- Analysis of testicular cancer data using a frailty modelwith familial dependence
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- Download Frailty Modelling Of Testicular Cancer Incidence Using Scandinavian Data 2004
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- A Hierarchical Frailty Model for Familial Testicular Germ-Cell Tumors.

In both disease models, all individuals are assumed to start in the acute infection disease stage. In the no-heterogeneity simulations, the expected YLD, YLL, and DALYs were computed from the expected number of cases progressing through an outcome tree defined by the transitional probabilities and Dutch male life expectancies for the year [ 13 ], and given assumed disability weights and durations Fig. Disease stage duration was truncated if the simulated individual reached their 86th birthday while in that disease stage relevant for model X 2 only.

In the heterogeneity simulations, the central idea implemented was that the infected individuals who are most likely to transition to a subsequent disease stage, such as a complication or death, are those with the highest frailty. For these simulations, we first randomly sampled from the pre-defined frailty distributions see below and assigned frailty values to each individual.

For disease model X 1 , the number of cases transitioning from acute to chronic infection was constrained to equal the expected cases N determined using the no-heterogeneity variant of the same model to permit comparability between heterogeneity and no-heterogeneity variants. Stochastic sampling methods were used to determine which individuals transitioned from each health outcome. This procedure was then repeated for a total of times, with the median and 2.

For disease model X 2 , the disease burden will be largely determined by the number of individuals who reach the death stage; the risk of death is dependent on the annual progression probabilities from the chronic infection and severe sequela stages. In sensitivity analysis, the effect of the initial choice of these parameter values on the simulated burden and on the overestimation of DALYs due to assuming population-averaged transition probabilities is explored. Additional file 1 reports the results of simultaneously varying the annual transition probabilities for the final two transitions in model X 2 across a limited range.

In a second sensitivity analysis involving model X 2 , two further frailty distributions are specified, and burden in DALYs compared with that obtained using the rightward-skewed distribution. In the first, skewedness was reversed i. Then, the heterogeneity variant was run, to assess any change in the size of the vaccination effect.

Note that a more accurate simulation of the impact of an age-targeted vaccination program would employ a dynamic modeling approach to simulate the time-dependent influence of herd immunity on successive birth cohorts entering the model.

### Analysis of testicular cancer data using a frailty modelwith familial dependence

Simulations were carried out in the R statistical programming environment, version 3. In all cases, fewer DALYs are predicted under the heterogeneity variants than under the standard, no-heterogeneity variant. For both simple disease models, ignoring individual heterogeneity consistently overestimated disease burden. For disease model X 1 , although the number of individuals developing chronic infection was held constant across the no-heterogeneity and heterogeneity variants, the no-heterogeneity variant overestimated the total disease burden by a factor of 1.

## Download Frailty Modelling Of Testicular Cancer Incidence Using Scandinavian Data

In Fig. The frailest individuals, in general and within a given age-group, are more likely to progress to a more advanced disease stage. The mean frailty values for individuals within the acute and chronic infection disease stages was 2. Frailty distributions of individuals in the acute infection and chronic infection disease stages in disease model X 1. Two selected age-groups are plotted, before dashed line and after solid line the transition from acute to chronic infection.

For disease model X 2 , in which a disease with a long natural history was simulated via specification of annual transition probabilities, overestimation of total disease burden by the no-heterogeneity variant was by a factor of 1. This difference was driven by YLL overestimated by a factor of 1.

The expected rightward shift in frailty distribution with disease stage is illustrated by Fig. Frailty distributions of the members of the infected cohort entering each disease stage, for disease model X 2 upper panel. Comparison of estimated disease burden over age-group at acute infection for disease model X 2 , with and without heterogeneity in disease progression rates main panel : heterogeneity leads to an overall lower burden.

The two smaller plots show disease burden by age-group split into YLD and YLL, for the no-heterogeneity upper right panel and heterogeneity lower right panel model variants. The results of the first sensitivity analysis indicated that the values initially chosen for the progression probabilities from the chronic infection and severe sequela stages resulted in a disease burden overestimation factor on the high end for the range of parameter values investigated Additional file 1. This factor tended to increase as either annual probability increased leading to more mortality at a younger age , with a range of 1.

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## Download Frailty Modelling Of Testicular Cancer Incidence Using Scandinavian Data 2004

In the second sensitivity analysis, leftward-skewed and peaked symmetrical frailty distributions were investigated; the resulting greater DALYs compared with the rightward-skewed distribution main analysis obtained with both alternatives lends support to our central finding from disease model X 2 : burden is lower when there are a relatively greater number of slow- than fast-progressors, because of the smaller number of premature deaths.

