Evaluating sampling strategies and logistic regression methods for modelling complex land cover changes

The role of land cover change as a significant component of global change has become increasingly recognized in recent decades. Large databases measuring land cover change, and the data which can potentially be used to explain the observed changes, are also becoming more commonly available. When developing statistical models to investigate observed changes, it is important to be aware that the chosen sampling strategy and modelling techniques can influence results. We present a comparison of three sampling strategies and two forms of grouped logistic regression models (multinomial and ordinal) in the investigation of patterns of successional change after agricultural land abandonment in Switzerland. Results indicated that both ordinal and nominal transitional change occurs in the landscape and that the use of different sampling regimes and modelling techniques as investigative tools yield different results. Synthesis and applications. Our multimodel inference identified successfully a set of consistently selected indicators of land cover change, which can be used to predict further change, including annual average temperature, the number of already overgrown neighbouring areas of land and distance to historically destructive avalanche sites. This allows for more reliable decision making and planning with respect to landscape management. Although both model approaches gave similar results, ordinal regression yielded more parsimonious models that identified the important predictors of land cover change more efficiently. Thus, this approach is favourable where land cover change pattern can be interpreted as an ordinal process. Otherwise, multinomial logistic regression is a viable alternative.

Suicidal expression among school-attending adolescents in a middle-income sub-Saharan country.

We investigated correlates for suicidal expression among adolescents in the Seychelles. Data on 1,432 students (52% females) were derived from the Global School-based Health Survey. Participants were divided into three groups: those with no suicidal behavior (N = 1,199); those with suicide ideation/SI (N = 89); and those reporting SI with a plan to carry out a suicide attempt/SISP (N = 139), each within a 12-month recall period. Using multinomial logistic regression, we examined the strength of associations with social, behavioral and economic indicators while adjusting for covariates. Sixteen percent of school-attending adolescents reported a suicidal expression (10% with a plan/6.2% without). Those reporting SI were younger (relative risk ratio RRR = 0.81; CI = 0.68-0.96), indicated signs of depression (RRR = 1.69; CI = 1.05-2.72) and loneliness (RRR=3.36; CI =1.93-5.84). Tobacco use (RRR = 2.34; CI = 1.32-4.12) and not having close friends (RRR = 3.32; CI = 1.54-7.15) were significantly associated with SI. Those with SISP were more likely to be female (RRR = 0.47; 0.30-0.74), anxious (RRR = 3.04; CI = 1.89-4.88) and lonely (RRR = 1.74; CI = 1.07-2.84). Having no close friends (RRR = 2.98; 1.56-5.69) and using tobacco (RRR = 2.41; 1.48-3.91) were also strongly associated. Having parents who were understanding was protective (RRR = 0.50; CI = 0.31-0.82). Our results suggest that school health promotion programs may benefit from targeting multiple factors associated with suicidal expression. More research, particularly multilevel designs are needed to identify peer and family influences which may modify associations with suicidality.

Stability and change in party preferences.

This article analyses stability and volatility of party preferences using data from the Swiss Household-Panel (SHP), which, for the first time, allow studying transitions and stability of voters over several years in Switzerland. Analyses cover the years 1999- 2007 and systematically distinguish changes between party blocks and changes within party blocks. The first part looks at different patterns of change, which show relatively high volatility. The second part tests several theories on causes of such changes applying a multinomial random-effects model. Results show that party preferences stabilise with their duration and with age and that the electoral cycle, political sophistication, socio-structural predispositions, the household-context as well as party size and the number of parties each explain part of electoral volatility. Different results for withinand between party-block changes underlie the importance of that differentiation.

Pre-Election Positions and Voting Behaviour in Parliament: Consistency among Swiss MPs

This article examines the determinants of positional incongruence between pre-election statements and post-election behaviour in the Swiss parliament between 2003 and 2009. The question is examined at the individual MP level, which is appropriate for dispersion-of-powers systems like Switzerland. While the overall rate of political congruence reaches about 85%, a multilevel logit analysis detects the underlying factors which push or curb a candidate's propensity to change his or her mind once elected. The results show that positional changes are more likely when (1) MPs are freshmen, (2) individual voting behaviour is invisible to the public, (3) the electoral district magnitude is not small, (4) the vote is not about a party's core issue, (5) the MP belongs to a party which is located in the political centre, and (6) if the pre-election statement dissents from the majority position of the legislative party group. Of these factors, the last one is paramount.

