A negative binomial model for sampling mosquitoes in a malaria survey

Sampling models are investigated for counts of mosquitoes from a malaria field survey conducted by the World Health Organization in Nigeria. The data can be described by a negative binomial model for two-way classified counted data, where the cell means are constrained to satisfy row-by-column independence and the parameter k is constant across rows. An algorithm, based on iterative proportional fitting, is devised for finding maximum likelihood estimates. Sampling properties of the estimates and likelihood-ratio statistics for the small sample sizes of the data are investigated by Monte Carlo experiments. The WHO reported an observation that the relative efficiencies of four trapping methods vary over time. Out of eight villages in the survey area, this observation is found to be true in only the one village that is near a swamp.     

The prevalence of malaria in Garki, Nigeria: double sampling with a fallible expert

Data from the Garki Project are analyzed to assess how misdiagnosis affects the estimated prevalence of Plasmodium falciparum. Three double-sampling models that account for the fallibility of the expert are derived and applied. The models incorporate information about the density of parasites in the blood to varying degrees. The error in the estimation of prevalence is quantified; and its dependence on calendar time, age, prevalence, and density is investigated. Prevalence and average density are discovered to be good predictors of the error, with the latter being better. Implications of the double-sampling models for the design of epidemiological surveys similar to the one in Garki are investigated.     

Introductory review some new thoughts about some old malaria models

Simple models for the dynamics of endemic malaria are reviewed. A reanalysis of Ross's models explains Lotka's interpretation of them, and finds a historical context for the vectorial-capacity construction of an inoculation rate. Important epidemiological parameters are scrutinized. Inference problems are discussed concerning estimating mosquito density, recognizing the maternal-antibody effect, choosing among models for superinfection, and accounting for diagnostic error.     

Inference for an age-dependent,multitype branching-process model of mast cells

We consider an age-dependent, multitype model for the growth of mast cells in culture. After a colony of cells is established by an initiator type, the two possible types of cells are resting and proliferative. Using novel inferential procedures, we estimate the generation-time distribution and the offspring distribution of proliferative cells, and the waiting-time distribution of resting cells.List of Notations B _i cumulative distribution function for the time until branching of a cell of type i - b _i probability density function for the time until branching of a cell of type i - b _i b _i (1–D _i ) - D _i cumulative distribution function for the time until death of a cell of type i - d _i probability density function for the time until death of a cell of type i - probability density function of a gamma distribution - G _i cumulative distribution function for the lifetime of a cell of type i - G _1*2 Convolution of G ₁ and G ₂ - ¯G _i 1–G _i - g _i probability density function for the lifetime of a cell of type i - L _i likelihood of a history of type i - m average number of proliferative daughters produced by dividing cells - M _ij (t) the expected number of type-j cells in a colony at time t if that colony began at time 0 with one type-i cell - M _i+ (t) M _i0 (t) + M _i 1(t) + M _i 2(t) - p _rs probability that a dividing cell produces r proliferative and s resting daughters - t _i times defining colony histories. See IV.2.1 - T ₀ time to division of an initiator cell - T ₁, T ₂ times from birth to division of the two daughters of an initiator cell - T ₍₁₎, T ₍₂₎ order statistics of T ₁ and T ₂ - minimum value of a gamma distribution - scale parameter of a gamma distribution or of an exponential distribution - probability per unit time of death for proliferative and resting cells - _rs expected value of p _rs when there is heterogeneity - shape parameter of a gamma distribution     

Investigation into the experimental kinetic support of the two-state model of the cell cycle

