State and private pensions, retirement behaviour and personal capital accumulation

The aim of this thesis has been to investigate the relationship between state and private pensions and personal savings. A theoretical framework has been developed to facilitate the a priori determination of the relationship and an empirical investigation then undertaken using data for the U. K. in the postwar period. These two aspects of the thesis will firstly be summarised. Initially, the standard life cycle model of individual accumulation is extended to include a flat rate pension scheme. The introduction of the scheme will have an impact on savings determined by a savings replacement effect, where pension saving is substituted for alternative forms personal saving, and an induced retirement effect, where savings is increased to finance a longer retirement period. The net effect on savings will depend on the rate of return to pension contributions, and therefore lifetime income, implied by the combination of the two effects. As membership of state pension schemes is usually compulsory there exists the possibility that the implied rate of return can be above or below the market rate, indeed it may even be negative, with the result that lifetime income may be higher or lower than prior to the introduction of the pension scheme. The impact on savings cannot therefore be determined at a theoretical level. Increasing pension contributions and benefits always lead to a reduction in work period and, under the usual assumptions, aggregate savings. These changes also induce early retirement. Having analysed the state pension case the model is further modified to include private pension schemes, in particular a terminal salary scheme, membership of which is assumed to be compulsory, and a money purchase scheme, the joining of which is a voluntary decision. Again, for the reasons outlined above, the effect on personal savings of introducing the private schemes cannot be determined a priori. It is still possible though to say something about the effect of changes in pension contributions and benefits. When considering the increasing of pension contributions and state pension benefits, the outcomes are as in the state pension case alone. If attention is confined to increasing private pension benefit functions by constant absolute amounts then early retirement and a reduction in work period savings are the unambiguous outcomes. In the case of the money purchase scheme early retirement also implies a larger private pension fund. The empirical estimation of the relationship has been attempted through the inclusion of pension wealth variables in the aggregate life cycle consumption function. Two definitions of pension wealth were used. Gross pension wealth has been defined as the discounted present value of future pension receipts weighted by survival probabilities whilst net pension wealth is gross pension wealth less the discounted present value of future pension contributions weighted by survival probabilities (termed liabilities). Unfortunately these definitions could only be used with state pensions - data was not available to evaluate these types of wealth variable in the case of private pensions. Over the period 1949-73 gross state pension wealth appears to have no impact on consumption, and therefore savings, whilst net pension wealth depresses consumption. The growth of the market value of the assets of superannuation- funds was used as a proxy for the growth of private pension wealth. This data was available for the period 1958-73. Whilst private pension wealth was found to be insignificant in the regressions in these same equations gross state pension wealth becomes significant and positive. If net pension wealth is substituted for the gross alternative its coefficient remains negative but its significance falls. Over both periods there was found to be no evidence of an induced retirement effect. Various estimates of the effect of the existence of pension schemes and changes in pension contributions and benefits were made on the basis of a range of estimated coefficients. As one would expect these estimates varied widely given the different signs of the coefficients on gross and net state pension wealth. There are four aspects of the work that, at the end of the day, give cause for concern. The two relating to the theoretical work are probably less serious than the two relating to the empirical work. In the development of the theoretical analysis the individuals work/leisure decision was given only passing consideration. Indeed it was only shown that if the individual moved continuously from the work to the retirement period then leisure considerations would be irrelevant. Nevertheless recognition was accorded to the possibility that if this move is discontinuous, which is highly likely to be the case, not only might the optimal retirement date be different to that derived in the basic model but also the earlier comparative statics results might no longer apply. In a recent paper Ulph (58) has begun to consider this problem in a model incorporating a terminal salary based private pension scheme. Employing an iso-elastic utility function in consumption and leisure he shows that certain assumptions relating to the parameters of the utility function imply that not all the comparative statics results of earlier chapters necessarily go through. Thus leisure considerations are not irrelevant to the analysis of pensions. The results also imply that analyses of the individuals life cycle problem which do not include pensions, and where the individual retires when the marginal utility of consumption falls below the marginal utility derived from spending all ones time in leisure, might be substantially changed when leisure considerations are taken into account. An obvious, extension of pension theory would then be to integrate it into a model of the above type, such as that of Blinder (13). Another important feature of the pension decision,, which again has only been covered rather briefly, is uncertainty about the length of lifetime. It has been shown that if it is assumed that there exists a perfect insurance market then the problem reduces to an analysis under certainty, the insurance asset obviating any problem arising from a probabilistic date of death. Ulph and Hemming (59) have since dropped this last assumption and shown how the results of this thesis are affected. Although this turns out to be to an extent: that gives little cause for