Selection Bias In Estimates Research Articles

Estimating survival in photographic capture–recapture studies: overcoming misidentification error

Summary1. For many species, noninvasive photographic identification offers a powerful and cost–effective method for estimating demographic parameters and testing ecological hypotheses in large populations. However, this technique is prone to misidentification errors that can severely bias capture–recapture estimates.2. We present a simple ad hoc data conditioning technique that minimizes bias in survival estimates across all rates of misidentification. We use simulated data sets to characterize trade‐offs in bias, precision and accuracy of survival estimators for a range of misidentification probabilities, sampling intensities, survival rates and population sizes using this conditional approach.3. Misidentification errors resulted in mean survival estimates that were negatively biased by as much as −24·9% when errors were ignored. Applying the conditional approach resulted in very low levels of bias across parameter space. However, the main cost of conditioning is a loss of precision, which was particularly severe at low sampling intensities. Overall, the conditional approach was superior to the nonconditional approach [in terms of root mean square error (RMSE) of survival estimates] in 51% of the parameter combinations that we explored.4. We apply the data conditioning technique to a 3‐sample capture–recapture data set compiled from 2551 images of a migratory wildebeest, Connochaetes taurinus, population in northern Tanzania. We estimate the false rejection rate (i.e., the probability of failing to match two photographs of the same individual) using a test set of ‘known‐identity’ individuals. With this information, we compare survival estimates derived from conditioned data ( = 0·698 ± 0·176), unconditioned data ( = 0·706 ± 0·121) and simulated data to illustrate some of the key considerations for deciding whether to apply a conditional approach to a photographic data set.5. These analyses demonstrate that ignoring misidentification error can lead to substantial bias in survival estimates. When sampling intensity and misclassification error rates are both relatively high, use of our conditioned data approach is preferred and yields survival estimates with lower RMSE. However, when sampling intensity and misclassification error are both small, the standard approach using unconditioned data yields smaller RMSE.

Estimating demographic parameters for capture–recapture data in the presence of multiple mark types

In mark-recapture studies, various techniques can be used to uniquely identify individual animals, such as ringing, tagging or photo-identification using natural markings. In some long-term studies more than one type of marking procedure may be implemented during the study period. In these circumstances, ignoring the different mark types can produce biased survival estimates since the assumption that the different mark types are equally catchable (homogeneous capture probability across mark types) may be incorrect. We implement an integrated approach where we simultaneously analyse data obtained using three different marking techniques, assuming that animals can be cross-classified across the different mark types. We discriminate between competing models using the AIC statistic. This technique also allows us to estimate both relative mark-loss probabilities and relative recapture efficiency rates for the different marking methods. We initially perform a simulation study to explore the different biases that can be introduced if we assume a homogeneous recapture probability over mark type, before applying the method to a real dataset. We make use of data obtained from an intensive long-term observational study of UK female grey seals (Halichoerus grypus) at a single breeding colony, where three different methods are used to identify individuals within a single study: branding, tagging and photo-identification based on seal coat pattern or pelage.

Capture-recapture models with heterogeneity to study survival senescence in the wild

Detecting senescence in wild populations and estimating its strength raise three challenges. First, in the presence of individual heterogeneity in survival probability, the proportion of high-survival individuals increases with age. This increase can mask a senescence-related decrease in survival probability when the probability is estimated at the population level. To accommodate individual heterogeneity we use a mixture model structure (discrete classes of individuals). Second, the study individuals can elude the observers in the field, and their detection rate can be heterogeneous. To account for detectability issues we use capture–mark–recapture (CMR) methodology, mixture models and data that provide information on individuals’ detectability. Last, emigration to non-monitored sites can bias survival estimates, because it can occur at the end of the individuals’ histories and mimic earlier death. To model emigration we use Markovian transitions to and from an unobservable state. These different model structures are merged together using hidden Markov chain CMR models, or multievent models. Simulation studies illustrate that reliable evidence for survival senescence can be obtained using highly heterogeneous data from non site-faithful individuals. We then design a tailored application for a dataset from a colony of black-headed gull Chroicocephalus ridibundus. Survival probabilities do not appear individually variable, but evidence for survival senescence becomes significant only when accounting for other sources of heterogeneity. This result suggests that not accounting for heterogeneity leads to flawed inference and/or that emigration heterogeneity mimics survival heterogeneity and biases senescence estimates.

