Evaluating the administration costs of biologic drugs: Development of a cost algorithm

Tetteh, Ebenezer K.; Morris, Stephen Article Evaluating the administration costs of biologic drugs: Development of a cost algorithm Health Economics Review Provided in Cooperation with: Springer Nature Suggested Citation: Tetteh, Ebenezer K.; Morris, Stephen (2014) : Evaluating the administration costs of biologic drugs: Development of a cost algorithm, Health Economics Review, ISSN 2191-1991, Springer, Heidelberg, Vol. 4, Iss. 26, pp. 1-16, https://doi.org/10.1186/s13561-014-0026-2 This Version is available at: https://hdl.handle.net/10419/150442 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ RESEARCH Open Access Evaluating the administration costs of biologic drugs: development of a cost algorithm Ebenezer K Tetteh *† and Stephen Morris † Abstract Biologic drugs, as with all other medical technologies, are subject to a number of regulatory, marketing, reimbursement (financing) and other demand-restricting hurdles applied by healthcare payers. One example is the routine use of cost-effectiveness analyses or health technology assessments to determine which medical technologies offer value-for-money. The manner in which these assessments are conducted suggests that, holding all else equal, the economic value of biologic drugs may be determined by how much is spent on administering these drugs or trade-offs between drug acquisition and administration costs. Yet, on the supply-side, it seems very little attention is given to how manufacturing and formulation choices affect healthcare delivery costs. This paper evaluates variations in the administration costs of biologic drugs, taking care to ensure consistent inclusion of all relevant cost resources. From this, it develops a regression-based algorithm with which manufacturers could possibly predict, during process development, how their manufacturing and formulation choices may impact on the healthcare delivery costs of their products. Keywords: Administration costs; Biologics; Economic evaluation; Formulation; Manufacturing Background The adoption and utilization of beneficial medical technologies including biologic drugs has, in recent times, been subject to a number of regulatory, marketing, reimbursement (coverage) and other demand-side hurdles including the so-called risk-sharing arrangements. These demand-side hurdles have evolved out of increasing healthcare payer concerns about the high acquisition costs and budgetary impacts of these medical technologies. Notably, healthcare payers have turned to the use of cost-effectiveness analysis (CEA), budget impact analysis or health technology assessments (HTA) to estimate cost-effectiveness and affordability prior to deciding whether to adopt or reimburse the utilization of biologics within their original or restricted marketing authorization or not. This typically involves comparing, over a specified time period, total healthcare delivery costs (i.e., the sum of drug acquisition costs plus administration and future healthcare-related costs) associated with a given technology and the total health benefits expected. Holding all else constant, the estimated cost-effectiveness of a biologic drug may be dictated by how much of healthcare resources are spent on drug administration, and whether trade-offs exist between drug acquisition and administration costs. On the supply-side, it has been observed that biological drug candidates are developed with a skewed focus on clinical efficacy and safety to the neglect of issues related to the ease of manufacturing, affordability and costeffectiveness of these therapies to healthcare payers. This often leads to unnecessary waste and excessive reworking of manufactured products, and a growing concern over the failures and struggles manufacturers face in passing through what is becoming an increasingly complex set of regulatory and demand-restricting hurdles. That latter is known to be associated with significant delays in market launch, in addition to the time and revenue lost in price negotiations [1]. So besides worrying about the ease of manufacturing, it is also useful for manufacturers to, at least, consider prior to market launch, the administration and total healthcare delivery costs associated with the different ways they choose to manufacture and formulate their products. In that case, manufacturers’evaluation of drug administration costs should be done in the same manner as it will be conducted by healthcare payers. The * Correspondence: [email protected] † Equal contributors Department of Applied Health Research, EPSRC Centre for Innovative Manufacturing in Emergent Macromolecular Therapies, University College London, 1-19 Torrington Place, London WC1E 7HB, UK © 2014 Tetteh and Morris; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. Tetteh and Morris Health Economics Review 2014, 4:26 http://www.healtheconomicsreview.com/content/4/1/26 aim of this study is to evaluate the administration costs of biologic drugs, to identify the factors that affect variation in these costs, and argue why such evaluations are an important step in biopharmaceutical manufacturing. That is, we explore why pharmaceutical manufacturers should consider the link between administration costs (and how this is influenced by formulation and manufacturing), total healthcare delivery costs and value-for-money when making their go-no-go R&D decisions. Our study objectives and design are motivated by two key points. First, in a systematic review of the economic value of reducing medication dosing frequency using drug delivery systems, Cheng et al. [2] found that, in