Analyse de facteurs déterminants de la substitution par des médicaments génériques en Suisse

Cadre de l'étude La part des dépenses de santé dans les budgets des pays occidentaux est importante et tend à croître depuis plusieurs décennies. Une des conséquences, notamment pour la Suisse, est une augmentation régulière des primes d'assurance maladie, dont l'impopularité incite les responsables politiques à trouver des stratégies de frein à la croissance des coûts de la santé. Les médicaments, qui contribuent notablement à l'augmentation de ces coûts, constituent l'une des cibles classiques d'interventions visant à une réduction des dépenses de santé. Le niveau de coûts des médicaments représente plus de 20% des dépenses de soins du domaine ambulatoire à la charge de l'assurance obligatoire des soins (AOS), soit une dépense annuelle de plus de 4 milliards de francs. Différentes mesures peuvent être utilisées par le gouvernement pour contenir cette facture à charge de la collectivité : baisse du prix des médicaments, limitation du nombre de produits remboursés par l'assurance de base et incitations à la concurrence sur les prix en autorisant les importations parallèles. Depuis que de plus en plus de brevets pour des médicaments sont arrivés à échéance, un autre angle d'attaque s'est concrétisé avec l'incitation à la prescription de médicaments génériques. Les génériques sont définis comme des produits thérapeutiques chimiquement identiques à des composés déjà utilisés, appelés médicaments originaux. En principe, une économie substantielle devrait pouvoir être réalisée sur les coûts totaux des médicaments si tous les génériques disponibles sur le marché étaient systématiquement prescrits par les professionnels et acceptés par les patients. Les résultats publiés par les caisses maladie et les offices fédéraux sont des estimations globales et les montants publiés par l'industrie pharmaceutique concernent l'ensemble du marché, incluant les médicaments utilisés dans les séjours hospitaliers, sont par ailleurs exprimés en prix de fabrique. De plus, aucune étude n'a tenu compte de la substituabilité des produits d'un point de vue pharmaceutique. L'objectif général de la thèse est d'évaluer aussi précisément que possible l'économie pouvant être encore réalisée dans le secteur ambulatoire en substituant aux médicaments originaux les produits génériques présents sur le marché et de caractériser plusieurs facteurs qui influencent la substitution générique. Pour cette étude, nous avons pu disposer de l'ensemble des factures pharmaceutiques de la caisse maladie CSS, pour tous ses assurés des cantons d'Argovie, du Tessin et de Vaud, soit plus de 169'000 assurés représentant les trois régions linguistiques de la Suisse. Les 1'341'197 prescriptions médicales qui ont été analysées concernent l'année 2003. C'est un moment critique dans l'histoire des génériques en Suisse, approprié pour établir un premier bilan après l'entrée en vigueur de la première mesure relative au droit de substituer octroyé en 2001 aux pharmaciens et, pour identifier idéalement les principaux déterminants de la substitution par les praticiens avant l'introduction de la quote-part différenciée en 2006. La présence d'un même principe actif n'est pas une condition suffisante pour permettre une substitution et pour ce travail des critères tenant compte des caractéristiques pharmaceutiques des produits ont été établis et appliqués pour valider la substituabilité des originaux par les génériques disponibles sur le marché. Ces critères concernent notamment le mode d'administration, le dosage et le nombre de doses dans l'emballage. L'étude a été réalisée selon deux approches, d'abord par une analyse descriptive sur l'ensemble de la population source pour estimer le marché des génériques et ensuite par une analyse statistique (régression logit multivariée) sur 173'212 prescriptions agrégées, qui concernent spécifiquement soit un générique soit un original substituable, pour caractériser les facteurs déterminants de la substitution générique. Résultats Dans l'ensemble de la population source, les génériques et les originaux substituables représentent 17,4% du marché en termes de coûts facturés, avec 3,4% de génériques et 14,0% d'originaux substituables ce qui correspond à un taux de substitution de 19,5%. En termes de dépenses, les substitutions génériques réalisées représentent une économie de 1,3% du total du marché étudié alors qu'il reste un potentiel notable d'économie par la substitution de 4,6%. Les taux de substitution sont très variables selon les cantons : 10,1% au Tessin, 29,0% pour