concern, the new model does produce the results within a framework that is more realistic. The above paper also has important implications for another aspect of pension analysis. When lifetime is uncertain the purchase of a pension asset or annuity provides insurance and the individual should therefore be prepared to purchase it even if its return were less than actuarially fair. Now in evaluating the value of anticipated state pension wealth the average market rate of interest has been used to discount the expected value of future returns. This is an approximation of the actuarially fair rate of interest. But under uncertainty this is not the appropriate rate of discount - what ought to be used is the lowest rate of return at which the individual is just willing to purchase the annuity. In fact Ulph and Hemming show that whilst the individual is holding non-pension assets the appropriate rate of discount is the rate on those assets. Once the individual has run down his stock of these assets the appropriate rate of discount will be the subjective rate of discount incorporating a risk factor. Thus if the individual is holding the alternative asset the appropriate rate of discount is less than the actuarially fair rate, (see (3.6.4)). Pension wealth will therefore be underestimated. When none of the alternative assets are held the value of pension wealth can be under- or over-estimated depending on the relative magnitudes of the rates of interest and the subjective rate of discount. Not only do these results suggest that pension wealth might be evaluated incorrectly but it could be that the optimal bequest decision, which did not affect the earlier analysis, now becomes important in that individuals will be holding capital through the later part of their life. When they choose to make their bequest will affect their valuation of pension wealth. This interrelationship could produce some interesting results and is worth exploring further. Turning now to the problems arising on the estimation side one can consider firstly the general insignificance of the pension variables in the regression equations and the inconsistency of the short and long period estimates. In retrospect, it should have been realised that the wealth approach could present a problem in attempting to reconcile the theoretical and empirical results. Recall that increases in both state pension contributions and benefits always lead to a reduction in savings - when using the net state pension wealth variable in the estimated equations, no matter what the sign of its coefficient, both the above predictions cannot be confirmed simultaneously. This follows since increasing contributions and benefits respectively decreases and increases net state pension wealth. Only if the coefficient on gross state pension wealth had been positive and significant could both predictions have been borne out, That net state pension wealth alone should turn out to be significant, and then negative, implies that only the effect on savings of increasing contributions is confirmed. Possibly this result was to have been expected since the only acceptable way of explaining the difference between the coefficients on the two pension wealth variables is through the significance of liabilities. Unfortunately there appears to be no reasonable argument which explains why individual behaviour should be determined by liabilities rather than gross wealth. One has to be rather surprised about the apparent change in the relationship between the long and short data periods. A somewhat similar case of this arose when Feldstein (19) changed his data period. Since in both analyses the regressors: are all income and wealth variables it is difficult to believe that this is not a classic symptom of the multi-collinearity which is quite clearly present rather than some structural change in the relationship over time. In the theoretical developments an induced retirement effect played a prominent part in the discussion. When it came to estimation the effect was found to be non-existent. Indeed the data suggested that retirement patterns had not changed markedly over the postwar period. This is not surprising. Under the state pension scheme coverage was universal by 1946 and whilst subsequent changes in contributions and benefits have hardly had marginal effects on lifetime income it is unlikely that this will be affected by induced retirement because either many people will retire at the official retirement date or, for those retiring later, the retirement date is not a continuous variable. Even if this were not the case in practice estimation of the effect would be difficult since the retirement date is discrete as far as official statistics are concerned. As far as private pensions are concerned significant growth has taken place over the postwar period but still only half the working population are covered - many of these are younger workers whose retirement behaviour will not yet have been observed. Indeed this last point is one that applies to the study of private pensions as a whole. The empirical analysis of relationships involving private pensions has been scant and highly unsatisfactory. That no attempt was made to calculate a private pension wealth variable was simply due to data inadequacy: that no attempt was made to collect the data is explained by comparative advantage. As mentioned earlier the Government Actuaries Department are currently engaged in providing estimates. When these are available and the regression equations re-estimated some more useful results may emerge. Even when the specification and data problems are overcome there still might exist one reason why the results produced might not be convincing. When a life cycle model of individual behaviour has carefully been built up, and no one could disagree that when considering pension problems this is the appropriate type of model, it will always be disappointing that the model cannot truly be tested with the data currently available. All the methods considered for estimating such a model are only approximations - there can be no substitute for cross-section data relating to the behaviour of the same individuals over fairly long periods of time. Whilst this pessimism about the reliability of the results is clearly very healthy one is now only left to ponder whether the attitude would have been the same if the estimated coefficients had all been statistically significant and of the theoretically anticipated signs. One has to hope so