most cases, drug products with less-frequent dosing schedules tend to be cost effective when compared to conventional (standard) formulations containing the same active moiety –although these ‘advanced’or ‘improved’ delivery systems may be expensive to make. Second, a recent systematic review of studies reporting on the costs of administering biologics within the United Kingdom (UK) National Health Service (NHS) identified possible trade-offs between acquisition and administration costs: a drug that appears cheap to buy may (in the long-run) have higher total healthcare delivery costs as more NHS resources are spent on drug administration. The budgetary impact of a biologic with high acquisition costs but relatively low administration costs could be the same as or lower than that of a less expensive biologic with higher administration costs. The study also found that there are inconsistencies in how studies define administration costs and consequently, differences in the type of costs included or excluded from estimates of drug administration costs [3]. These differences in what cost items are included or excluded means some of the reported differentials in administration costs for biologic drugs may not be real and cannot be used unreservedly in economic analyses. Once differences in cost estimates simply reflect differences in methods of measurement, one cannot tell for sure whether trade-offs exist between administration costs and drug acquisition costs or not; and to what extent administration costs could influence conclusions reached about cost-effectiveness. Taking into account these points, we evaluate variations in the administration costs for a sample of eighteen biologic drugs listed for use in the UK NHS, taking care to ensure consistent inclusion or exclusion of all relevant costs related to drug administration. We do this to ensure very little variation in drug administration costs can be attributed to differences in the method of measurement. We develop an administration-cost algorithm to help manufacturers predict, prior to market launch, the administration costs associated with their formulation choice for each biologic drug candidate in their portfolio. We believe this, together with manufacturers’expectations of product prices, should help them consider the possible trade-offs between drug acquisition and administration costs; and generate credible estimates of total healthcare delivery costs of their drug products and the likelihood that these products will receive favourable recommendations from healthcare payers. The paper is structured as follows. We first describe in Section Methods our methodological approach, underlying assumptions made in our analyses, and the data sources used. This is followed by Sections Results and Discussion with our results and discussion points. Section Conclusions completes the paper with our conclusions. Methods To avoid overcomplicating our analyses, we will assume clinical outcome neutrality; that is, for any comparison of different modes of administering a biologic drug, there are no differences in net health benefits (i.e., efficacy minus safety concerns) or that differences in net health benefits have no bearing on the magnitude or variation in administration costs. For example, differences in the incidence and severity of adverse events between two or more formulations of a given biologic drug will have no bearing as to how much is spent on drug administration costs. We also ignore other costs associated with disease management. Identifying and measuring administration costs From an economic perspective, costs measured should reflect the opportunity costs of NHS resources deployed in administering biologic drugs that could otherwise have been used elsewhere had the drug in question not been administered. An accurate measurement of drug administration costs thus requires identifying all resources that will be expended or the ‘cost centres’where resources will be consumed and costs incurred [4]. To identify the ‘cost centres’related to the administration of biologic drugs (from a healthcare payer perspective), we employ the framework described by Tetteh and Morris [3] that makes a distinction between the proximal costs of drug administration and the costs of physical administration. In that framework (see Figure 1), proximal administration costs (Pc) refer to costs incurred before or after physical administration of the drug into the body whilst physical administration costs (PAc) refer to the costs of physically introducing the drug into a patient via one of the established routes for administration. Each component labelled in that framework constitutes a (micro-level) cost centre where resources are consumed and costs incurred. We use this framework to ensure consistency in what type of administration costs are included or excluded in the analysis. Using a common yardstick should support (1) complete or near complete accounting of the opportunity costs associated with drug administration, and (2) “apples to apples”comparison of the administration costs Tetteh and Morris Health Economics Review 2014, 4:26 Page 2 of 16 http://www.healtheconomicsreview.com/content/4/1/26 of biologic drugs such that very little variation in administration costs can be attributed to the method of measurement. For the same reasons, we defined a common time frame over which drug administration costs will be estimated. We chose to evaluate annual costs of drug administration costs as this fitted well with the dosing regimens of all products in our sample. For simplicity, we base our analysis on a single patient who successfully completes a