le canton de Vaud et 35,8% pour Argovie. L'analyse univariée des 173'212 prescriptions de génériques ou d'originaux substituables, montre des taux de substitution plus élevés chez les patients jeunes et lorsqu'il y a d'importantes différences de prix entre les originaux et les génériques. Des taux de substitution peu élevés sont observés chez les patients les plus âgés et pour ceux qui ont des traitements médicamenteux complexes. Les patients ayant plus de 10 médicaments différents durant la même année, présentent une probabilité relative de substituer inférieure (-24%) par rapport aux patients ayant 6 à 10 médicaments différents dans l'année. Cependant, l'analyse multivariée montre que l'effet négatif sur le taux de substitution de l'âge combiné à la complexité des traitements n'excède pas 3%. Bien que le niveau de franchises et la participation financière à la quote-part soient liées à une augmentation de la prescription de génériques, leurs effets sont modérés pour les patients avec des franchises supérieures à 300 francs (effet marginal de 1%) et pour les patients qui n'ont pas atteint le plafond de participation (effet marginal de 2%). La différence de taux substitution entre les médecins hospitaliers et les spécialistes est diminuée de façon notable (effet marginal de -13%) et elle est cependant moins marquée avec les médecins généralistes (effet marginal de -3%). Les facteurs associés au marché ont une influence notable sur la substitution générique et des effets positifs sont observés avec l'augmentation de la taille du marché, du nombre de génériques pour un même original substituable et de l'économie relative entre l'original et le générique. Par contre, la diversification des formes galéniques et des tailles d'emballages au niveau de l'offre des médicaments originaux a des effets fortement négatifs sur la substitution générique (-7%). Le canton de domicile a aussi un impact notable sur la substitution et le canton du Tessin présente un taux plus bas (-26%) que le canton d'Argovie. Conclusion et perspectives Ce travail a montré qu'il y a encore un important potentiel d'économies à réaliser par la substitution générique, calculé à plus de 4% des dépenses pharmaceutiques prises en charge par l'AOS en ambulatoires. Une extrapolation à l'ensemble du marché suisse, qui doit être faite avec prudence, fait apparaître un potentiel d'économies de 127 millions pour les médicaments délivrés par les pharmacies en 2003. L'étude a mis en évidence un certain nombre de déterminants qui freinent la substitution générique, notamment la prescription par un médecin hospitalier. Sur ce point la prescription en DCI (dénomination commune internationale) pourrait favoriser la dispensation de génériques moins chers. Un taux de substitution plus faible est observé chez les patients âgés avec des traitements complexes. Ce constat peut être mis en relation avec la crainte d'avoir un traitement moins efficace ou moins bien supporté et les risques de confusion lors du passage d'un original substituable à un générique ou d'un générique à un autre générique. Sur ces éléments, l'indication claire et précise du nom de la substance, aussi bien sur les emballages des originaux substituables que sur ceux des génériques, pourrait rassurer les patients et diminuer les risques d'erreurs dans la prise des médicaments. Certaines précautions à prendre lors de la prescription de génériques sont reconnues, notamment pour les médicaments à faible marge thérapeutique, et des informations sur la bioéquivalence, régulièrement mises à jour et à disposition des professionnels, pourraient augmenter la confiance dans l'utilisation des génériques. Les industries pharmaceutiques préservent par différentes tactiques leurs parts de marché et notamment avec succès en introduisant de nouvelles formes galéniques juste avant l'expiration des brevets. Des directives complémentaires sur la fixation des prix pour le remboursement, en particulier l'introduction d'un prix de référence quelle que soit la forme galénique, pourraient diminuer l'effet de barrage des médicaments originaux. Les incitations économiques, telles que la franchise et les participations sont efficaces si l'on considère l'impact sur les taux de substitution. Leur effet global reste toutefois modeste et il serait nécessaire de mesurer concrètement l'impact de l'introduction en 2006 de la quote-part différenciée. Les différences de prix entre les originaux et les génériques exigées à 50% pour les gros marchés, c'est-à-dire de plus de 16 millions, devraient aussi avoir un impact qu'il serait opportun de mesurer.