Five previously published cell generation-time distribution functions have been examined in an effort to elucidate the parameters of the two-state model of the cell cycle. These parameters are the fractional number of cells that bypass the G₀ state, the probability of exit from G₀ and the distribution of traversal times through the active state. To explain observed β-curve behavior of cell populations, it is necessary to define the parameters in terms of pairwise behavior of newborn sister cells. From the β-curve, we demonstrate that at least 50% of the cells must pass through the G₀ state. The α-curve is consistent with any positive fraction of newborn cells passing through the G₀ state, and provides no further information. We explore a possible method for resolving the remaining indeterminacy regarding the number of cells bypassing the G₀ state, namely, examination of the generation-time distribution functions of fast sister cells only. Such an approach, although theoretically attractive, presents formidable experimental difficulties, however. If it should turn out that indeed only 50% of the cells are apparently passing through a randomexiting phase of the cell cycle, then an alternative plausible biological mechanism for the observed variability in generation times is supplied by Prescott's hypothesis: variability is a consequence of the inequality in the metabolic content of sister cells at birth.     

Estimation for a model of multiple malaria infections

The Macdonald-Dietz model for superinfection in malaria is a time-dependent infinite-server queue. However, the queue is only partially observable; it can be ascertained only as not empty or empty. Moreover, continuous observation of the queue is impossible. This paper derives likelihoods for the model's parameters with incomplete, multiwave panel data, and numerically maximizes those likelihoods for some data from a field study in Nigeria.     

Quantitative PCR with internal controls

We examine the use of internal controls for estimating the expectedinitial copy number of the target in a polymerase chain reaction(PCR). We base our investigation on an extended branching-processmodel. In terms of that model, we delineate the necessary assumptionsfor this methodology to yield approximately unbiased answers,and we provide means for testing some of those assumptions.We show how to design a series of PCRs to attain optimal precisionof the estimate. We provide an algorithm for conducting thestatistical analysis of the data, including a formula for aconfidence interval for the unknown expected initial copy number.     

Error analysis in flow microfluorometry

Sources of error in a typical algorithm for the analysis of single flow-microfluorometric histograms are identified. A new statistical model for such data is presented, by means of which the error sources are quantitatively investigated. These theoretical investigations lead to three practical observations: A more detailed characterization of the fluorescence dispersion process is needed for a more refined algorithm. Levels of dispersion typically experienced are such that from a single histogram the distribution of cells within S-phase cannot be finely resolved; but the crude distribution of cells among the three phases G1, S, and G2-M may be accurately estimated. If currently typical levels of dispersion can be halved, then the S-phase distribution can be finely resolved.     

Enhanced kidney clearance with an ester-linked 99mTc-radiolabeled antibody Fab'-chelator conjugate

Bifunctional chelators for labeling antibodies with 99mTc based on the N3S core of (mercaptoacetyl)-triglycine having ester or amide linking moieties were synthesized and site-specifically attached to the sulfhydryl groups of the Fab' fragment of antimyosin. Protein labeling was quantitative after 15 min; postlabeling purification was not necessary. The radiolabeled conjugates exhibited no loss of immunoreactivity. Under basic conditions, the ester-linked conjugate lost 95% of the radiolabel in the form of the 99mTc complex of (mercaptoacetyl)triglycine as determined by RP-HPLC, while the radioactivity in the amide-linked conjugate remained completely bound to the protein. In a mouse biodistribution study, the ester-linked conjugate showed a 2-fold enhancement in clearance from the kidney when compared to the amide-linked product.     

Inoculation and recovery rates in the malaria model of Dietz,Molineaux, and Thomas

In the malaria model of Dietz, Molineaux, and Thomas [Bull. WHO 50:347–357 (1974)] the iroculation rate depends on a pseudoequilibrium approximation to a differential equation describing mosquito dynamics. By biasing a key parameter, the approximation can match the predictions of the differential equation; with fixed parameters, the approximation sometimes predicts qualitatively different disease behavior than does its approximand. The model's recovery rate depends on an approximation to a full time-dependent formulation of Macdonald's superinfection hypothesis. Judged by the ability to fit data, the approximation performs better than its approximand. Alternative implementations of the model yield significantly different estimates of scientifically meaningful parameters.