Postbranding Survival of Steller Sea Lion Pups at Lowrie Island in Southeast Alaska

ABSTRACT Steller sea lion (Eumetopias jubatus) pups (n = 366) were hot‐branded at Lowrie Island, Southeast Alaska, USA, in June 2001 and 2002 for vital‐rates studies. To assess potential mortality following branding, we estimated weekly survival to 12 weeks postbranding using mark‐recapture models. Survival estimates ranged from 0.984/week to 0.988/week, or 0.868 over the 12‐week period; varied little with sex, year, and capture area; and were higher for larger than smaller male pups and unexpectedly lower for larger than smaller female pups. Inclusion of resights at 1–3 years of age prevented a −4.5% bias in cumulative survival to 12 weeks postbranding by accounting for pups that survived but permanently emigrated from Lowrie Island during the 12‐week survey. Data from double‐marked pups (i.e., branded and flipper‐tagged) indicated the low brand‐misreading probability of 3.1% did not bias survival estimates. Assuming survival differences between the first 2 weeks postbranding and later weeks were due entirely to the branding event, potential postbranding mortality of branded pups attributable to the branding event was 0.5–0.7%, or one pup for every 200 marked. Weekly survival of branded pups was nearly identical to estimates from a control group of undisturbed, unbranded pups born to 10–11‐year‐old branded adult females in 2005 (0.987–0.988/week) and similar to pup survival estimates from other otariid studies. Available data did not indicate substantial mortality to 12 weeks postbranding resulting from the branding disturbance, suggesting branding of Steller sea lion pups can be used effectively for investigations of population declines without significantly affecting population health or study goals.

Inside the house of learning: the relative performance of public and private schools in Orissa

Empirical evidence shows that the quality of learning in public schools is very low in India. There is also a robust belief that private schools offer better‐quality learning at a lower cost and are a cost‐effective alternative to public schools. Most of the evidence on which this latter claim is based does not correct for selection bias – students who go to private schools may differ systematically from students who go to public schools on observable and unobservable characteristics. In this context, it is entirely plausible that public schools may be no worse or even better than private schools although the latter may still be more cost‐effective. In this paper, we use a strategy suggested by Altonji, Elder, and Taber to estimate selection bias in the positive private school effect on test scores. We use test scores data on Grade Four students attending public and private schools in the eastern state of Orissa in India. Our findings suggest that there is a true private school effect as only 12–13% of the adjusted test score difference is due to selection on unobserved factors.

Estimating Duration of Short‐Term Acute Effects of Capture Handling and Radiomarking

ABSTRACT Radiotelemetry is used extensively in zoographic studies of wildlife species, including northern bobwhite (Colinus virginianus). These studies assume that radiomarking does not affect survival of marked individuals. However, most researchers implicitly acknowledge that capture, handling, and radiomarking may have short‐term deleterious effects on individuals and, therefore, include in analyses only animals that survive an adjustment period of arbitrary length (often 7 days) following capture and marking. Length of adjustment period is rarely empirically based and may potentially bias survival estimates. We outline an analytical approach to determine an appropriate adjustment period and illustrate this approach by examining effects of time‐since‐marking on survival of 410 northern bobwhite captured during winter from 1997 to 2001, in Mississippi, USA. We modeled daily survival rates using time‐since‐marking as a covariate in the nest‐survival model of Program MARK. Although survival varied among and within years, we found no evidence to suggest that standard adjustment periods of 7–14 days were appropriate for our sample. If adjustment periods are used in radiotelemetry studies, those that are empirically based may be more appropriate than arbitrarily set periods.

Are survival predictions reliable? Hospital volume versus standardisation of histopathologic reporting for accuracy of survival estimates after pancreatoduodenectomy for adenocarcinoma

Histopathologic reporting after pancreatoduodenectomy is often non-standardised. Inappropriate reporting may bias survival estimates and make comparison between institutions difficult. Using population-based nationwide data from the Cancer Registry of Norway, we examined the influence on survival estimates of standardised histopathologic reporting versus non-standardised histopathologic reporting after pancreatoduodenectomy for adenocarcinomas in the pancreas, distal bile duct, ampulla and duodenum ( n = 506). Standardised histopathologic reports from a study hospital ( n = 113) were compared with reports from all other institutions (24 hospitals; n = 393) discriminating between high/medium-volume and low-volume institutions. In the study hospital, more tissue blocks were sampled, more nodes were evaluated, and more details about resection margins, size, origin and vascular and perineural infiltration were reported ( p < 0.001). Multivariable survival analysis identified lymph node involvement as the factor that is most dependent on standardised reporting to discriminate between favourable and poor prognostic subgroups ( p = 0.018). Standardised evaluation was more important than hospital volume for completeness of histopathologic reporting and for accuracy of survival estimates.