single full treatment course over a 12 month period. It might be argued that this will introduce bias against biologics indicated for an acute illness with typically ‘short’treatment episodes. However, extending the time frame beyond one-year period will actually amplify the cost differences between acute and chronic biologics whilst a 6-month period will not fit with the dosing regimen of some of the products in our sample. What is more, we do not consider repeat treatment episodes over the one-year period. Hence, our estimates of annual drug administration costs should not be biased against biologics indicated for acute illnesses. Product sample and dosing regimens modelled Our analysis makes use of an unbalanced sample of 18 therapeutically-active biologics; of which eight are administered intravenously, eight given by subcutaneous delivery and two given intramuscularly. Within this sample, fifteen of the products are humanized monoclonal antibodies (mAb) with the remainder comprising of one fragmented monoclonal antibody (fAb), a fusion protein and an interferon protein. The characteristics of this product sample are presented in Table 1. We make no argument that this sample is representative of all existing or emergent biologics or macromolecular therapies. To estimate the costs of administering the biologic drugs in our sample, some idea or knowledge of the dosing regimen for patients considered eligible to receive a given biologic drug is needed. We follow the dosing regimen indicated by the marketing authorisation for a given biologic drug, gathering this information from the posology described in the drug’s package inserts, the summary of product characteristics (SmPC) posted on the European Medicines Agency (EMA) website; the British National Formulary (BNF) or the electronic Medicines Compendium (eMC). Obviously, within UK NHS settings, the prescribed pathway suggested by the regulatory license or marketing authorization may not necessarily coincide with actual clinical practice –bearing in mind possible gaps between recommendations in HTA guidance or clinical guidelines and implementation of these recommendations in routine practice; as well as practice-specific watch-andwait treatment strategies. To avoid the complexity introduced by what happens in routine clinical practice, we simply modelled the dosing instructions given in the products’package inserts or the SmPC. For this, we assumed continuous dosing of a given biologic for the whole year unless the marketing authorization or SmPC clearly states the maximum number of doses or recommended duration of treatment. This is because we found it hard to make any unquestionable assumption about the proportion of treatment-responders and non-responders. The dosing regimens modelled will be found in Additional file 1: Appendix A. Analysis We first conducted a deterministic analysis with the estimated costs of drug administration disaggregated into Proximal costs. 1. GP and clinic visits (outpatient and/or inpatient attendance) 2. Costs of education or training for selfadministration 3. Costs of pre-therapy counselling 4. Pharmacy costs (inventory, preparation and dispensing) 5. Pre-treatment medication costs 6. Costs of post-treatment, progress checks 7. Cost of (laboratory) tests, assessment or evaluations. Costs of physical administration. 1. Staff (doctor/nurse) costs 2. Cost of equipment and consumables 3. Cost of concomitant medications. Components of drug administration costs Figure 1 Framework of drug administration costs. Tetteh and Morris Health Economics Review 2014, 4:26 Page 3 of 16 http://www.healtheconomicsreview.com/content/4/1/26 proximal costs and the cost of physically administering the drug. We used Figure 1 as a guide to selecting which cost item to include as long as we found publicly-available data for that cost item. Our analysis was done using a spreadsheet model with data inputs from the BNF and eMC, the NHS Reference Costs 2011-2012, the NHS electronic Drug Tariff and the 2012 edition of the PSSRU (Personal Social Services Research Unit) Costs for Health and Social Care, and from published and grey literature. A summary of the data inputs will be found in Additional file 2: Appendix B. One issue with our deterministic analysis is the well-known fact that there is: (1) uncertainty in the incidence and severity of illness and for that matter, demands for health intervention using biologic drugs plus (2) uncertainty with regards to treatment outcomes, which fuels future demands for healthcare intervention; for example, dose reduction or escalation; modifications to dosing regimens and treatment protocols and/or deployment of alternative (salvage) interventions in complementary or substitutive ways [5,6]. For this reason, the quantity and costs of NHS resources expended on the administration of biologic drugs cannot be described by fixed values – considering also deviations of what happens in routine clinical practice from the EMA-approved posology. We attempt to resolve this issue by introducing parameter uncertainty into our analysis –by fitting a gamma distribution to the deterministic estimates of Pc as well as PAc, and running 1000 Monte Carlo simulations a for each product. Note that the choice of a gamma distribution is not arbitrary but reflects the observation that healthcare resource use and costs are skewed with non-negative values ranging from zero to positive infinity. As argued by Nixon & Thompson [7], skewed parametric (gamma, log-logistic, lognormal) distributions fit medical cost data better than a normal distribution and should in principle be preferred for estimation. What is not