me regression or discrete-ti me survival analysis[43]is an ingenious approach to fi tti ng a ti me to event or survival analyti c model in a parametric way using standard logisti c regression soft ware. The basic idea is to discreti ze ti me into a set of smaller intervals and to then record the number of subjects at risk in each interval， the number experiencing the event （e.g.，suicide att empt）， and the number censored. A similar approach can be taken using unstructured data in which each subject contributes nirecords either to the point in ti me in which the event was first experienced or to the end of the follow-up period. Advantages of the approach are that: （a） ti me-varying predictors are easily accommodated， （b） random-effects such as the nesti ng of pati ents within hospitals or clinics， or counti es can be easily included， （c） competing risks such as death by suicide or other causes of mortality can be examined， and （d） non-proporti onal hazard models can be esti mated.[41，44]The net result is that we can relax the assumpti on that once a subject is exposed they are always exposed and replace it with any exposure patt ern （e.g.， monthly） and produce a within-subject esti mate of the eff ect of the exposure on the probability of experiencing the adverse event.Note that unlike a traditi onal mixed-eff ects logisti c regression for a repeated binary event， these models are restricted to a single event per person and as such， the repeated observati ons within individuals are conditi onally independent.[43]

5.3 Causal Inference

Since larger sample sizes are required to study events such as suicide attempts， this generally leads to largescale pharmacoepidemiologic studies of medical claims data， which suffer from the usual problems associated with the analysis of observati onal data. To insulate inferences from bias produced by the selecti on of patients to treatments （either self-selected or selected by their treating physician based on observable characteristics such as severity of illness） we turn to methods designed to draw causal inferences from observational studies.The now classic approach is based on propensity score matching[45，46]in which patients who do or do not receive a particular treatment of interest are matched on a large number of potential confounders （e.g.， age， sex，concomitant treatments， comorbid diagnoses， prior attempts） and the likelihood of receiving treatment （e.g.，an anti depressant）. The fundamental idea is to carve a RCT out of an observati onal study， without eliminati ng so much of the data that the ‘RCT’ is no longer generalizable.

While propensity score matching is useful conceptually， drug exposures are typically dynamic and the exposure status takes on diff erent values over ti me. Traditi onal propensity score matching assumes that treatment status does not change overti me. While some work has been done in the area of dynamic propensity score matching，[47]an equally if not more promising approach for dynamic treatment exposures is based on the idea of marginal structural models （NSN）.[48]The basic idea of NSN is that we compute the probability of treatment at each of Tti me-points and then combine these probabiliti es to compute the likelihood of treatment up to a particular point in ti me. These probabiliti es are then standardized and used as weights in a second stage regression that models the dynamic eff ects of treatment on the adverse event of interest （e.g.， suicide att empt）weighted by the likelihood to receive treatment at any particular point in ti me. While the traditi onal approach described by Robins and co-workers rests strongly on the assumption that all of the important confounders have been measured and are available for the analysis，the analysis may be further expanded to include the effects of unmeasured confounders by adding one or more random effects to the treatment selecti on model as described by Leon and Fedeker[49]in the context of computing dynamic propensity score adjustments.

6. Where do we go from here?

The area of drug safety in general and suicide in particular is an enormously important problem that has traditionally been investi gated using quite simple approaches which oft en yield questionable results. Improving the quality of analytic work in this important area should be a major goal of future applicati ons.

Conf l ict of interest

This work was supported by NINF grant R01NF8012201.Dr. Gibbons has served as an expert witness for the US Department of Justi ce， Wyeth and Pf i zer Pharmaceuti cals on suicide-related cases.

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38. Gibbons RD， Bock RD， Fedeker D， Weiss D， Segawa E， Bhaumik DK， et al. Full-Informati on Item bi-factor analysis of graded response data. Appl Psychol Meas 2007； 31: 4-19.

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49. Leon AC， Fedeker D. Quanti le strati fi cati on based on a misspecified propensity score in longitudinal treatment eff ec-ti veness analyses of ordinal doses. Comput Stat Data Anal 2007； 51: 6114-6122.

10.3969/j.issn.1002-0829.2013.02.011

University of Chicago， Chicago， USA

*correspondence: rdg@uchicago.edu

Robert Gibbons is a Professor of Biostatistics in the Departments of Medicine and Health Studies and Director of the Center for Health Stati sti cs at the University of Chicago. He is interested in the areas of biostatistics， environmental statistics， and psychometrics. Major themes in his work include development of linear and non-linear mixed effects regression models for analysis of longitudinal data， analysis of environmental monitoring data and inter-laboratory calibration， item response theory and computerized adaptive testing， and the development of new statistical methods in pharmacoepidemiology and drug safety. Dr.Gibbons is a fellow of the American Statistical Association and an elected member of the Institute of Medicine of the National Academy of Sciences.

ERRATUM

In the February 2013 issue， there were two errors on the right column of page 56 of the Biostatistics in Psychiatry（13） article. （Lê Cook B， Nanning WG. Thinking beyond the mean: a practical guide for using quantile regression methods for health services research. Shanghai Archives of Psychiatry 2013； 25（1）: 55-59.） The phrase ‘…a 75th quantile regression fits a regression line through the data so that 90 percent of the observations…’ should read:‘…a 75th quantile regression fits a regression line through the data so that 75 percent of the observations...’ And the phrase ‘…and the observed values above the line （positive residuals） by 1.75.’ should read: ‘…and the observed values above the line （positive residuals） by 1.5.’ We apologize for the errors.