Disagreements among cohabiting and married couples in 22 European countries

Background: Cross-national research suggests that married people have higher levels of well-being than cohabiting people. However, relationship quality has both positive and negative dimensions. Researchers have paid little attention to disagreements within cohabiting and married couples. Objective: This study aims to improve our understanding of the meaning of cohabitation by examining disagreements within marital and cohabiting relationships. We examine variations in couples' disagreements about housework, paid work and money by country and gender. Methods: The data come from the 2004 European Social Survey. We selected respondents living in a heterosexual couple relationship and aged between 18 and 45. In total, the study makes use of data from 22 European countries and 9,657 people. Given that our dependent variable was dichotomous, we estimated multilevel logit models, with (1) disagree and (0) never disagree. Results: We find that cohabitors had more disagreements about housework, the same disagreements about money, but fewer disagreements about paid work than did married people. These findings could not be explained by socio-economic or demographic measures, nor did we find gender or cross-country differences in the association between union status and conflict. Conclusions: Cohabiting couples have more disagreements about housework but fewer disagreements about paid work than married people. There are no gender or cross-country differences in these associations. The results provide further evidence that the meaning of cohabitation differs from that of marriage, and that this difference remains consistent across nations.

Alcohol and nonlethal injuries: a Swiss emergency department study on the risk relationship between acute alcohol consumption and type of injury.

BACKGROUND: Acute alcohol consumption has been reported to be an important risk factor for injury, but clear scientific evidence on issues such as injury type is not available. The present study aims to improve the knowledge of the importance of alcohol consumption as an injury determinant with regards to two dimensions of the type of injury, namely the nature and the body region involved. METHODS: Risk relationships between two injury type components and acute alcohol use were estimated through multinomial and logistic regression models based on data from 7,529 patients-among whom 3,682 had injury diagnoses-gathered in a Swiss emergency department. RESULTS: Depending on the type of injury, between 31.1% and 48.7% of casualties report alcohol use before emergency department attendance. The multinomial regression models show that even low alcohol levels are consistently associated with nearly all natures of injury and body regions. A persistent dose-response effect between alcohol levels and risk associations was observed for almost all injury types. CONCLUSIONS: The results highlight the importance and consistency of the risk association between low and moderate levels of acute alcohol consumption and all types of injury. None of the body regions and natures of injury could pride on absence of association between alcohol and injury. Public health, prevention, and care implications are considered.

The European Respiratory Society spirometry tent: a unique form of screening for airway obstruction.

In order to raise public awareness of the importance of early detection of airway obstruction and to enable many people who had not been tested previously to have their lung function measured, the European Lung Foundation and the European Respiratory Society (ERS) organised a spirometry testing tent during the annual ERS Congresses in 2004-2009. Spirometry was performed during the ERS Congresses in volunteers; all participants answered a simple, brief questionnaire on their descriptive characteristics, smoking and asthma. Portable spirometers were freely provided by the manufacturer. Nurses and doctors from pulmonary departments of local hospitals/universities gave their service for free. Lower limit of normal (LLN) and Global Initiative for Chronic Obstructive Lung Disease (GOLD) criteria for diagnosing and grading airway obstruction were used. Of 12,448 participants in six congress cities, 10,395 (83.5%) performed acceptable spirometry (mean age 51.0 ± 18.4 yrs; 25.5% smokers; 5.5% asthmatic). Airway obstruction was present in 12.4% of investigated subjects according to LLN criteria and 20.3% according to GOLD criteria. Through multinomial logistic regression analysis, age, smoking habits and asthma were significant risk factors for airway obstruction. Relative risk ratio and 95% confidence interval for LLN stage I, for example, was 2.9 (2.0-4.1) for the youngest age (≤ 19 yrs), 1.9 (1.2-3.0) for the oldest age (≥ 80 yrs), 2.4 (2.0-2.9) for current smokers and 2.8 (2.2-3.6) for reported asthma diagnosis. In addition to being a useful advocacy tool, the spirometry tent represents an unusual occasion for early detection of airway obstruction in large numbers of city residents with an important public health perspective.

Origin and outcome of multiple pregnancies in Bern, Switzerland, 1995-2006 and the current proposal of the Swiss parliament to revise the Swiss law of reproductive medicine: Switzerland quo vadis?