Stepped-wedge cluster randomised controlled trials : a generic framework including parallel and multiple-level designs

Stepped-wedge cluster randomised trials (SW-CRTs) are being used with increasing frequency in health service evaluation. Conventionally, these studies are cross-sectional in design with equally spaced steps, with an equal number of clusters randomised at each step and data collected at each and every step. Here we introduce several variations on this design and consider implications for power. One modification we consider is the incomplete cross-sectional SW-CRT, where the number of clusters varies at each step or where at some steps, for example, implementation or transition periods, data are not collected. We show that the parallel CRT with staggered but balanced randomisation can be considered a special case of the incomplete SW-CRT. As too can the parallel CRT with baseline measures. And we extend these designs to allow for multiple layers of clustering, for example, wards within a hospital. Building on results for complete designs, power and detectable difference are derived using a Wald test and obtaining the variance–covariance matrix of the treatment effect assuming a generalised linear mixed model. These variations are illustrated by several real examples. We recommend that whilst the impact of transition periods on power is likely to be small, where they are a feature of the design they should be incorporated. We also show examples in which the power of a SW-CRT increases as the intra-cluster correlation (ICC) increases and demonstrate that the impact of the ICC is likely to be smaller in a SW-CRT compared with a parallel CRT, especially where there are multiple levels of clustering. Finally, through this unified framework, the efficiency of the SW-CRT and the parallel CRT can be compared

Stepped wedge trials with continuous recruitment require new ways of thinking.

OBJECTIVES: There is substantial variation in the design of stepped wedge trials. Many recruit participants continuously over time, although the methodological literature has tended not to differentiate closely between continuous recruitment and discrete sampling. We argue for a deeper understanding of the special features of stepped wedge trials with continuous recruitment. STUDY DESIGN AND SETTING: This is a commentary and informal review. RESULTS: We discuss the scheduling of recruitment and implementation in continuous time and how contamination might be avoided. We also offer some suggestions on reporting and terminology for stepped wedge trials with continuous recruitment and comment on issues for analysis. CONCLUSION: Repeated cross-section and continuous recruitment stepped wedge trials are not the same thing. More work is needed to develop the theory and practice of stepped wedge designs with continuous recruitment. Thoughtful approaches to design and clarity of reporting are vital

Bayesian Cohort and Cross-Sectional Analyses of the PINCER Trial: A Pharmacist-Led Intervention to Reduce Medication Errors in Primary Care

Background Medication errors are an important source of potentially preventable morbidity and mortality. The PINCER study, a cluster randomised controlled trial, is one of the world’s first experimental studies aiming to reduce the risk of such medication related potential for harm in general practice. Bayesian analyses can improve the clinical interpretability of trial findings. Methods Experts were asked to complete a questionnaire to elicit opinions of the likely effectiveness of the intervention for the key outcomes of interest - three important primary care medication errors. These were averaged to generate collective prior distributions, which were then combined with trial data to generate Bayesian posterior distributions. The trial data were analysed in two ways: firstly replicating the trial reported cohort analysis acknowledging pairing of observations, but excluding non-paired observations; and secondly as cross-sectional data, with no exclusions, but without acknowledgement of the pairing. Frequentist and Bayesian analyses were compared. Findings Bayesian evaluations suggest that the intervention is able to reduce the likelihood of one of the medication errors by about 50 (estimated to be between 20% and 70%). However, for the other two main outcomes considered, the evidence that the intervention is able to reduce the likelihood of prescription errors is less conclusive. Conclusions Clinicians are interested in what trial results mean to them, as opposed to what trial results suggest for future experiments. This analysis suggests that the PINCER intervention is strongly effective in reducing the likelihood of one of the important errors; not necessarily effective in reducing the other errors. Depending on the clinical importance of the respective errors, careful consideration should be given before implementation, and refinement targeted at the other errors may be something to consider

Is convalescent plasma futile in COVID-19?:A Bayesian re-analysis of the RECOVERY randomized controlled trial