clear, however, is Table 1 Characteristics of product sample Product name Product type Clinical indication considered Disease type Biologics given intravenously Basiliximab † , Simulect® mAb Prophylaxis of acute organ rejection in allogeneic renal transplantation. Acute Bevacizumab, Avastin® mAb First-line treatment of adult patients with non-small cell lung cancer. Chronic Cetuximab, Erbitux® mAb Treatment of epidermal-growth-factor-receptor (EGFR)-expressing, Kirsten Rat Sarcoma-2 (KRAS) wild-type metastatic colorectal cancer. Chronic Infliximab, Remicade® mAb Treatment of active rheumatoid arthritis that is unresponsive to disease modifying anti-rheumatic drugs (DMARDs) or those with severe active disease not previously treated with methotrexate (MTX) or DMARDs. Chronic Oftamumab † , Arzerra® mAb Treatment of chronic lymphocytic leukaemia that is refractory to fludarabine and alemtuzumab. Chronic Panitumumab, Vectibix® mAb Treatment of wild-type KRAS metastatic colorectal cancer. Chronic Tocilizumab, Actemra® mAb Treatment of moderate-to-severe active rheumatoid arthritis. Chronic Trastuzumab, Herceptin® mAb Treatment of advanced and metastatic breast cancer. Chronic Biologics given subcutaneously Adalimumab † , Humira® mAb Treatment of moderate-to-severely active Crohn’s disease in children. Chronic Canakinumab † , Ilaris® mAb Treatment of cryopyrin-associated periodic syndromes (CAPS) in adults. Chronic Certolizumab pegol † , Cimzia® fAb Treatment of moderate-to-severe active rheumatoid arthritis in adults when response to DMARDs including MTX has been inadequate. Chronic Denosumab † , Prolia® mAb Treatment of osteoporosis in post-menopausal women at increased risk of fractures. Chronic Etanercept † , Enbrel® Fusion protein Treatment of active and progressive psoriatic arthritis that has not responded adequately to DMARDs. Chronic Golimumab † , Simponi® mAb Treatment of moderate-to-severe active ankylosing spondylitis. Chronic Omalizumab † , Xolair® mAb Management of immunoglobulin-E mediated asthma. Chronic Ustekinumab † , Stelara® mAb Treatment of moderate-to-severe plaque psoriasis. Chronic Biologics given intramuscularly Palivizumab † , Synagis® mAb Prevention of serious lower respiratory tract disease caused by respiratory syncytial virus (RSV) in children at high risk of RSV disease. Acute Interferon beta-1a † , Avonex® Interferon protein Treatment of relapsing multiple sclerosis in adult patients, i.e., two or more acute exacerbations in the previous three years without evidence of progressive disease. Chronic Notes: † refers to biologics that are sold bundled with some of the equipment and consumables used in drug administration. Tetteh and Morris Health Economics Review 2014, 4:26 Page 4 of 16 http://www.healtheconomicsreview.com/content/4/1/26 which skewed parametric distribution is best. Here we chose a two-parameter (α,β) gamma distribution, and given the absence of real-life data that reflects the uncertainty of healthcare demands requiring intervention with biologics, we adopted the simplest assumption that the mean and SE for administration costs for any given biologic drug in our sample is the same (see Briggs et al. [8]). That is, we apply a gamma distribution defined by α=1 and β= ADMINCOST. We do not expect this to introduce any systematic bias as the assumption will apply to all products within our sample. From the synthetic dataset generated, we estimated the proportion of total administration costs that is due to Pc or PAc for our sample of biologic drugs (categorized according to their respective routes of administration) by graphing a log-log plot of Pc versus PAc. We took logs of Pc and PAc because of the skewness of a gammadistributed cost data and to narrow down the range of (large) values. We then estimated the proportion of simulations where the ratio of proximal costs to physical administration costs (PAc/Pc) is greater than or equal to 1. The essence of this exercise is to identify the source of administration cost savings from changes in drug formulation and manufacturing. Identifying the algorithm Recall that one of our study objectives is to develop an algorithm that will allow manufacturers to predict how administration costs change with how they choose to manufacture and formulate a given biologic drug candidate. On a priori grounds, we defined this algorithm as a sample regression function linking drug administration costs (ADMINCOST) and a number of independent explanatory variables (X). The explanatory variables we chose are those that we believe (bio)pharmaceutical manufacturers will have some information on, or an idea of, as they work on a number of promising biologic drug candidates, and decide which candidates to take forward to the next stage of process R&D or product development, and which ones to reserve as contingency or backup options. Given the expected skewness of our simulated data for ADMINCOST (on the raw scale), we estimate the following with a log-transformed dependent variable: ln ADMINCOSTðÞ¼αþβ0SUBCUTANEOUS þβ1INTRAMUSCULAR þβ2DOSFREQ þβ3PRODUCTBUND þβ4INDICATN þβ5DOSFREQ2 þβ6DOSFREQ:INDICATN þ The intercept is αand the error term ( )represents any unexplained variation in administration costs. SUBCUTANEOUS is a dummy variable that takes the value of one if a product is given subcutaneously and zero otherwise. Equally, the dummy variable INTRAMUSCULAR takes on the value of one if a product is administered intramuscularly and zero otherwise. Intravenous administration is therefore the baseline, benchmark or reference category. We do this because for most biologics, intravenous infusion is the default (conventional) drug