Effect of current reproduction on apparent survival, breeding dispersal, and future reproduction in barn swallows assessed by multistate capture–recapture models

1. Theoretical models predict a negative effect of current reproduction on breeding dispersal, survival and future reproduction, and many studies confirm these predictions. Yet, results of most previous studies may be difficult to interpret because the fate of the affected individuals cannot always be observed. Detection is almost always imperfect and some individuals emigrate from the study area, resulting in biased estimates of both survival and dispersal. 2. Most studies bypass these problems with strong assumptions. We use a multistate capture-recapture model that does not require these assumptions. States are defined based on classes of reproductive success and on observed dispersal events within the study area. By accounting for imperfect detection within the study area, the model allows estimation of the effect of reproductive success on apparent survival, dispersal probabilities within the study area and the annual transition probabilities among classes of reproductive success. Based on an assumption about the estimate of real survival, the model allows the estimation of total dispersal that is not specific to a fixed study area. 3. We applied this model to capture-recapture data of 2262 adult barn swallows (Hirundo rustica) sampled from 1997-2004 in eight local populations in Switzerland. 4. We found that dispersal within the study area decreased with increasing reproductive success in both sexes, that reproductive success was not affected by preceding dispersal and that apparent survival of females but not of males increased with increasing reproductive success. Apparent survival of females with high reproductive success was identical to apparent survival of males suggesting that this estimate of apparent survival (0.48) was close to true survival. Total breeding dispersal was generally higher in females and it increased with decreasing reproductive success in both sexes. Current reproductive success depended on reproductive success in the preceding year suggesting that individual differences were of importance. 5. Our study highlights that reproductive success was an important factor affecting breeding dispersal and population turnover. While unsuccessful males mainly remained in the local populations, many unsuccessful females left them. Population turnover of adult swallows was mainly due to unsuccessful females.

Evaluation of a Computer-assisted Photograph-matching System to Monitor Naturally Marked Harbor Seals at Tugidak Island, Alaska

Monitoring the dynamics and status of populations of harbor seals (Phoca vitulina richardii) requires efficient methods for estimating population parameters from mark-resight data. We used a test set of photographs from 182 individuals identified by flipper tags, scars, or unique pelage markings to test whether individuals could be identified accurately by their ventral pelage markings; to document efficiency and misidentification error rate associated with a computer-assisted photograph-matching system; and to test for bias in mark-recapture survival estimates resulting from misidentification errors. Pelage patterns of seals that were not of dark-intermediate or intermediate color phase were unique and stable from birth until 6–8 years, and from year to year as adults. The computer-assisted system greatly improved efficiency of photograph matching: 93.3% of good photographs and 69.9% of all photographs ranked 1st, and 95.2% of good photographs ranked in the top 0.3% of the ordered list for visual checking. Additional visual matching error averaged <3.0% for good photographs, and overall misidentification error rate was low at 1.8%, due to the availability of multiple photographs for matching. Inclusion of poor-quality photographs reduced ranking success by ∼20% and increased additional visual matching error up to 20%. Bias in survival estimates was –7.0% for a misidentification rate of 8.8%, but was ≤ 1.1 % for misidentification rates of <2.7%, achieved by restricting data to only good photos. Our study suggests that estimation of misidentification error rate, inclusion of only high-quality photographs, or use of models that account for misidentification error, are required to prevent bias in mark-recapture survival estimates when using data from natural-marking studies.

Radiotelemetry Survival Estimates of Lesser Prairie-Chickens in Kansas: Are There Transmitter Biases?

Radiotelemetry has provided wildlife biologists with a tool to estimate survival where fates of individuals likely are known. Analyses of known-fate data can yield accurate survival estimates if 5 assumptions are met. Two of these assumptions are rarely tested: that transmitters have no effect on survival of study animals and that right-censoring (i.e., any animal not located is as likely to be alive as dead) is random with respect to the survival of study animals. Using joint-models originally developed for live-encounter and dead-recovery data, we examined the potential for bias in survival estimates of radiomarked male lesser prairie-chickens (Tympanuchus pallidicinctus) in a 3-year study in southwestern Kansas, USA. Additionally, we examined the potential bias of right-censoring by comparing the return rates of known-fate and right-censored individuals. We captured 216 male lesser prairie-chickens and marked them with a combination of leg bands and a radio (n = 72) or leg bands only (n = 144). We applied joint-models to capture histories based on live-capture and telemetry data. The model best supported by the data indicated that 6-month survival was constant (Šc = 0.679, SE = 0.050) across radiomarked and banded birds. Eight of 16 (50%, SE = 12.5%) right-censored birds not detected because of radio failure were subsequently recaptured, which was not different from the return rates for known-fate birds (23 of 59; 39%, SE = 6.3%). Survival estimates of male lesser prairie-chickens in this study were not measurably biased by radiomarking, as their survival was greater than or equal to those of banded birds, and right-censored birds had similar return rates to those of known-fate individuals. Our results are encouraging because they indicate that 2 critical assumptions underlying analyses of known-fate data can be met with radiotransmitters and attachment techniques currently used in field studies of wild populations of lesser prairie-chickens.