Background: Randomized trials are generally performed from a frequentist perspective, which can conflate absence of evidence with evidence of absence. The RECOVERY trial evaluated convalescent plasma for patients hospitalized with coronavirus disease 2019 (COVID-19) and concluded that there was no evidence of an effect. Re-analysis from a Bayesian perspective is warranted. Methods: Outcome data were extracted from the RECOVERY trial by serostatus and time of presentation. A Bayesian re-analysis with a wide variety of priors (vague, optimistic, sceptical, and pessimistic) was performed, calculating the posterior probability for: any benefit, an absolute risk difference of 0.5% (small benefit, number needed to treat 200), and an absolute risk difference of one percentage point (modest benefit, number needed to treat 100). Results: Across all patients, when analysed with a vague prior, the likelihood of any benefit or a modest benefit with convalescent plasma was estimated to be 64% and 18%, respectively. The estimated chance of any benefit was 95% if presenting within 7 days of symptoms, or 17% if presenting after this. In patients without a detectable antibody response at presentation, the chance of any benefit was 85%. However, it was only 20% in patients with a detectable antibody response at presentation. Conclusions: Bayesian re-analysis suggests that convalescent plasma reduces mortality by at least one percentage point among the 39% of patients who present within 7 days of symptoms, and that there is a 67% chance of the same mortality reduction in the 38% who are seronegative at the time of presentation. This is in contrast to the results in people who already have antibodies when they present. This biologically plausible finding bears witness to the advantage of Bayesian analyses over misuse of hypothesis tests to inform decisions

siRNAdb: a database of siRNA sequences

Short interfering RNAs (siRNAs) are a popular method for gene-knockdown, acting by degrading the target mRNA. Before performing experiments it is invaluable to locate and evaluate previous knockdown experiments for the gene of interest. The siRNA database provides a gene-centric view of siRNA experimental data, including siRNAs of known efficacy and siRNAs predicted to be of high efficacy by a combination of methods. Linked to these sequences is information such as siRNA thermodynamic properties and the potential for sequence-specific off-target effects. The database enables the user to evaluate an siRNA's potential for inhibition and non-specific effects. The database is available at http://siRNA.cgb.ki.se

Statistical analysis plan for cluster randomised trial to evaluate a community-level complementary food safety and hygiene and nutrition intervention in Mali:the MaaCiwara study

Background: Diarrheal disease is a significant cause of morbidity and mortality in under-fives in many low- and middle-income countries. Changes in food safety, hygiene practices, and nutrition around the weaning period may reduce the risk of disease and improve infant development. The MaaCiwara study aims to evaluate the effectiveness of a community-based educational intervention designed to improve food safety and hygiene behaviours, as well as child nutrition. This update article describes the statistical analysis plan for the MaaCiwara study in detail. Methods and design: The MaaCiwara study is a parallel group, two-arm, superiority cluster randomised controlled trial with baseline measures, involving 120 clusters of rural and urban communities. These clusters are randomised to either receive the community-based behaviour change intervention or to the control group. The study participants will be mother–child pairs, with children aged between 6 and 36 months. Data collection involves a day of observation and interviews with each participating mother–child pair, conducted at baseline, 4 months, and 15 months post-intervention. The primary analysis aims to estimate the effectiveness of the intervention on changes to complementary food safety and preparation behaviours, food and water contamination, and diarrhoea. The primary outcomes will be analysed generalised linear mixed models, at individual level, accounting for clusters and rural/urban status to estimate the difference in outcomes between the intervention and control groups. Secondary outcomes include maternal autonomy, enteric infection, nutrition, child anthropometry, and development scores. In addition, structural equation analysis will be conducted to examine the causal relationships between the different outcomes. Trial registration: International Standard Randomised Controlled Trial Number (ISRCTN) register: ISRCTN14390796. Registered on 13 December 2021

Sample size calculations for cluster randomised controlled trials with a fixed number of clusters

Background\ud Cluster randomised controlled trials (CRCTs) are frequently used in health service evaluation. Assuming an average cluster size, required sample sizes are readily computed for both binary and continuous outcomes, by estimating a design effect or inflation factor. However, where the number of clusters are fixed in advance, but where it is possible to increase the number of individuals within each cluster, as is frequently the case in health service evaluation, sample size formulae have been less well studied. \ud \ud Methods\ud We systematically outline sample size formulae (including required number of randomisation units, detectable difference and power) for CRCTs with a fixed number of clusters, to provide a concise summary for both binary and continuous outcomes. Extensions to the case of unequal cluster sizes are provided. \ud \ud Results\ud For trials with a fixed number of equal sized clusters (k), the trial will be feasible provided the number of clusters is greater than the product of the number of individuals required under individual randomisation ($n_i$) and the estimated intra-cluster correlation ($\rho$). So, a simple rule is that the number of clusters ($\kappa$) will be sufficient provided: \ud \ud $\kappa$ > $n_i$ x $\rho$\ud \ud Where this is not the case, investigators can determine the maximum available power to detect the pre-specified difference, or the minimum detectable difference under the pre-specified value for power. \ud \ud Conclusions\ud Designing a CRCT with a fixed number of clusters might mean that the study will not be feasible, leading to the notion of a minimum detectable difference (or a maximum achievable power), irrespective of how many individuals are included within each cluster. \ud \u