A lean additive frailty model: With an application to clustering of melanoma in Norwegian families

Additive frailty models are used to model correlated survival data. However, the complexity of the models increases with cluster size to the extent that practical usage becomes increasingly challenging. We present a modification of the additive genetic gamma frailty (AGGF) model, the lean AGGF (L-AGGF) model, which alleviates some of these challenges by using a leaner additive decomposition of the frailty. The performances of the models were compared and evaluated in a simulation study. The L-AGGF model was used to analyze population-wide data on clustering of melanoma in 2 391 125 two-generational Norwegian families, 1960-2015. Using this model, we could analyze the complete data set, while the original model limited the analysis to a restricted data set (with cluster sizes≤ 7 $$ \le 7 $$ ). We found a substantial clustering of melanoma in Norwegian families and large heterogeneity in melanoma risk across the population, where 52% of the frailty was attributed to the 10% of the population at highest unobserved risk. Due to the improved scalability, the L-AGGF model enables a wider range of analyses of population-wide data compared to the AGGF model. Moreover, the methods outlined here make it possible to perform these analyses in a computationally efficient manner.

Prostate-specific antigen testing for prostate cancer: Depleting a limited pool of susceptible individuals?

After the introduction of the prostate specific antigen (PSA) test in the 1980s, a sharp increase in the incidence rate of prostate cancer was seen in the United States. The age-specific incidence patterns exhibited remarkable shifts to younger ages, and declining rates were observed at old ages. Similar trends were seen in Norway. We investigate whether these features could, in combination with PSA testing, be explained by a varying degree of susceptibility to prostate cancer in the populations. We analyzed incidence data from the United States' Surveillance, Epidemiology, and End Results program for 1973-2010, comprising 511,027 prostate cancers in men ≥40 years old, and Norwegian national incidence data for 1953-2011, comprising 113,837 prostate cancers in men ≥50 years old. We developed a frailty model where only a proportion of the population could develop prostate cancer, and where the increased risk of diagnosis due to the massive use of PSA testing was modelled by encompassing this heterogeneity in risk. The frailty model fits the observed data well, and captures the changing age-specific incidence patterns across birth cohorts. The susceptible proportion of men is [Formula: see text] in the United States and [Formula: see text] in Norway. Cumulative incidence rates at old age are unchanged across birth cohort exposed to PSA testing at younger and younger ages. The peaking cohort-specific age-incidence curves of prostate cancer may be explained by the underlying heterogeneity in prostate cancer risk. The introduction of the PSA test has led to a larger number of diagnosed men. However, no more cases are being diagnosed in total in birth cohorts exposed to the PSA era at younger and younger ages, even though they are diagnosed at younger ages. Together with the earlier peak in the age-incidence curves for younger cohorts, and the strong familial association of the cancer, this constitutes convincing evidence that the PSA test has led to a higher proportion, and an earlier timing, of diagnoses in a limited pool of susceptible individuals.

Expected 10-year treatment cost of breast cancer detected within and outside a public screening program in Norway

BACKGROUND

The shift towards earlier stages of disease advancement at diagnosis when introducing mammography screening is expected to affect the treatment costs of breast cancer.

MATERIALS AND METHODS

We collected data on hospital resource use in Norway following a breast cancer diagnosis for the period 1 January, 2008 through 31 December, 2009 for women aged 50-69 years, diagnosed with breast cancer during the period 1 January, 1999 through 31 December, 2009. We estimated treatment costs using a function that included the probability of being at risk for receiving treatment, estimated by means of the Cox proportional hazard model.

RESULTS

In total, 16,045 patients were included for the analyses among which 10.5 % died during the study period. The mean 10-year per-person treatment cost was €31,940 (95 % CI €31,030-32,880), and lower for cancers detected within the public screening program (€30,730) than for those detected elsewhere (€36,230). For ductal carcinoma in situ (DCIS) and cancers in stages I thru IV, treatment costs were €15,740, €23,570, €46,550, €55,230 and €60,430, respectively. Interval cancers occurring within the screening program were generally more resource demanding than both cancers detected at screening or elsewhere.

CONCLUSIONS

Ten-year treatment costs increased by increasing stage at diagnosis. Patients whose cancer was detected within the public screening program had lower treatment costs than those detected elsewhere. Interval cancers had higher costs than others.