Reply to the comment by Franklin et al. on “Are survival rates for northern spotted owls biased?”Appears in Can. J. Zool. 83: 1386–1390.

We reply to Franklin et al.’s critique of our recent work in which we computed survival for northern spotted owls ( Strix occidentalis caurina (Merriam, 1898)) from sites in western Oregon and northern California based on 197 radio-collared owls. Several methods gave similar results and we noted that our estimated survival rates might be closer to the true value than those derived from mark–recapture studies. We included an errant reference to Anthony et al. (Wildl. Monogr. No. 163, pp. 1–47 (2006)) in comments about bias in prior estimates of survival and hence of λ, a mistake for which we published an erratum. In spite of our erratum, Franklin et al. correct our presumed misunderstanding of the re-parameterized Jolly–Seber methods used in the article by Anthony et al. We never intended our comments to refer to the article by Anthony et al. The commentary also states that we overestimated survival because birds that left the study area might actually have died simultaneously with radio-collar destruction. However, in our earlier paper, we stated quite clearly that the fate of virtually every bird was accounted for by tracking them down if they left the study area or until the body was found if dead. They secondarily state that birds that emigrated might have a higher mortality rate and cited as evidence a study based on four owls. We do not consider that study sufficient to determine whether mortality rates for emigrating owls may be elevated. We also dispute several other criticisms but concur with them that several issues related to owl demography could benefit from further study.

Instrumental variables methods in experimental criminological research: what, why and how

Quantitative criminology focuses on straightforward causal questions that are ideally addressed with randomized experiments. In practice, however, traditional randomized trials are difficult to implement in the untidy world of criminal justice. Even when randomized trials are implemented, not everyone is treated as intended and some control subjects may obtain experimental services. Treatments may also be more complicated than a simple yes/no coding can capture. This paper argues that the instrumental variables methods (IV) used by economists to solve omitted variables bias problems in observational studies also solve the major statistical problems that arise in imperfect criminological experiments. In general, IV methods estimate causal effects on subjects who comply with a randomly assigned treatment. The use of IV in criminology is illustrated through a re-analysis of the Minneapolis domestic violence experiment. The results point to substantial selection bias in estimates using treatment delivered as the causal variable, and IV estimation generates deterrent effects of arrest that are about one-third larger than the corresponding intention-to-treat effects.

Reconsidering the Effectiveness of International Economic Sanctions: An Examination of Selection Bias

One major concern in the study of international economic sanctions is the potential problem of selection bias. Game-theoretical analyses assert that the private suggestion of sanctions could bring about the desired change in behaviour: sanctions are least likely to be imposed when they are most likely to be effective. If this were true frequently enough, the study of sanctions implemented by states (such as in the data developed by Hufbauer, Schott, and Elliott [HSE]) would provide an incomplete picture of the effectiveness of the sanctions approach. In this article, we adapt Boolean analytic techniques to estimate selection bias in the HSE data. This analysis yields evidence of selection bias — suggesting that we should reconsider existing empirical research based on those data. We conclude by considering research approaches that could capture the cases lost to selection bias in the HSE data.