INTRODUCTION: Infertility treatments are a major source of the increase in multiple pregnancies (MPs). AIMS: The aims of the present study were (1.) to investigate the origin and maternal/neonatal outcomes of MP and (2.) to review the different measures that can be adopted to reduce these serious complications. METHODS: The study included all women with multiple births between 1 January 1995 and 31 December 2006 at the University Hospital of Bern, Switzerland. The outcomes associated with the various origins of MP (natural conception, ovarian stimulation [OS] ‒ in-vitro fertilisation [IVF-ICSI]) were analysed using a multinomial logistic regression model. An analysis of the Swiss law on reproductive medicine and its current proposed revision, as well as a literature review using Pubmed, was carried out. RESULTS: A total of 592 MP were registered, 91% (n = 537) resulted in live births. There was significantly more neonatal/maternal morbidity in MP after OS compared with natural conception and even with the IVF-ICSI group. With a policy of elective single embryo transfer (eSET), twin rates after IVF-ICSI can be reduced to <5% and triplets to <1%. CONCLUSIONS: After OS, more triplets are found and the outcome of MP is worse. MP is known to be associated with morbidity, mortality, and economic and social risks. To counteract these complications (1.) better training for physicians performing OS should be encouraged and (2.) the Swiss law on reproductive medicine needs to be changed, with the introduction of eSET policies. This would lead to a dramatic decrease in neonatal and maternal morbidity/mortality as well as significant cost reductions for the Swiss healthcare system.

PACIC Instrument: disentangling dimensions using published validation models.

OBJECTIVE: To better understand the structure of the Patient Assessment of Chronic Illness Care (PACIC) instrument. More specifically to test all published validation models, using one single data set and appropriate statistical tools. DESIGN: Validation study using data from cross-sectional survey. PARTICIPANTS: A population-based sample of non-institutionalized adults with diabetes residing in Switzerland (canton of Vaud). MAIN OUTCOME MEASURE: French version of the 20-items PACIC instrument (5-point response scale). We conducted validation analyses using confirmatory factor analysis (CFA). The original five-dimension model and other published models were tested with three types of CFA: based on (i) a Pearson estimator of variance-covariance matrix, (ii) a polychoric correlation matrix and (iii) a likelihood estimation with a multinomial distribution for the manifest variables. All models were assessed using loadings and goodness-of-fit measures. RESULTS: The analytical sample included 406 patients. Mean age was 64.4 years and 59% were men. Median of item responses varied between 1 and 4 (range 1-5), and range of missing values was between 5.7 and 12.3%. Strong floor and ceiling effects were present. Even though loadings of the tested models were relatively high, the only model showing acceptable fit was the 11-item single-dimension model. PACIC was associated with the expected variables of the field. CONCLUSIONS: Our results showed that the model considering 11 items in a single dimension exhibited the best fit for our data. A single score, in complement to the consideration of single-item results, might be used instead of the five dimensions usually described.

To use it or not to use it: differences between adolescent males carrying a weapon and those using it in a fight

Purpose Data indicate that 19% of male adolescents living in Switzerland carried a weapon in the last 12 months. The main objective of this research is to compare the characteristics of male adolescents carrying a weapon and having used it in a fight from those who have carried but not used it in the previous 12 months. Methods Data were drawn from the 2002 Swiss Multicenter Adolescent Survey on Health (SMASH02) data base, a survey including 7,548[3,710 males] in-school adolescents aged 16-20 years in Switzerland. Only males declaring having carried a weapon (N = 711; 19.2% of the sample) were included in the analysis. Three groups were created: those not having used a weapon (WO; N = 538 subjects), those having used a weapon in a fight once or twice (W12; N = 127), and those having used a weapon in a fight 3 or more times (W3+; N = 46). Multinomial logistic regression was performed to compare the 3 groups on individual, family, school, and social factors using WO as the reference category. Analyses were performed with STATA9. Results are presented as relative risk ratios (RRR). Results W12 males were significantly more likely to perceive their puberty as advanced compared to their peers (RRR: 2.1), to be foreign born (RRR: 2.6), to live in an urban environment (RRR: 1.9), to be in vocational school (RRR: 4.7), to have a poor school connectedness (RRR: 1.8), to skip classes (RRR: 2.1) and to quarrel while intoxicated (RRR: 5.3). W3+ males were significantly more likely to be foreign born (RRR: 3.6) and to live in an urban environment (RRR: 2.4), to be current users of illegal drugs other than cannabis (RRR: 3.8) and to quarrel while intoxicated (RRR: 4.1). No differences were found between groups for tobacco, alcohol, or cannabis use. Conclusions Within a national sample of Swiss youth aged 16-20 years, almost one fifth of male adolescents have carried a weapon in the previous 12 months. Nevertheless, most of them (75.7%) have never used a weapon in a fight. Whether they carry a weapon for defense purposes or as a manly behavior remains to be elucidated. However, urban foreign-born adolescents who quarrel while intoxicated are the most at risk of using a weapon in a fight, and therefore culturally-sensitive prevention approaches need to be developed to decrease violence in this specific population of youth. Having school problems or using illegal drugs other than cannabis seem to differentiate between those who use it in a fight occasionally (once or twice) and those who do it more often.