delivery or formulation choice given the fragility and poor oral bioavailability of macromolecular proteins. The variable DOSFREQ refers to the frequency (intensity) of dosing, which we define as the number of ‘unit administrations’ in a given year. PRODUCTBUND is a zero-one dummy variable indicating whether a given biologic product is sold together with some of the equipment and consumables used in drug administration (1) or not (0). Similarly, INDICATN is a zero-one dummy variable indicating whether a biologic drug is for the management of an acute illness (0) or for a chronic illness (1). The interaction term DOSFREQ.INDICATN is intended to capture the notion that treatments for acute illnesses tend to have less ‘complex’dosing regimens compared to those for chronic illnesses; and the quadratic term DOSFREQ 2 is intended to determine whether the marginal effects of DOSFREQ are increasing or diminishing as the frequency (intensity) of dosing increases. We estimate the four nested models using linear ordinary least squares (OLS) regression. We labelled the four nested models as A, B, C and D –all of which rely on different combinations of the explanatory variables defined above. We designate C as the full unrestricted model as it includes all the explanatory variables above. Robustness checks A well-known problem with OLS regression using a logtransformed dependent variable is that retransformation of ln d ADMINCOST to the raw untransformed scale gives the geometric mean for d ADMINCOST (which is often close to the median) rather than the arithmetic mean, the parameter of interest. (The hat on ADMINCOST indicates an estimated or predicted value). The problem is resolved by using what is called a smearing factor to minimize the prediction error. The name is derived from the fact that the factor distributes (smears) the ‘excess’ or prediction error in one observation to other observations proportionally when adjusting unlogged median estimates to unlogged mean estimates. Generally, this takes the form: d ADMINCOST ¼exp Xβk ∧  •ф ∧, where ф ∧ is the smearing factor. We looked at three ways of deriving less-biased smearing estimates of ADMINCOST (on the raw untransformed scale). Tetteh and Morris Health Economics Review 2014, 4:26 Page 5 of 16 http://www.healtheconomicsreview.com/content/4/1/26 The first method yields what is called ‘normal theory estimates’that are derived under the assumption that the error term for ln d ADMINCOST is normally distributed, in which case the smearing estimate of ADMINCOST ¼exp X^ βkþ0:5^ σ2  where b σ2is the square of SE(ln d ADMINCOST) and the smearing factor b ф¼exp 0:5^ σ2  . If errors are not normally distributed but are homoscedastic (i.e., constant variance), then the second method, which uses non-parametric (sub-group specific) smearing factors can be used to minimize prediction errors. The non-parametric smearing factor is given by: b ф¼N−1XN i¼1exp c iÞð ,whereNisthenumber of observations and b iis the log-scale residuals from the regression. When the errors are heteroskedastic (i.e., nonconstant variance), or they depend on the explanatory variables, it is “better”to use a subgroup-specific smearing factor for each intravenous, subcutaneous or intramuscular product category [9,10,11]. The third method uses a regression-through-the-origin approach suggested by Wooldridge [12]. This is as follows: obtain for each observation the naïve estimates c mi¼exp d lnADMINCOST  ; then perform a regression of ADMINCOST on c mi through the origin and obtain the only coefficient b α0 as the smearing factor. Irrespective of the smearing factor used, its value in minimizing prediction error depends crucially on the presence and nature of heteroskedasticity in the log scale residuals. For example, the subgroup smearing factors assume that log scale heteroskedasticity varies across the mutually-exclusive subgroups specified. If, however, heteroskedasticity varies according to one or more (continuous, discrete or interacted) explanatory variables in the log-OLS regression, then we will have smearing estimates of ADMINCOST that are still biased. It is possible to run an auxiliary regression of the heteroskedastic variance as a function of one or more of the explanatory variables, i.e., b ф¼exp b iÞ¼ρXðÞð;whereρis a vector of regression coefficients. This crucially depends on how much of the heteroskedastic variance is explained by the chosen set of explanatory variables. Generally, this auxiliary-regression approach is thought to be cumbersome and there is no simple fix if the form of heteroskedasticity is unknown. An alternative estimator, however, exists in the form of generalized linear modelling (GLM) to overcome the retransformation problem. GLM does this by directly and independently specifying: (1) a link function between the raw scale ADMINCOST and the linear index (Xβ k ), and (2) a family of parametric distributions to reflect any heteroskedastic relationship between the raw scale error variance and d ADMINCOST ; i.e., var ADMINCOSTðÞ≅φ:d ADMINCOST hi δ,whereδ is the over-dispersion parameter and φis a constant [11,13,14]. Independent specification of the link function (i.e., the scale of estimation) and family distributions (i.e., the variance function) under GLM allows d ADMINCOST to be estimated directly (or from the natural exponent of ln d ADMINCOSTÞwithout the need for smearing factors. In most applications, three types of link functions are specified: “identity”,“log” and “power”.Hereanidentitylinkspecifiesthefollowing relationship: d ADMINCOST ¼Xβk;andthelog links takes the form d ADMINCOST ¼exp Xβk  .The family distributions commonly