Cost-effectiveness of TNF inhibitors vs synthetic disease-modifying antirheumatic drugs in patients with rheumatoid arthritis: a Markov model study based on two longitudinal observational studies

Objective. The objective of this study was to estimate the additional costs and health benefits of adding a TNF inhibitor (TNFi) (adalimumab, certolizumab, etanercept, golimumab, infliximab) to a synthetic DMARD (sDMARD), e.g. MTX, in patients with RA.

Methods. We developed the Norwegian RA model as a Markov model simulating 10 years of treatment with either TNFi plus sDMARDs (TNFi strategy) or sDMARDs alone (synthetic strategy). Patients in both strategies started in one of seven health states, based on the Short Form-6 Dimensions (SF-6D). The patients could move to better or worse health states according to transition probabilities. In the TNFi strategy, patients could stay on TNFi (including switch of TNFi), or switch to non-TNFi-biologics (abatacept, rituximab, tocilizumab), sDMARDs or no DMARD. In the synthetic strategy, patients remained on sDMARDs. Data from two observational studies were used for the assessment of resource use and utilities in the health states. Health benefits were evaluated using the EuroQol-5 Dimensions (EQ-5D) and SF-6D.

Results. The Norwegian RA model predicted that 10-year discounted health care costs totalled €124 942 (€475 266 including production losses) for the TNFi strategy and €65 584 (€436 517) for the synthetic strategy. The cost per additionally gained quality-adjusted life-year of adding a TNFi was €92 557 (€60 227 including production losses) using SF-6D and €61 285 (€39 841) using EQ-5D. Including health care costs only, the probability that TNFi treatment was cost-effective was 90% when using EQ-5D, assuming a Norwegian willingness-to-pay level of €67 300.

Conclusion. TNFi treatment for RA is cost-effective when accounting for production losses. Excluding production losses, TNFi treatment is cost-effective using EQ-5D, but not SF-6D.

A hierarchical frailty model for familial testicular germ-cell tumors

Using a 2-level hierarchical frailty model, we analyzed population-wide data on testicular germ-cell tumor (TGCT) status in 1,135,320 two-generational Norwegian families to examine the risk of TGCT in family members of patients. Follow-up extended from 1954 (cases) or 1960 (unaffected persons) to 2008. The first-level frailty variable was compound Poisson-distributed. The underlying Poisson parameter was randomized to model the frailty variation between families and was decomposed additively to characterize the correlation structure within a family. The frailty relative risk (FRR) for a son, given a diseased father, was 4.03 (95% confidence interval (CI): 3.12, 5.19), with a borderline significantly higher FRR for nonseminoma than for seminoma (P = 0.06). Given 1 affected brother, the lifetime FRR was 5.88 (95% CI: 4.70, 7.36), with no difference between subtypes. Given 2 affected brothers, the FRR was 21.71 (95% CI: 8.93, 52.76). These estimates decreased with the number of additional healthy brothers. The estimated FRRs support previous findings. However, the present hierarchical frailty approach allows for a very precise definition of familial risk. These FRRs, estimated according to numbers of affected/nonaffected family members, provide new insight into familial TGCT. Furthermore, new light is shed on the different familial risks of seminoma and nonseminoma.

How are drug regimen changes during hospitalisation handled after discharge: a cohort study

OBJECTIVES

To investigate drug regimen changes during hospitalisation and explore how these changes are handled after patients are transferred back into the care of their general practitioners (GPs).

DESIGN

Cohort study.

SETTING

Patients in this multicentre study had undergone at least one change in their drug regimens at discharge from the general medicine departments at six hospitals in Norway. These changes were altered doses, discontinuation of drugs or start of new drugs. Clinical pharmacists visited the patients' GPs 4-5 months after patient discharge and recorded any additional drug regimen changes.

RESULTS

In total, 105 patients (mean age 76.1 years, 54.3% women) completed the study. On average, they used 5.6 drugs at admission (range 0-16) and 7.6 drugs at discharge (range 1-17). On average, 4.4 drug changes per patient (SD 2.7, range 1-16) were made at the hospital, and 3.4 drug changes per patient (SD 2.9, range 0-14) within 4-5 months of discharge. Of the 465 drug changes made in hospital, 153 were changed again after discharge (mean 1.5 per patient, SD 1.8, range 0-13). The drug regimens of 90 of these 105 patients were changed after discharge. The OR for extensive drug changes after discharge (≥ 4 changes) increased significantly with the number of drugs used at discharge from hospital (OR=1.29, 95% CI 1.04 to 1.59). Only 68 of 105 discharge notes contained complete drug lists, and only 24 of the discharge notes were received by the GPs within 7 days.

