Statistical design for a small serial dilution series

Abstract

We describe statistical plans for a serial dilution series designed to detect and estimate the number of viral particles in a solution. The design addresses a problem when a very limited number of aliquots are available for proliferation. A gamma prior distribution on the number of viral particles allows us to describe the marginal probability distribution of all experimental outcomes. We examine a design that minimizes the expected reciprocal information and compare this with the maximum entropy design. We argue that the maximum entropy design is more useful from the point of view of the laboratory technician. The problem and design are motivated by our study of the viability of human immunodeficiency virus in syringes and other equipment that might mediate blood-borne viral transmission.

Comparison of Use of Concentrated Saliva with Serial Dilution Method in Determination of Candida Colonies in Oral Samples

“…Serial dilution, also called limiting dilution series, is a standard laboratory procedure; [19] the objective of the serial dilution method is to estimate the concentration (number of colonies, organisms, bacteria, or viruses) of an unknown sample by counting the number of colonies cultured from serial dilutions of the sample, and then back track the measured counts to the unknown concentration. Serial dilution techniques are routinely used in hospitals, public health, virology, immunology, and microbiology.…”

A Two-Stage Experimental Design for Dilution Assays

“…In our empirical example we estimated standard errors that were 50% smaller than a standard design with the same sample size, a result consistent with predictions from our simulation study. In contrast to our approach, previous work has focused on SDLA designs that are efficient in the statistical sense (e.g., De St. Groth, 1982;Strijbosch et al, 1987;Matthews, 1998;Zelterman et al, 2010), but the requirements to implement these designs may often be impractical for everyday use by scientists.…”

“…These fractions are then used to define a range of dilutions. Finally, Zelterman et al (2010) proposed using maximum entropy as an alternative to the Fisher information; this accounts for the expected variation in the fraction of nonresponsive wells at each level of dilution. These approaches require experimenters to determine a range of plausible values for .…”

Processing length bias of time intervals between the last episode and the interview in Gamma-Poisson models of behavior

“…= 0 Go to #8 I only drank an alcoholic beverage once in the past 6 months. = 12 , ,..., n T T T  длины временных интервалов между моментом интервью и последним эпизодом, полученные по результатам опроса.…”

“…Вместе с тем стоит учитывать, что указанный опросный инструментарий разрабатывался без учета потребностей, которые возникли позже, например -получение количественных оценок интенсивности рискованного поведения и риска, с ним связанного в эпидемиологических исследованиях ВИЧ/СПИД. Одной из возможных альтернатив представляется опрос респондента об одном или нескольких последних эпизодах его поведения [5][6][7][9][10][11][12]. Заметим, что ответы респондента на такие вопросы о послед-Труды СПИИРАН.…”