investigated or used to model heteroskedasticity are Gaussian if the parameter δ= 0; Poisson if δ= 1, Gamma or heteroskedastic normal if δ= 2 and inverse Gaussian if δ=3. The appropriate family distribution is often identified using the so-called modified Park test, that involves a loggamma GLM regression of var(ADMINCOST)onln d ADMINCOST. The coefficient on ln d ADMINCOST approximates b δ. Notwithstanding, GLM is known to suffer prediction losses if one has heavy tailed data (kurtosis) even after log retransformation of the dependent variable. GLM prediction losses (relative to the log-OLS estimator) increases with the coefficient of kurtosis of the log scale error or when the true underlying model is a log normal with constant error variance (on the log scale). For this reason, Manning and Mullahy [11] and Manning et al. [15] suggest, before using GLM, to assess the form of the log-scale residuals of the OLS regression. If the logscale residuals are heavy-tailed: leptokurtotic (coefficient of kurtosis > 3) or the log-scale error variance (which increases with skewness of the dependent variable) is greater than or equal to one, then log-OLS regression (with the appropriate retransformation for heteroskedastic variance) may be preferable to GLM. If, however, the log-scale residuals are both leptokurtotic and heteroskedastic, then the results from both log-OLS regression and GLM should be reported and compared. If the probability density function (pdf) of the raw-scale residuals from one of the GLM estimators with a log link are not bell-shaped or skewed bell-shaped, then log-OLS models may be less precise. If the pdf of the raw-scale residuals from GLM are monotonically declining then the appropriate family distribution should be identified using a modified Park test. Still another problem with GLM is that independent specification of the link and variance functions could lead to bias and estimation inefficiency. Whilst the Tetteh and Morris Health Economics Review 2014, 4:26 Page 6 of 16 http://www.healtheconomicsreview.com/content/4/1/26 appropriate variance function may be identified from the modified Park test, one obtains different regression coefficients and inferences on incremental/marginal effects as the link function selected varies. We therefore consider an extended estimating equations (EEE) version of GLM (also referred to as power-GLM or PGLM) that doesn’t require a priori specification of the link and variance functions. The PGLM/EEE estimator utilizes the following Box-Cox transformation for the link function: Xβk¼d ADMINCOSTλ−1  =λ;if λ≠0 ln d ADMINCOST  ;if λ¼0 8 > < > : Two broad family distributions can be specified: (1) a “power variance”family characterised by: var ADMINCOST;θ1;θ2 ðÞ¼θ1d ADMINCOST  θ2and (2) a “quadratic variance”family characterised by: var ADMINCOST;θ1;θ2 ðÞ¼θ1d ADMINCOST  þθ2d ADMINCOSTðÞ 2, where θ 1 ,θ 2 together index the appropriate variance distribution for the dataset analysed. By simultaneous specification of the link and variance functions, and joint estimation of the parameters above, PGLM/EEE is a more flexible and robust estimator especially when no specific link or variance function can be identified. For example, if the GLM overdispersion parameter b δis a non-integer, then choosing the closest family distribution could lead to efficiency losses [16,17]. All our analyses were conducted in Microsoft Excel and STATA v. 11. Results Simulations Figure 2 below shows the log-log plot of Pc versus PAc from outputs of the simulations for performed for our product sample. The simulations confirm our expectations that the costs of administering biologics subcutaneously or intramuscularly are mainly from the costs incurred before or after physical administration of a drug –although some deviations (inconsistencies) are evident. Observe that for biologics administered subcutaneously or intramuscularly, most of the simulations lie above the 45° line, which equates Pc to PAc. In contrast, the simulations for intravenous biologics fall on either side of the 45° line with the exception of two drugs: trastuzumab and basiliximab. For trastuzumab, most of the simulations fall above the 45° line, which suggests that the associated proximal cost of administering this drug is higher (relative to the physical administration costs). In the case of basiliximab, most the simulations fall below the 45° line indicating that physical administration costs are higher for that drug. Although Figure 2 provides an idea of the general location of the simulated values for Pc and PAc for each product category, the overlap of data points makes it difficult to tell the pattern for each biologic product. The exact percentage of simulations with the ratio PAc/ Pc ≥1 can, however, be easily computed from the synthesized data. For the intravenous products, the percentage of simulations with the ratio PAc/Pc ≥1 is as follows: basiliximab (95%), bevacizumab (35%), cetuximab (28%), infliximab (28%), oftamumab (49%), panitumumab (46%), tocilizumab (49%) and trastuzumab (9%). For the subcutaneous products, this is as follows: adalimumab (2%), canakinumab (7%), certolizumab pegol (1%), denosumab (22%), etanercept (20%), golimumab (22%), omalizaumab (33%) and ustekinumab (1%). For the intramuscular biologics, we have 17% for palivizumab and 25% for interferon beta-1a. In general, we can say that a higher proportion of the administration costs of biologic drugs given subcutaneously or intramuscularly come from the proximal costs incurred before or after drug administration while for intravenous products, costs are incurred in both cost centres. An aggregated picture of