CONCLUSIONS

In addition to the extensive changes in drug regimens during hospitalisation, almost equally extensive changes were made in the initial months after discharge. Surveillance of drug regimens is particularly necessary in the period immediately after hospital discharge.

Frailty modeling of the bimodal age-incidence of Hodgkin lymphoma in the Nordic countries

BACKGROUND

The bimodality of the age-incidence curve of Hodgkin lymphoma (HL) has been ascribed to the existence of subgroups with distinct etiologies. Frailty models can be usefully applied to age-incidence curves of cancer to aid the understanding of biological phenomena in these instances. The models imply that for a given disease, a minority of individuals are at high risk, compared with the low-risk majority.

METHODS

Frailty modeling is applied to interpret HL incidence on the basis of population-based cancer registry data from the five Nordic countries for the period 1993 to 2007. There were a total of 8,045 incident cases and 362,843,875 person-years at risk in the study period.

RESULTS

A bimodal frailty analysis provides a reasonable fit to the age-incidence curves, employing 2 prototype models, which differ by having the sex covariate included in the frailty component (model 1) or in the baseline Weibull hazard (model 2). Model 2 seemed to fit better with our current understanding of HL than model 1 for the male-to-female ratio, number of rate-limiting steps in the carcinogenic process, and proportion of susceptibles; whereas model 1 performed better related to the heterogeneity in HL among elderly males.

CONCLUSION

The present analysis shows that HL age-incidence data are consistent with a bimodal frailty model, indicating that heterogeneity in cancer susceptibility may give rise to bimodality at the population level, although the individual risk remains simple and monotonically increasing by age.

IMPACT

Frailty modeling adds to the existing body of knowledge on the heterogeneity in risk of acquiring HL.

Drugs with narrow therapeutic index as indicators in the risk management of hospitalised patients

Drugs with narrow therapeutic index (NTI-drugs) are drugs with small differences between therapeutic and toxic doses. The pattern of drug-related problems (DRPs) associated with these drugs has not been explored.

Frailty modeling of bimodal age-incidence curves of nasopharyngeal carcinoma in low-risk populations

The incidence of nasopharyngeal carcinoma (NPC) varies widely according to age at diagnosis, geographic location, and ethnic background. On a global scale, NPC incidence is common among specific populations primarily living in southern and eastern Asia and northern Africa, but in most areas, including almost all western countries, it remains a relatively uncommon malignancy. Specific to these low-risk populations is a general observation of possible bimodality in the observed age-incidence curves. We have developed a multiplicative frailty model that allows for the demonstrated points of inflection at ages 15–24 and 65–74. The bimodal frailty model has 2 independent compound Poisson-distributed frailties and gives a significant improvement in fit over a unimodal frailty model. Applying the model to population-based cancer registry data worldwide, 2 biologically relevant estimates are derived, namely the proportion of susceptible individuals and the number of genetic and epigenetic events required for the tumor to develop. The results are critically compared and discussed in the context of existing knowledge of the epidemiology and pathogenesis of NPC.

Age-incidence curves of nasopharyngeal carcinoma worldwide: bimodality in low-risk populations and aetiologic implications

The distinct geographic variation in the global incidence of nasopharyngeal carcinoma reflects a complex etiology involving viral, environmental, and genetic components. The high to intermediate rates observed in endemic areas contrast markedly with the uniformly low rates seen in much of the world. An interesting epidemiologic observation is the early peak in age-incidence curves observed in certain geographically disparate populations, suggestive of distinct causal entities and the possible exhaustion of susceptible individuals from the population at a certain age. The aim of this study was to systematically evaluate the age-incidence profiles of NPC worldwide on partitioning populations according to level of risk, in an effort to provide clues about the importance of early-in-life factors and genetic susceptibility. Using data from 23 high-quality population-based cancer registries for the period 1983-1997, a key finding was the consistent pattern of bimodality that emerged across low-risk populations, irrespective of geographic location. Continual increases in NPC risk by age up to a first peak in late adolescence/early adulthood (ages 15-24 years) were observed, followed by a second peak later in life (ages 65-79 years). No such early peak in NPC incidence by age group was evident among the high-risk populations studied. These findings are discussed according to existing lines of biological and epidemiologic evidence related to level of population risk, age at diagnosis, and histologic subtype. A modified model for NPC tumor development is proposed on the basis of these observations.