To what extent does individual heterogeneity in disease progression rates affect the computation of composite disease burden measures, such as the DALY? Our principal finding is the following: if the degree of individual heterogeneity that we simulated in transition probability distributions mimics the extent of unmeasured heterogeneity in the population, then ignoring this heterogeneity can result in inflated disease burden estimates.

In the case of disease model X 1 , the simulated dependence of mean frailty on age in the heterogeneity variant is responsible for the lower disease burden compared with the no-heterogeneity variant.

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With a skewed frailty distribution, a minority of patients die young, with the majority living to an older age, compared with application of a population-averaged transition probability. For disease model X 2 , in which frailty distributions were specified as age-independent i. This is because even though the most frail individuals progress the most rapidly through the disease course, and therefore have a higher probability of developing severe sequelae and dying at a younger age, on average disease progression is slower than if heterogeneity is ignored.

Due to the skewedness of the frailty distribution, only a minority of patients are fast progressors; for the majority of patients, disease progression is slow, and the severe disease stages, if experienced during their lifetime, are reached at a later age. The lower estimated burden for the heterogeneity variant is therefore due to fewer members of an acutely infected cohort reaching the age at which severe sequela or death due to the disease can occur and thus resulting in a lower YLL ; however, individuals in this variant tended to spend longer in chronic infection and severe sequela stages compared with the no-heterogeneity model, which resulted in a higher YLD.

It might be argued that the X 1 simulations only demonstrate that availability of age-dependent transition probabilities in place of a single age-independent transition probability is vital, if the incident case population covers a wide age range and the risk of developing a complication or dying is greater for older than for younger patients.

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Because in disease model X 1 the frailest patients are the most likely to transition, assuming increasing mean frailty with age effectively translates to a statistical preference for older patients transitioning to chronic infection before younger patients. Disease model X 2 — which explicitly simulates aging of an acutely infected cohort simultaneously with progression through the various disease stages — illustrates that the assumption of age-dependent mean frailty is unnecessary for longer natural history diseases. For disease model X 1 , ignoring age-dependent heterogeneity leads to overestimation of disease burden; but is it plausible that mean frailty would increase with age?

Although there are health states for which the young are at the greatest risk, frailty in general may be roughly monotonic with age. Also, declining mortality rates or increasing life expectancy over a period of time would give rise to an age-related frailty effect [ 15 ]. Finally, in the case of infectious diseases, immunosenescence age-associated decline in immune function could contribute to an increasing susceptibility to development of complications and death [ 16 ].

If the prioritization of public health resources are informed by a ranking of diseases according to overall burden or mortality burden, differential overestimation i. However, in our X 2 simulation incorporating individual heterogeneity, the vaccination effect size on DALYs was virtually identical to the projected effect size for the no-heterogeneity variant. Application of the concepts investigated in the current paper to epidemiological studies in which disease burden is estimated is relatively unexplored. Estimation of the extent of unmeasured heterogeneity can in principle be done by fitting a statistical model to a longitudinal dataset that records disease state transition times among a cohort of infected individuals, but certain assumptions are required [ 2 ], and interpretation must be made with caution.

In conclusion, the current findings corroborate what has been reported regarding the influence of heterogeneity in Markov models for cost-effectiveness [ 6 , 7 ]: ignoring heterogeneity can produce either optimistic or pessimistic cost-effectiveness ratios, with consequent impact on the use of such ratios for the planning of interventions. The heterogeneity issue could apply to every transition in a Markov model used for disease burden calculation; therefore, when selecting parameters for this type of model and interpreting the resulting burden estimates, the analyst should consider the consequences of assuming that the population within each health outcome is homogenous with regard to transition rates.

If this homogeneity assumption cannot be made, an individual-based modeling approach is the most appropriate solution. The impact of heterogeneity in individual frailty on the dynamics of mortality. Aalen OO. Effects of frailty in survival analysis. Stat Methods Med Res. Understanding variation in disease risk: the elusive concept of frailty. Int J Epidemiol. Alter G, Riley JC.

Frailty, sickness, and death: models of morbidity and mortality in historical populations. Popul Stud Camb. Frailty modelling of testicular cancer incidence using Scandinavian data. Assessing the sensitivity of decision-analytic results to unobserved markers of risk: defining the effects of heterogeneity bias. Med Decis Making. Zaric GS. The impact of ignoring population heterogeneity when Markov models are used in cost-effectiveness analysis.

## A Hierarchical Frailty Model for Familial Testicular Germ-Cell Tumors.

Disease burden in The Netherlands due to infections with Shiga toxin-producing Escherichia coli O Epidemiol Infect. Impact of epidemic and individual heterogeneity on the population distribution of disease progression rates. An example from patient populations in trials of human immunodeficiency virus infection. Am J Epidemiol. The pathogen- and incidence-based DALY approach: an appropriate [corrected] methodology for estimating the burden of infectious diseases.

PLoS One.