the simulation outputs above is presented below in the histogram with a kernel density overlay (Figure 3). This shows the empirical distribution of ADMINCOST values averaged over the 1000 simulations for each of the 18 sample products. It is right skewed (coefficient of skewness = 2.3568) with heavy tails (coefficient of kurtosis = 8.6048) –thus confirming the overconcentration of gamma-distributed values. The minimum and maximum values are £35.58 and £18,348.85 respectively; and as often observed of skewed and kurtotic data, the median ADMINCOST (£1414.79) is less than half the mean (£3075.77) and the standard deviation (£4477.94) is greater than the mean. A different picture of the distribution of simulated ADMINCOST values is shown in Figure 4 above. This confirms our prior expectations that the costs of administering biologics given subcutaneously or intramuscularly are lower than that of biologics given intravenously. However, the numbers on top of each stacked bar in Figure 4 suggests that one has to be cautious when using cost per unit administration to illustrate variations in biologic drug administration costs. Tetteh and Morris [3], for instance, using a selected set of studies offering a comparable scale of measurement for cost per unit administration, report that the administration costs of intravenous biologics appear to be six to eight times that of biologics given subcutaneously or intramuscularly. Differences observed (on the basis of cost per unit administration) disappear, are attenuated or reversed when one considers drug administration costs over a defined Tetteh and Morris Health Economics Review 2014, 4:26 Page 7 of 16 http://www.healtheconomicsreview.com/content/4/1/26 period of time. It seems to us that differences in dosing frequency is, at least, one of the reasons why cost per unit administration may not be an appropriate indicator of the variation in administration costs. This unfortunately still leaves unanswered the question: by how much do administration costs differ between biologics given intravenously, subcutaneously or intramuscularly? Administration cost algorithm To answer the question above, we turn to the results of our regression-based algorithm shown in Table 2. Note that the results are for ln d ADMINCOST,not d ADMINCOST. The regression coefficients, nevertheless, carry the desired information as to the link between biologic administration costs and the frequency or route of drug administration. As mentioned earlier, we estimate four nested models A, B, C and D with C as the full unrestricted model. From Table 2, model C offers the best fit with our simulated dataset, having the highest adjusted R 2 , lowest sum of squared residuals and the lowest prediction variance, i.e., the square of SE(ln d ADMINCOST ). To ensure robustness, we explore 0.0001 0.001 0.01 0.1 1 10 100 0.0001 0.001 0.01 0.1 1 10 100 Infliximab Basiliximab Bevacizumab Cetuximab Ofatumumab Tocilizumab Panitumumab Trastuzumab 45 degree line 0.00001 0.0001 0.001 0.01 0.1 1 10 0.000001 0.00001 0.0001 0.001 0.01 0.1 1 10 Adalimumab Certolizumab pegol Canakinumab Denosumab Etanercept Golimumab Omalizumab Ustekinumab 45 degree line 0.00001 0.0001 0.001 0.01 0.1 1 10 0.00001 0.0001 0.001 0.01 0.1 1 10 Palivizumab Interferon 45 degree line Figure 2 Simulation outputs. Tetteh and Morris Health Economics Review 2014, 4:26 Page 8 of 16 http://www.healtheconomicsreview.com/content/4/1/26 following subcutaneous administration [27]. Assuming the net effect of SUBCUTANEOUS or INTRAMUSUCLAR and DOSFREQ is a reduction in administration costs, this cost saving might be offset by the fact for a given fixed price per dose, a higher DOSFREQ increases the acquisition costs for that biologic drug. Again, depending on the trade-off between acquisition and administration costs, the overall impact might not be a reduction in disease management or total healthcare delivery costs. Likewise, for the same DOSFREQ, if it costs more to make the reformulated product then to maintain the same pricecost margin, this will lead to a higher product price per dose assuming price demand elasticity remains the same. That said, our regression-based algorithm in these situations should help manufacturers quantify the net impact of their (re) formulation choices on drug administration costs. This, together with considerations of expected product prices, will allow them to generate credible estimates of the total healthcare delivery costs of their products and the likelihood that these products will find favourable recommendations from healthcare payers or providers. It might be argued that our regression-based algorithm is tied to the product sample selected; that different results may be obtained if a different biologic drug sample is used, perhaps one that has a lot more products that are administered intramuscularly. Besides the observation that biologics are rarely formulated for intramuscular administration, that argument is not specific to our case: it is applicable to almost algorithm that has been developed for one purpose or the other. Our regressionbased algorithm may not yield the desired predictions in all situations. That aside, there are non-monetary aspects of drug administration that we haven’t considered here; for example, needle phobia and patient discomfort; inconvenience, disruption of daily activities (from more frequent drug dosing) and non-compliance issues that might negatively affect patients’health. We will argue that it is even possible to have an expanded algorithm that when used to predict the impact on drug formulation choice on healthcare delivery considers both the monetary and