Identification of drug interactions in hospitals--computerized screening vs. bedside recording

BACKGROUND AND OBJECTIVE

Managing drug interactions in hospitalized patients is important and challenging. The objective of the study was to compare two methods for identification of drug interactions (DDIs)--computerized screening and prospective bedside recording--with regard to capability of identifying DDIs.

METHODS

Patient characteristics were recorded for patients admitted to five hospitals. By bedside evaluation drug-related problems, including DDIs, were prospectively recorded by pharmacists and discussed in multidisciplinary teams. A computer screening programme was used to identify DDIs retrospectively--dividing DDIs into four classes: A, avoid; B, avoid/take precautions; C, take precautions; D, no action needed.

RESULTS

Among 827 patients, computer screening identified DDIs in 544 patients (66%); 351 had DDIs introduced in hospital. The 1513 computer-identified DDIs had the following distribution: type A 78; type B 915; type C 38; type D 482. By bedside evaluation, 99 DDIs were identified in 73 patients (9%). The proportions of computer recorded DDIs which were also identified at the bedside were: 5%, 8%, 8%, 2% DDIs of types A, B, C and D respectively. In 10 patients, DDIs not registered by computer screening were identified by bedside evaluation. The drugs most frequently involved in DDIs, identified by computerized screening were acetylsalicylic acid, warfarin, furosemide and digitoxin compared with warfarin, simvastatin, theophylline and carbamazepine, by bedside evaluation.

CONCLUSION

Despite an active prospective bedside search for DDIs, this approach identified less than one in 10 of the DDIs recorded by computer screening, including those regarded as hazardous. However, computer screening overestimates considerably when the objective is to identify clinically relevant DDIs.

A secondstep in development of a checklist for screening risk for violence in acute psychiatric patients: evaluation of interrater reliability of the Preliminary Scheme 33

The Acute Project is a research project conducted on acute psychiatric admission wards in Norway. The objective is to develop and validate a structured, easy-to-use screening checklist for assessment of risk for violence in patients both during their stay in the ward and after discharge. The Preliminary Scheme 33 is a 33-item screening checklist with content domain inspired by the Historical-Clinical-Risk Management Scheme (HCR-20), the Brøset Violence Checklist, and eight risk factors extracted from the literature on risk assessment. The Preliminary Scheme 33 was designed and tested in two steps by a research group which includes the authors. The common aim of both steps was to develop this into a time economical, reliable, and valid checklist. In the first step in 2006 the predictive validity of the individual items was tested. The present work presents results from the second step, a study conducted to assess the interrater reliability of the 33 items. Eight clinicians working in an acute psychiatric unit volunteered to be raters and were trained to score the 33 items on a three-point scale in relation to 15 clinical vignettes, which contained information from 15 acute psychiatric patients' files. Analysis showed high interrater reliability for the total score with an intraclass correlation coefficient (ICC) of .86 (95% CI: 0.74-0.94). However, a substantial proportion of the items had medium to low ICCs. Consequences of this finding for further development of these items into a brief screen are discussed.

Frailty modelling of colorectal cancer incidence in Norway: indications that individual heterogeneity in risk is related to birth cohort

Some cancer types level off or decrease in incidence at older age groups, not following the Weibull hazard rate. This stagnation can be explained by the frailty model, which describes the population effect of mixing individuals who are susceptible, with high risk of cancer, with those that are "non-susceptible", with a low risk of cancer even in the oldest age groups. The aim of the study was to apply a frailty model on colorectal cancer incidence data for the Norwegian population aged 40-99 years, diagnosed 1956-2000. The model provided an acceptable fit to the data. The estimated proportion of susceptibles increased from about 5% to about 24% from the first cohort (1851-1855) to the last cohort (1946-1950), in line with the rise in incidence of the disease during this period. According to the frailty modelling, the estimated number of genetic events necessary for a malignant lesion to develop in the colorectum is seven to eight, which accords with the present knowledge regarding colorectal carcinogenesis. The frailty phenomenon may thus be present in this cancer form. The findings indicate that it is possible to model the development of colorectal cancer in the population based on large heterogeneity in risk between individuals, in such a manner that a small group of individuals are susceptible to develop the disease, whereas the remaining majority have a low susceptibility.