Extra burden of psychosomatic complaints among adolescents suffering from chronic conditions.

OBJECTIVE:: To determine whether there are differences in health perception and health care use among adolescents with psychosomatic symptoms (PS), with chronic conditions (CCs), and with both conditions compared with healthy controls. METHODS:: By using the SMASH02 database, 4 groups were created: youths with PS but no CCs (N = 1010); youths with CCs but no PS (N = 497); youths with both psychosomatic symptoms and chronic conditions (PSCC, N = 213); and youths with neither PS nor CC (control, N = 5709). We used χ tests and analysis of variance to compare each variable between the 4 groups. In a second step, all health and health care use variables were included in a multinomial regression analysis controlling for significant (p < .05) background variables and using the control group as the reference. RESULTS:: Overall, PS and PSCC youths were significantly more likely to rate their health as poor, to be depressed, and to have consulted several times their primary health care provider or a mental health professional than their healthy peers. With the exception of being depressed, PSCC adolescents reported worse health perception and higher health care use than CC and PS. CONCLUSIONS:: Although PS youths do not define PS as a CC, it should be considered as one. Moreover, having PS represents an additional burden to chronically ill adolescents. Health professionals dealing with adolescents must be aware of the deleterious health effects that PS can have on adolescents and have this diagnosis in mind to better target the treatment and improve their management.

Acute alcohol consumption and injury: risk associations and attributable fractions for different injury mechanisms.

OBJECTIVE: Most studies on alcohol as a risk factor for injuries have been mechanism specific, and few have considered several mechanisms simultaneously or reported alcohol-attributable fractions (AAFs)-which was the aim of the current study. METHOD: Data from 3,592 injured and 3,489 noninjured patients collected between January 2003 and June 2004 in the surgical ward of the emergency department of the Lausanne University Hospital (Switzerland) were analyzed. Four injury mechanisms derived from the International Classification of Diseases, 10th Revision, were considered: transportation-related injuries, falls, exposure to forces and other events, and interpersonal violence. Multinomial logistic regression models were calculated to estimate the risk relationships of different levels of alcohol consumption, using noninjured patients as quasi-controls. The AAFs were then calculated. RESULTS: Risk relationships between injury and acute consumption were found across all mechanisms, commonly resulting in dose-response relationships. Marked differences between mechanisms were observed for relative risks and AAFs, which varied between 15.2% and 33.1% and between 10.1% and 35.9%, depending on the time window of consumption (either 6 hours or 24 hours before injury, respectively). Low and medium levels of alcohol consumption generally were associated with the most AAFs. CONCLUSIONS: This study underscores the implications of even low levels of alcohol consumption on the risk of sustaining injuries through any of the mechanisms considered. Substantial AAFs are reported for each mechanism, particularly for injuries resulting from interpersonal violence. Observation of a so-called preventive paradox phenomenon is discussed, and prevention or intervention measures are described.

Malaria haplotype frequency estimation.

We present a Bayesian approach for estimating the relative frequencies of multi-single nucleotide polymorphism (SNP) haplotypes in populations of the malaria parasite Plasmodium falciparum by using microarray SNP data from human blood samples. Each sample comes from a malaria patient and contains one or several parasite clones that may genetically differ. Samples containing multiple parasite clones with different genetic markers pose a special challenge. The situation is comparable with a polyploid organism. The data from each blood sample indicates whether the parasites in the blood carry a mutant or a wildtype allele at various selected genomic positions. If both mutant and wildtype alleles are detected at a given position in a multiply infected sample, the data indicates the presence of both alleles, but the ratio is unknown. Thus, the data only partially reveals which specific combinations of genetic markers (i.e. haplotypes across the examined SNPs) occur in distinct parasite clones. In addition, SNP data may contain errors at non-negligible rates. We use a multinomial mixture model with partially missing observations to represent this data and a Markov chain Monte Carlo method to estimate the haplotype frequencies in a population. Our approach addresses both challenges, multiple infections and data errors.