Consequences of violating the recapture duration assumption of mark–recapture models: a test using simulated and empirical data from an endangered tortoise population

Summary Mark–recapture methods are frequently used to estimate survival rates, which inform wildlife management policies. Mark–recapture models assume zero mortality of marked animals during the period of recapture and therefore that this period is of negligible duration relative to the interval between recapture events. This ‘recapture duration assumption’ is frequently violated yet is rarely tested for its potential to bias survival estimates. We investigated whether violating the recapture duration assumption increased precision at the cost of increased bias in estimates of survival. Using both simulation and empirical approaches, annual survival and recapture rates were estimated under recapture period durations that either conformed to, or violated, the recapture duration assumption. Empirical data were derived from a population of endangered Madagascar ploughshare tortoises Geochelone yniphora. Estimates of ploughshare tortoise survival were higher and had smaller standard errors when the recapture duration assumption was violated. As the ‘true’ ploughshare tortoise survivorship was unknown, a simulation approach was used to assess whether short or long recapture periods gave the most reliable estimates. The simulation study showed that violating the recapture duration assumption increased precision but did not increase bias in parameter estimates, even if up to 50% of the annual mortality occurred during the recapture period. The most precise and least biased survival estimates were obtained when sample size (number of marked individuals) was greatest, i.e. when both survival and recapture rates were high. Bias in survival estimates was negligible unless the recapture rate during the recapture period was &lt; 0·2. We conclude that the most precise ploughshare tortoise parameter estimates were generated by using lengthy recapture occasions that violated the recapture duration assumption. Synthesis and applications. To achieve the most precise and least biased survival estimates we recommend violating the recapture duration assumption and using a recapture period that maximizes sample size and achieves a recapture rate of &gt; 0·2 during the recapture period. If both survival and recapture rates are relatively constant during the recapture period, survival estimates will then have negligible bias. If a recapture rate of &gt; 0·2 during the recapture period cannot be achieved, methods other than mark–recapture should be used to quantify demographics. These recommendations apply to any species with an annual survival rate &gt; 0·05.

Lin et al. Respond to “Assessment of Respiratory Symptoms after September 11”

We appreciate the observations made by Drs. Vlahov and Galea in their invited commentary (1) on our paper (2). Given that the World Trade Center (WTC) disaster was an unprecedented event, this was not a traditional epidemiologic study but rather a community health investigation designed to respond to the public’s concerns, as well as the first step in examining the potential health effects on local residents. Many constraints made this study difficult to design, including a lack of baseline prevalence and exposure data and unknown mobility patterns. As we explain below, most of the problems discussed by Vlahov and Galea were considered in our article and addressed to the extent possible. Selection bias is one of their main concerns. Since a significant number of residents moved out of the affected area after September 11, the actual response rate might have been higher than estimated. In addition, the response rates were similar in the affected and control areas, and the demographic distribution of the participants was similar to that of the underlying population. To estimate selection bias, we targeted a subset of buildings in the affected and control areas for increased recruitment efforts and achieved higher response rates in both areas. The risk estimates from the targeted buildings, in which the samples are assumed to be more representative, were not only consistent with but also higher than those in the nontargeted buildings. Another potential problem is information bias. We reported that ‘‘we emphasized the importance of participation for people with and without breathing problems’’ and that we used ‘‘general terms such as ‘breathing or lung problems’ rather than specific terms like ‘asthma’ ’’ (2, p. 505). We also stated that ‘‘we asked symptom questions not only qualitatively but also quantitatively, by including questions on specific time frames, severity, and frequency, which are less prone to recall bias’’ (2, p. 505). In addition, the symptom questions that we chose for the questionnaire have been validated in many epidemiologic studies. To reduce reporting bias, we asked participants about prescription medications and listed the names of the medications. We also used more objective measures by asking participants about new diagnoses by a physician, unplanned medical visits, and hospitalizations (including the dates and reasons for hospitalization). We checked the differences between the two areas for WTC-unrelated variables (e.g., physical disabilities) and excluded participants who responded affirmatively to every question. To estimate reporting bias, we compared the proportions of unplanned medical visits among participants with specific respiratory symptoms and found them be similar in the affected and control areas for most symptoms. Finally, as we described in another article (3), screening spirometry was conducted in some participants to validate self-reported symptoms. Although there were no significant differences between the affectedarea residents and the control-area residents (screening spirometry might not be sensitive for this exposure), the results of a pilot methacholine challenge test showed a higher proportion of positive findings in the participants with persistent new-onset symptoms than in asymptomatic participants. We are conducting additional studies to address some of these concerns. A follow-up study will use nitric oxide in exhaled breath (eNO) as an objective measure of airway inflammation. Self-reported symptoms will be correlated with eNO measurements and validated. Another study will estimate changes in hospitalizations (an objective indicator of outcome) for respiratory and cardiovascular diseases before and after September 11, 2001, and compare the rates in both areas. The WTC Health Registry, which has recruited a larger cohort, also plans to follow this population. The ambient air monitoring site located at the WTC was destroyed in the collapse, so ambient pollution levels immediately after September 11 were not available for exposure assessment. For this reason, we did not attribute our findings