Polypharmacy as commonly defined is an indicator of limited value in the assessment of drug-related problems

AIM

To investigate whether polypharmacy defined as a definite number of drugs is a suitable indicator for describing the risk of occurrence of drug-related problems (DRPs) in a hospital setting.

METHODS

Patients admitted to six internal medicine and two rheumatology departments in five hospitals were consecutively included and followed during the hospital stay, with particular attention to medication and DRPs. Comparisons were made between patients admitted with five or more drugs and with less than five drugs. Clinical pharmacists assessed DRPs by reviewing medical records and by participating in multidisciplinary team discussions.

RESULTS

Of a total of 827 patients, 391 (47%) used five or more drugs on admission. Patients admitted with five or more and less than five drugs were prescribed the same number of drugs after admission: 4.1 vs. 3.9 drugs [P = 0.4, 95% confidence interval (CI) - 0.57, 0.23], respectively. The proportion of drugs used on admission which was associated with DRPs was similar in the patient group admitted with five or more drugs and in those admitted with less than five drugs. The number of DRPs per patient increased approximately linearly with the increase in number of drugs used; one unit increase in number of drugs yielded a 8.6% increase in the number of DRPs (95% CI 1.07, 1.10).

CONCLUSION

The number of DRPs per patient was linearly related to the number of drugs used on admission. To set a strict cut-off to identify polypharmacy and declare that using more than this number of drugs represents a potential risk for occurrence of DRPs, is of limited value when assessing DRPs in a clinical setting.

Interview of patients by pharmacists contributes significantly to the identification of drug-related problems (DRPs)

PURPOSE

To investigate whether pharmacist interviews of hospitalised patients about their medication would result in identification of more drug-related problems (DRPs) than those found by usual care procedures and further to characterise the DRPs revealed at the interviews.

METHODS

Patients from five internal medicine and two rheumatology departments in four hospitals in Norway were prospectively included in the study. Clinical pharmacists assessed DRPs by reviewing medical records and by participating in multidisciplinary team discussions. Drugs used, medical history, laboratory data and clinical/pharmacological risk factors were recorded (usual care procedure). A proportion of patients were randomly selected for interview with pharmacists. A quality team assessed the clinical significance of the DRPs.

RESULTS

Seven hundred and twenty seven patients were included. Significantly more DRPs were found in the interview group (96 patients), an average of 4.4 DRPs per patient as compared to 2.4 DRPs in the non-interview group (631 patients) (p < 0.01). Of a total of 431 DRPs recorded in the interview group, 168 DRPs (39.9%) were disclosed through interviews. 'Need for additional drug', 'medical chart error', 'patient adherence' and 'need for patient education' were significantly more often recorded in this group. The quality team assessed 63% of the DRPs revealed in the interviews to be of major clinical significance.

CONCLUSION

Significantly more DRPs were identified among the patients who were interviewed compared to those patients having only usual care examination. A high proportion of the DRPs identified in the interviews were of major clinical significance. The clinical pharmacists, with their way of interviewing, seem to fill a gap, ensuring that significant DRPs do not escape detection.

Brief checklists for assessing violence risk among patients discharged from acute psychiatric facilities: a preliminary study

Violence risk assessment instruments are increasingly being used. Their use has, however, mostly been confined to forensic psychiatry for assessing the risk among perpetrators to repeat violent acts. In general psychiatry, very few studies of violence risk among discharged persons from acute inpatient units have been conducted. The available instruments are extensive and time consuming. This study aimed at the construction of a brief checklist. A 33-item scale, the PS (Preliminary Scheme), strongly influenced by the established HCR-20 (Historical, Clinical and Risk Management Assessment Scheme) was developed to undergo logistic regression analysis and possible item reduction. One hundred and ten patients from an acute inpatient unit, scored with PS at discharge, were monitored for violent episodes throughout the following year. Risk assessments and violence registrations were then compared. Of the 110 patients, 29 (26%) had acted violently during the follow-up, with the PS showing a definite association with post-discharge violence. Receiver operating characteristics (ROC) for the instrument yielded an area under the curve (AUC) of 0.71 (P<0.01). Regression analysis indicated that the number of PS items could be strongly reduced without losing predictive validity. Even a four-item checklist showed a higher AUC (0.77) than the PS did with all 33 items. The four items were: 1) Previous violence, 2) Substance use problems, 3) Lack of empathy and 4) Stress. The development of a brief risk assessment instrument with good predictive properties seems possible. Further clinical trials are planned. Ethical aspects of violence prediction must always be considered.