non-monetary aspects of drug administration. We suggest that further research is undertaken to evaluate, if possible in monetary terms, the non-monetary attributes of drug administration. Even then an unanswered question is whether biopharmaceutical manufacturers are faced with adequate incentives to consider alternative drug delivery systems or alter their formulation choices as early as possible. From the perspective of the rational or responsible private biopharmaceutical manufacturer, developing alternative drug delivery systemsisworththetime,effort and money if the net present value of that decision is positive (see Chess [28]). That is to say, the discounted present value of the stream of incremental quasi-rents (i.e.,additionalrevenueminusthecostofgoods)thata reformulated biologic product or an alternative drug delivery system is expected to bring should exceed the discounted present value of the incremental costs of developing the alternative drug delivery system or reformulating a product. Within the UK NHS the use of CEA (HTA) and current efforts to implement value-based pricing (partly based on estimated costeffectiveness) could and should provide some incentive for manufacturers to consider the relationship between formulation choices and healthcare delivery costs as early as possible in product development but here we cannot say anything about whether this, on its own, will get manufacturers to change their tact. We believe this is also worth considering in future research. Conclusions In this paper, we have evaluated variations in the magnitude of administration costs of biologic drugs, taking care to ensure consistent inclusion of all relevant cost resources. From this, we developed a regression-based algorithm with which manufacturers could possibly predict, during process development, how their choices on manufacturing and formulation may impact on the healthcare delivery costs of their products. Our results confirm the general notion that the administration costs of intravenous products is higher than that or products administered subcutaneously or intramuscularly. We found that formulating a biologic drug for subcutaneous or intramuscular delivery relative to intravenous delivery is associated with lower administration costs that, holding all else equal, should lead to lower total healthcare delivery costs. Increasing the frequency of drug dosing generally will lead to an increase in administration costs but it is possible that this might not always be the case. There are, however, clinical considerations and manufacturing challenges that might militate against the potential efficiency savings in administration costs from reformulating biologic products or making use of alternative drug delivery systems. But where and when issues of technological feasibility can be dealt with, (bio)pharmaceutical manufacturers could use our algorithm to quantify the net impact on drug administration costs, which together with considerations on the impact on acquisition costs will allow them to generate credible estimates of the total healthcare delivery costs for their products and the likelihood that these products will find favourable recommendations from healthcare payers. Endnotes a Our choice of 1000 simulations is not arbitrary. A simulation convergence test, which is not reported in the paper, suggests a virtually flat administration-cost curve with the number of simulation trials ranging from Tetteh and Morris Health Economics Review 2014, 4:26 Page 15 of 16 http://www.healtheconomicsreview.com/content/4/1/26 1000 to 200,000. We do this by running each 1000 simulation 200 times. b In contrast to Basu & Rathouz [16], we found that the PGLM/EEE with a power variance function failed to converge. Misspecification tests for the PGLM/EEE (QV) suggested a good fit with the data: Pearson correlation between the raw-scale residuals and predicted values was not significantly different from zero, and there was no statistically-significant evidence of systematic patterns in the residuals plotted against predicted values. Additional files Additional file 1: Appendix A: Dosing regimens modelled. Additional file 2: Appendix B: Summary of cost inputs. Competing interests The authors declare that they have no competing interests. Authors’contributions All authors read and approved the final manuscript. Acknowledgements Funding from the UK Engineering & Physical Sciences Research Council (EPSRC) for the EPSRC Centre for Innovative Manufacturing in Emergent Macromolecular Therapies is gratefully acknowledged. Financial support from the consortium of industrial and governmental users is also acknowledged. We will like to thank Teresa Barata (UCL School of Pharmacy) for providing us with the initial list of biologic drugs from which we selected our product sample. Our utmost gratitude to Willard Manning (Harris School of Public Policy, University of Chicago) for statistical advice and support. Received: 6 February 2014 Accepted: 19 September 2014 References 1. Danzon PM, Wang YR, Wang L: The impact of price regulation on the launch delay of new drug - evidence from twenty-five major markets in the 1990s. 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Submit your manuscript to a journal and benefi t from: 7 Convenient online submission 7 Rigorous peer review 7 Immediate publication on acceptance 7 Open access: articles freely available online 7 High visibility within the fi eld 7 Retaining the copyright to your article Submit your next manuscript at 7 springeropen.com Tetteh and Morris Health Economics Review 2014, 4:26 Page 16 of 16 http://www.healtheconomicsreview.com/content/4/1/26