Estimating Long-Term Consequences of Teenage Childbearing - An Examination of the Siblings Approach

One of the remedies to selection bias in estimates of the labour market consequences of teenage motherhood has been to estimate within-family effects. A major critique, however, is that heterogeneity within the family might still bias the estimates. Using a large Swedish data set on biological sisters, I revisit the question of the consequences of teenage motherhood. My contribution is that I am able to control for heterogeneity within the family; I use grade-point-averages at age 16, a pre-motherhood characteristic that differs across sisters within the same family. My findings confirm the presumption that within-family heterogeneity can result in biased within-family estimates. Moreover, my results show that when controlling for school performance, the siblings approach and a traditional cross section yield similar coefficients.

Estimating Long-Term Consequences of Teenage Childbearing

Abstract Within-family estimates have been considered a remedy to selection bias in estimates of long-run consequences of teen motherhood. A major critique, however, is that heterogeneity within the family might still bias the estimates. Using Swedish data on biological sisters, I revisit the question of the consequences of teenage motherhood. My contribution lies in controlling for heterogeneity within the family by using premotherhood school performance, a characteristic that differs across sisters. My findings confirm the presumption that within-family heterogeneity can result in biased sibling estimates. Moreover, my results show that when controlling for school performance, the siblings approach and a traditional cross-section yield similar coefficients.

Exploring mark-resighting-recovery models to study savannah tree demographics

Despite their sessile nature, juvenile trees in savannah ecosystems are not always easy to encounter. Here, the remedy of choice in animal studies, capture-recapture modelling, is evaluated with respect to plants. During 7 censuses, 4,145 juvenile trees of 8 dominant species were monitored. Using models with joint analysis of live and dead encounters, resighting probabilities averaged 0.88±0.15 for seedlings and 0.92±0.10 for resprouts, while dead recovery probabilities averaged 0.71±0.25 for all age-classes. Ad hoc methods which did not consider encounter probabilities yielded biased survival estimates compared to the mark-resighting-recovery approaches. This occurred even for high encounter probabilities, so the use of capture-recapture models is recommended whenever the plant encounter probability is &lt; 1. Finally, survival probabilities estimated by models based only on live or on dead data might be different and less precise than ones estimated based on combined data. This highlights the advantages of models with joint analysis of live and dead encounters even when site fidelity is 1.

The effect on model identifiability of allowing different relocation rates for live and dead animals in the combined analysis of telemetry and recapture data

Models are described for the joint analysis of live-trapping and radio telemetry data from a study on black bears (Ursus americanus) in which all animals received ear tags and a subset also received radio tags. Concerns about bias in survival estimates led to investigation of identifiability and estimator precision for a series of models that allowed differenttelemetry relocation rates for living and dead animals, in addition to emigration and seasonal variation in survival. Identifiability was determined by showing that the expected information matrix was nonsingular. Models with fidelity constant across time, and with the same degree of time specificity for survival rates and relocation rates for dead animals, were determined to be nonidentifiable. More general models, with a greater degree of time specificity for survival rates, were near-singular, and estimators under these near-singular models had poor precision. Analysis of data from the study on black bears illustrated that estimates of survival have poor precision when relocation rates are estimated separately for live and dead animals. It is recommended that the effort expended to relocate both living and dead animals be consistently high in each telemetry survey, so that relocation rates will be high and constant across time and mortality status.

Joint models for efficient estimation in proportional hazards regression models.

In survival studies, information lost through censoring can be partially recaptured through repeated measures data which are predictive of survival. In addition, such data may be useful in removing bias in survival estimates, due to censoring which depends upon the repeated measures. Here we investigate joint models for survival T and repeated measurements Y, given a vector of covariates Z. Mixture models indexed as f (T/Z) f (Y/T,Z) are well suited for assessing covariate effects on survival time. Our objective is efficiency gains, using non-parametric models for Y in order to avoid introducing bias by misspecification of the distribution for Y. We model (T/Z) as a piecewise exponential distribution with proportional hazards covariate effect. The component (Y/T,Z) has a multinomial model. The joint likelihood for survival and longitudinal data is maximized, using the EM algorithm. The estimate of covariate effect is compared to the estimate based on the standard proportional hazards model and an alternative joint model based estimate. We demonstrate modest gains in efficiency when using the joint piecewise exponential joint model. In a simulation, the estimated efficiency gain over the standard proportional hazards model is 6.4 per cent. In clinical trial data, the estimated efficiency gain over the standard proportional hazards model is 10.2 per cent.