Comparison of Drug-Related Problems in Different Patient Groups

BACKGROUND:

There is a lack of knowledge concerning how drug-related problems (DRPs) vary in different patient groups. Possible dissimilarities need to be taken into consideration when guidelines for detecting and preventing DRPs are compiled.

OBJECTIVE:

To characterize and compare the frequency and categories of DRPs in different groups of hospitalized patients.

METHODS:

Patients admitted to 4 different types of departments at 5 hospitals in Norway were included consecutively. Medical records and information acquired at multidisciplinary morning meetings were sources for assessing the patients' DRPs.

RESULTS:

A total of 827 patients were included. Mean age was 70.8 years, 58.6% were female, and 81% had at least one DRP. An average of 1.9, 2.0, 2.1, and 2.3 DRPs per patient were found in the departments of cardiology, geriatrics, respiratory medicine, and rheumatology, respectively. Significant differences in the type of DRPs between the patient groups were found. The most frequent DRPs and the patient group in which they most often occurred were nonoptimal dose (cardiology, respiratory, geriatric) and need for additional drug (rheumatology).

CONCLUSIONS:

DRPs occurred in the majority of the patients in all departments. The type of DRP differed markedly between the patient groups. Knowledge of these differences is clinically valuable by enabling us to guide efforts toward prevention of DRPs. Antithrombotic agents, loop diuretics, angiotensin-converting enzyme inhibitors, penicillins, antiinflammatory drugs, and opioid analgesics commonly caused DRPs, even in departments where knowledge of these drugs is assumed to be extensive.

Frailty modelling of testicular cancer incidence using Scandinavian data

The incidence of testicular cancer is highest among young men, and then decreases sharply with age. This points towards a frailty effect, where some men have a much greater risk of testicular cancer than the majority of the male population. Those with the highest risk get cancer, drain the group of individuals at risk, and leave a healthy male population which has approximately zero risk of testicular cancer. This leads to the observed decrease in incidence. We discuss a frailty model, where the frailty is compound-Poisson-distributed. This allows for a non-susceptible group (of zero frailty). The model is successfully applied to incidence data from the Danish and Norwegian registries. It is indicated that there was a decrease in incidence for males born during World War II in both countries. Bootstrap analysis is used to find the degree of variation in the estimates. In the Armitage-Doll multistage model, the estimated number of transitions needed for a cell to become malignant is close to 3 for non-seminomas and 4 for seminomas in both the Danish and Norwegian data. This paper demonstrates that a model including a frailty effect fits the incidence data well and gives interesting results and interpretations, although this is no proof of the effect's truth.

Analysis of testicular cancer data using a frailty modelwith familial dependence

Previously published papers have indicated a fairly strong familial dependence intesticular cancer patients. This is particularly evident in brothers. We have applied a frailty model with familial dependence to family data on brothers of testicular cancer patients from the Norwegian Radium Hospital. The model is a two-level frailty, with variation in susceptibility at both the family and the individual level. Specifically, the frailty variable is assumed to be compound Poisson distributed to allow individuals to be non-susceptible. The underlying Poisson parameter is gamma distributed to model how testicular cancer is distributed among families. This is an extension of a previous compound Poisson frailty model developed for individual testicular cancer data, and an alternative to traditional modelling of survival time family data. The likelihood construction and ascertainment problems are looked at in detail. To avoid ascertainment bias, the likelihood is based on the probability of observing the disease status for each brother in a family, given that at least one brother is ascertained. The estimated relative risk for brothers is 7.4. This paper expands on a previous analysis of the data by using a frailty model, which makes it possible to examine how the cancer is distributed among families. The estimated gamma-shaped parameter is 0.151 (95 per cent confidence interval 0.078-0.294), and this indicates that in order to obtain the high relative risks observed for brothers of testicular cancer patients, the distribution of susceptibility has to be strongly skewed among the families. The vast majority of families have a very low risk and a small proportion have a high risk. In addition, a quantity similar to the relative risk is derived to show that the susceptibility is skewly distributed also if the Poisson parameter is Bernoulli or stable distributed. This indicates that the results are valid also if other distributions are used to model familial dependence in the compound Poisson frailty model.